[Fluorescence control of dental calculus removal].

PubMed

Bakhmutov, D N; Gonchukov, S A; Lonkina, T V; Sukhinina, A V

2012-01-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In the frames of this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise detection of tooth-calculus interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing (as ultrasonic or laser devices).

The Development of Newtonian Calculus in Britain, 1700-1800

NASA Astrophysics Data System (ADS)

Guicciardini, Niccoló

2003-11-01

Introduction; Overture: Newton's published work on the calculus of fluxions; Part I. The Early Period: 1. The diffusion of the calculus (1700-1730); 2. Developments in the calculus of fluxions (1714-1733); 3. The controversy on the foundations of the calculus (1734-1742); Part II. The Middle Period: 4. The textbooks on fluxions (1736-1758); 5. Some applications of the calculus (1740-1743); 6. The analytic art (1755-1785); Part III. The Reform: 7. Scotland (1785-1809); 8. The Military Schools (1773-1819); 9. Cambridge and Dublin (1790-1820); 10. Tables; Endnotes; Bibliography; Index.

The impacts of gingivitis and calculus on Thai children's quality of life.

PubMed

Krisdapong, Sudaduang; Prasertsom, Piyada; Rattanarangsima, Khanit; Sheiham, Aubrey; Tsakos, Georgios

2012-09-01

To assess associations of socio-demographic, behavioural and the extent of gingivitis and calculus with oral health-related quality of life (OHRQoL) in nationally representative samples of 12- and 15-year-old Thai children. In the Thailand National Oral Health Survey, 1,063 twelve-year olds and 811 fifteen-year olds were clinically examined and interviewed for OHRQoL using the Child-OIDP and OIDP indices, respectively, and completed a behavioural questionnaire. We assessed associations of condition-specific impacts (CS-impacts) with gingivitis and calculus, adjusted for socio-demographic and behavioural factors. Gingivitis and calculus were highly prevalent: 79.3% in 12-year and 81.5% in 15-year olds. CS-impacts relating to calculus and/or gingivitis were reported by 26.0% of 12-year and 29.6% of 15-year olds. Except for calculus without gingivitis, calculus and/or gingivitis in any form was significantly related to any level of CS-impacts. At a moderate or higher level of CS-impacts, there were significant relationships with extensive calculus and/or gingivitis in 12-year olds and for extensive gingivitis and gingivitis without calculus in 15-year olds. Gingivitis was generally associated with any level of CS-impacts attributed to calculus and/or gingivitis. CS-impacts were related more to gingivitis than to calculus. © 2012 John Wiley & Sons A/S.

Characteristics of subgingival calculus detection by multiphoton fluorescence microscopy

NASA Astrophysics Data System (ADS)

Tung, Oi-Hong; Lee, Shyh-Yuan; Lai, Yu-Lin; Chen, How-Foo

2011-06-01

Subgingival calculus has been recognized as a major cause of periodontitis, which is one of the main chronic infectious diseases of oral cavities and a principal cause of tooth loss in humans. Bacteria deposited in subgingival calculus or plaque cause gingival inflammation, function deterioration, and then periodontitis. However, subgingival calculus within the periodontal pocket is a complicated and potentially delicate structure to be detected with current dental armamentaria, namely dental x-rays and dental probes. Consequently, complete removal of subgingival calculus remains a challenge to periodontal therapies. In this study, the detection of subgingival calculus employing a multiphoton autofluorescence imaging method was characterized in comparison with a one-photon confocal fluorescence imaging technique. Feasibility of such a system was studied based on fluorescence response of gingiva, healthy teeth, and calculus with and without gingiva covered. The multiphoton fluorescence technology perceived the tissue-covered subgingival calculus that cannot be observed by the one-photon confocal fluorescence method.

College Readiness: The Evaluation of Students Participating in the Historically Black College and University Program in Pre-Calculus and the Calculus Sequence

ERIC Educational Resources Information Center

Hall, Angela Renee

2011-01-01

This investigative research focuses on the level of readiness of Science, Technology, Engineering, and Mathematics (STEM) students entering Historically Black Colleges and Universities (HBCU) in the college Calculus sequence. Calculus is a fundamental course for STEM courses. The level of readiness of the students for Calculus can very well play a…

Concepts and Skills in High School Calculus: An Examination of a Special Case in Japan and the United States

ERIC Educational Resources Information Center

Judson, Thomas W.; Nishimori, Toshiyuki

2005-01-01

In this study we investigated above-average high school calculus students from Japan and the United States in order to determine any differences in their conceptual understanding of calculus and their ability to use algebra to solve traditional calculus problems. We examined and interviewed 18 Calculus BC students in the United States and 26…

Dental Calculus Stimulates Interleukin-1β Secretion by Activating NLRP3 Inflammasome in Human and Mouse Phagocytes

PubMed Central

Montenegro Raudales, Jorge Luis; Yoshimura, Atsutoshi; SM, Ziauddin; Kaneko, Takashi; Ozaki, Yukio; Ukai, Takashi; Miyazaki, Toshihiro; Latz, Eicke; Hara, Yoshitaka

2016-01-01

Dental calculus is a mineralized deposit associated with periodontitis. The bacterial components contained in dental calculus can be recognized by host immune sensors, such as Toll-like receptors (TLRs), and induce transcription of proinflammatory cytokines, such as IL-1β. Studies have shown that cellular uptake of crystalline particles may trigger NLRP3 inflammasome activation, leading to the cleavage of the IL-1β precursor to its mature form. Phagocytosis of dental calculus in the periodontal pocket may therefore lead to the secretion of IL-1β, promoting inflammatory responses in periodontal tissues. However, the capacity of dental calculus to induce IL-1β secretion in human phagocytes has not been explored. To study this, we stimulated human polymorphonuclear leukocytes (PMNs) and peripheral blood mononuclear cells (PBMCs) with dental calculus collected from periodontitis patients, and measured IL-1β secretion by ELISA. We found that calculus induced IL-1β secretion in both human PMNs and PBMCs. Calculus also induced IL-1β in macrophages from wild-type mice, but not in macrophages from NLRP3- and ASC-deficient mice, indicating the involvement of NLRP3 and ASC. IL-1β induction was inhibited by polymyxin B, suggesting that LPS is one of the components of calculus that induces pro-IL-1β transcription. To analyze the effect of the inorganic structure, we baked calculus at 250°C for 1 h. This baked calculus failed to induce pro-IL-1β transcription. However, it did induce IL-1β secretion in lipid A-primed cells, indicating that the crystalline structure of calculus induces inflammasome activation. Furthermore, hydroxyapatite crystals, a component of dental calculus, induced IL-1β in mouse macrophages, and baked calculus induced IL-1β in lipid A-primed human PMNs and PBMCs. These results indicate that dental calculus stimulates IL-1β secretion via NLRP3 inflammasome in human and mouse phagocytes, and that the crystalline structure has a partial role in the activation of NLRP3 inflammasome. PMID:27632566

Dental Calculus Stimulates Interleukin-1β Secretion by Activating NLRP3 Inflammasome in Human and Mouse Phagocytes.

PubMed

Montenegro Raudales, Jorge Luis; Yoshimura, Atsutoshi; Sm, Ziauddin; Kaneko, Takashi; Ozaki, Yukio; Ukai, Takashi; Miyazaki, Toshihiro; Latz, Eicke; Hara, Yoshitaka

2016-01-01

Dental calculus is a mineralized deposit associated with periodontitis. The bacterial components contained in dental calculus can be recognized by host immune sensors, such as Toll-like receptors (TLRs), and induce transcription of proinflammatory cytokines, such as IL-1β. Studies have shown that cellular uptake of crystalline particles may trigger NLRP3 inflammasome activation, leading to the cleavage of the IL-1β precursor to its mature form. Phagocytosis of dental calculus in the periodontal pocket may therefore lead to the secretion of IL-1β, promoting inflammatory responses in periodontal tissues. However, the capacity of dental calculus to induce IL-1β secretion in human phagocytes has not been explored. To study this, we stimulated human polymorphonuclear leukocytes (PMNs) and peripheral blood mononuclear cells (PBMCs) with dental calculus collected from periodontitis patients, and measured IL-1β secretion by ELISA. We found that calculus induced IL-1β secretion in both human PMNs and PBMCs. Calculus also induced IL-1β in macrophages from wild-type mice, but not in macrophages from NLRP3- and ASC-deficient mice, indicating the involvement of NLRP3 and ASC. IL-1β induction was inhibited by polymyxin B, suggesting that LPS is one of the components of calculus that induces pro-IL-1β transcription. To analyze the effect of the inorganic structure, we baked calculus at 250°C for 1 h. This baked calculus failed to induce pro-IL-1β transcription. However, it did induce IL-1β secretion in lipid A-primed cells, indicating that the crystalline structure of calculus induces inflammasome activation. Furthermore, hydroxyapatite crystals, a component of dental calculus, induced IL-1β in mouse macrophages, and baked calculus induced IL-1β in lipid A-primed human PMNs and PBMCs. These results indicate that dental calculus stimulates IL-1β secretion via NLRP3 inflammasome in human and mouse phagocytes, and that the crystalline structure has a partial role in the activation of NLRP3 inflammasome.

[Single and combining effects of Calculus Bovis and zolpidem on inhibitive neurotransmitter of rat striatum corpora].

PubMed

Liu, Ping; He, Xinrong; Guo, Mei

2010-04-01

To investigate the correlation effects between single or combined administration of Calculus Bovis or zolpidem and changes of inhibitive neurotransmitter in rat striatum corpora. Sampling from rat striatum corpora was carried out through microdialysis. The content of two inhibitive neurotransmitters in rat corpus striatum- glycine (Gly) and gama aminobutyric acid (GABA), was determined by HPLC, which involved pre-column derivation with orthophthaladehyde, reversed-phase gradient elution and fluorescence detection. GABA content of rat striatum corpora in Calculus Bovis group was significantly increased compared with saline group (P < 0.01). GABA content of zolpidem group and Calculus Boris plus zolpidem group were increased largely compared with saline group as well (P < 0.05). GABA content of Calculus Bovis group was higher than combination group (P < 0.05). GABA content of zolpidem group was not significantly different from combination group. Gly content of Calculus Bovis or zolpidem group was markedly increased compared with saline group or combination group (P < 0.05). Contents of two inhibitive neurotransmitters in rat striatum corpora were all significantly increased in Calculus Bovis group, zolpidem group and combination group. The magnitude of increase was lower in combination group than in Calculus Bovis group and Zolpidem group, suggesting that Calculus Bovis promoted encephalon inhibition is more powerful than zolpidem. The increase in two inhibitive neurotransmitters did not show reinforcing effect in combination group, suggesting that Calculus Bovis and zolpidem may compete the same receptors. Therefore, combination of Calculus Bovis containing drugs and zolpidem has no clinical significance. Calculus Bovis shouldn't as an aperture-opening drugs be used for resuscitation therapy.

Some basic results on the sets of sequences with geometric calculus

NASA Astrophysics Data System (ADS)

Türkmen, Cengiz; Başar, Feyzi

2012-08-01

As an alternative to the classical calculus, Grossman and Katz [Non-Newtonian Calculus, Lee Press, Pigeon Cove, Massachusetts, 1972] introduced the non-Newtonian calculus consisting of the branches of geometric, anageometric and bigeometric calculus. Following Grossman and Katz, we construct the field C(G) of geometric complex numbers and the concept of geometric metric. Also we give the triangle and Minkowski's inequalities in the sense of geometric calculus. Later we respectively define the sets w(G), ℓ∞(G), c(G), c0(G) and ℓp(G) of all, bounded, convergent, null and p-absolutely summable sequences, in the sense of geometric calculus and show that each of the set forms a complete vector space on the field C(G).

Restricted diversity of dental calculus methanogens over five centuries, France.

PubMed

Huynh, Hong T T; Nkamga, Vanessa D; Signoli, Michel; Tzortzis, Stéfan; Pinguet, Romuald; Audoly, Gilles; Aboudharam, Gérard; Drancourt, Michel

2016-05-11

Methanogens are acknowledged archaeal members of modern dental calculus microbiota and dental pathogen complexes. Their repertoire in ancient dental calculus is poorly known. We therefore investigated archaea in one hundred dental calculus specimens collected from individuals recovered from six archaeological sites in France dated from the 14(th) to 19(th) centuries AD. Dental calculus was demonstrated by macroscopic and cone-beam observations. In 56 calculus specimens free of PCR inhibition, PCR sequencing identified Candidatus Methanobrevibacter sp. N13 in 44.6%, Methanobrevibacter oralis in 19.6%, a new Methanomassiliicoccus luminyensis-like methanogen in 12.5%, a Candidatus Nitrososphaera evergladensis-like in one and Methanoculleus bourgensis in one specimen, respectively. One Candidatus Methanobrevibacter sp. N13 dental calculus was further documented by fluorescent in situ hybridization. The prevalence of dental calculus M. oralis was significantly lower in past populations than in modern populations (P = 0.03, Chi-square test). This investigation revealed a previously unknown repertoire of archaea found in the oral cavity of past French populations as reflected in preserved dental calculus.

Convex functions and some inequalities in terms of the Non-Newtonian Calculus

NASA Astrophysics Data System (ADS)

Unluyol, Erdal; Salas, Seren; Iscan, Imdat

2017-04-01

Differentiation and integration are basic operations of calculus and analysis. Indeed, they are many versions of the subtraction and addition operations on numbers, respectively. From 1967 till 1970 Michael Grossman and Robert Katz [1] gave definitions of a new kind of derivative and integral, converting the roles of subtraction and addition into division and multiplication, and thus establish a new calculus, called Non-Newtonian Calculus. So, in this paper, it is investigated to the convex functions and some inequalities in terms of Non-Newtonian Calculus. Then we compare with the Newtonian and Non-Newtonian Calculus.

In vitro and clinical evaluation of optical coherence tomography for the detection of subgingival calculus and root cementum.

PubMed

Tsubokawa, Masaki; Aoki, Akira; Kakizaki, Sho; Taniguchi, Yoichi; Ejiri, Kenichiro; Mizutani, Koji; Koshy, Geena; Akizuki, Tatsuya; Oda, Shigeru; Sumi, Yasunori; Izumi, Yuichi

2018-05-24

This study evaluated the effectiveness of swept-source optical coherence tomography (ss-OCT) for detecting calculus and root cementum during periodontal therapy. Optical coherence tomography (OCT) images were taken before and after removal of subgingival calculus from extracted teeth and compared with non-decalcified histological sections. Porcine gingival sheets of various thicknesses were applied to the root surfaces of extracted teeth with calculus and OCT images were taken. OCT images were also taken before and after scaling and root planing (SRP) in human patients. In vitro, calculus was clearly detected as a white-gray amorphous structure on the root surface, which disappeared after removal. Cementum was identified as a thin, dark-gray layer. The calculus could not be clearly observed when soft tissues were present on the root surface. Clinically, supragingival calculus and cementum could be detected clearly with OCT, and subgingival calculus in the buccal cervical area of the anterior and premolar teeth was identified, which disappeared after SRP. Digital processing of the original OCT images was useful for clarifying the calculus. In conclusion, ss-OCT showed potential as a periodontal diagnostic tool for detecting cementum and subgingival calculus, although the practical applications of subgingival imaging remain limited.

Supragingival calculus in children with gastrostomy feeding: significant reduction with a caregiver-applied tartar-control dentifrice.

PubMed

Brown, Laurie M; Casamassimo, Paul S; Griffen, Ann; Tatakis, Dimitris

2006-01-01

This study assessed the anti-calculus benefit of Crest Dual Action Whitening Toothpaste in gastrostomy (GT) children compared to a control anti-caries dentifrice. A double-blind randomized crossover design was used to compare the two dentifrices. A convenience sample of 24 GT subjects, 3-12 years old, was given a consensus baseline Volpe-Manhold Index calculus score by 2 trained examiners, followed by a dental prophylaxis to remove all calculus. Each child was randomly assigned to either study or control dentifrice groups. Caregivers brushed subjects' teeth twice daily with the unlabelled dentifrice for at least 45 seconds. Calculus was scored at 8 weeks (+/- 1 week) by the same investigators. Subjects then had a prophylaxis and received the alternative dentifrice. Subjects returned 8 weeks (+/- 1 week) later for final calculus scoring. The study dentifrice significantly reduced supragingival calculus from baseline by 58% compared to control dentifrice (p<0.005 need exact p-value unless it is <.001; maybe it's reported in the paper). Calculus levels decreased by 68% over the study duration, irrespective of dentifrice. ANOVA found no significant differences in calculus scores based on gender, race, history of reflux, aspiration pneumonia, or oral intake of food. Calculus was significantly related to history of aspiration pneumonia (p<0.05 need exact p-value here). Crest Dual Action Whitening Toothpaste was effective and better than anti-caries control dentifrice in reducing calculus in GT children.

New picosecond laser emitting blue light for use in periodontology

NASA Astrophysics Data System (ADS)

Hennig, Thomas; Nieswand, Elmar; Rechmann, Peter

2001-04-01

Aim of the study was to investigate the impact of a new picosecond laser emitting blue light on tooth surfaces in order to remove calculus. The radiation may be comfortably transmitted via 25 micrometers diameter fiber optics. The resulting fluence at the tooth was found to be to low for ablation of calculus via nonlinear effects. Higher absorption of the 446 nm radiation by calculus compared to heathy tissues can provide preferential heating and evaporation of the calculus. The surface of thick calculus is irregular rough thus comprising a large interface to the surrounding cooling medium contra acting the preferential heating. In summary the study indicates the possibility flat layers of calculus by thermal effects. Carbonization in healthy tissues is the major problem concerning removal of subgingival calculus with thermal effects.

[Percentage of uric acid calculus and its metabolic character in Dongjiang River valley].

PubMed

Chong, Hong-Heng; An, Geng

2009-02-15

To study the percentage of uric acid calculus in uroliths and its metabolic character in Dongjiang River valley. To analyze the chemical composition of 290 urinary stones by infrared (IR) spectroscopy and study the ratio changes of uric acid calculus. Uric acid calculus patients and healthy people were studied. Personal characteristics, dietary habits were collected. Conditional logistic regression was used for data analysis and studied the dietary risk factors of uric acid calculus. Patients with uric acid calculus, calcium oxalate and those without urinary calculus were undergone metabolic evaluation analysis. The results of uric acid calculus patients compared to another two groups to analysis the relations between the formation of uric acid calculus and metabolism factors. Uric acid calculi were found in 53 cases (18.3%). The multiple logistic regression analysis suggested that low daily water intake, eating more salted and animal food, less vegetable were very closely associated with uric acid calculus. Comparing to calcium oxalate patients, the urine volume, the value of pH, urine calcium, urine oxalic acid were lower, but uric acid was higher than it. The value of pH, urine oxalic acid and citric acid were lower than them, but uric acid and urine calcium were higher than none urinary calculus peoples. Blood potassium and magnesium were lower than them. The percentage of uric acid stones had obvious advanced. Less daily water intake, eating salted food, eating more animal food, less vegetables and daily orange juice intake, eating sea food are the mainly dietary risk factors to the formation of uric acid calculus. Urine volume, the value of pH, citric acid, urine calcium, urine uric acid and the blood natrium, potassium, magnesium, calcium, uric acid have significant influence to the information of uric acid stones.

Dental Calculus Arrest of Dental Caries.

PubMed

Keyes, Paul H; Rams, Thomas E

An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. These observations further document the potential protective effects of dental calculus mineralization against dental caries.

Dental Calculus Arrest of Dental Caries

PubMed Central

Keyes, Paul H.; Rams, Thomas E.

2016-01-01

Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. Materials and methods A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Results Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. Conclusions These observations further document the potential protective effects of dental calculus mineralization against dental caries. PMID:27446993

A new method for identification of natural, artificial and in vitro cultured Calculus bovis using high-performance liquid chromatography-mass spectrometry

PubMed Central

Liu, Yonggang; Tan, Peng; Liu, Shanshan; Shi, Hang; Feng, Xin; Ma, Qun

2015-01-01

Objective: Calculus bovis have been widely used in Chinese herbology for the treatment of hyperpyrexia, convulsions, and epilepsy. Nowadays, due to the limited source and high market price, the substitutes, artificial and in vitro cultured Calculus bovis, are getting more and more commonly used. The adulteration phenomenon is serious. Therefore, it is crucial to establish a fast and simple method in discriminating the natural, artificial and in vitro cultured Calculus bovis. Bile acids, one of the main active constituents, are taken as an important indicator for evaluating the quality of Calculus bovis and the substitutes. Several techniques have been built to analyze bile acids in Calculus bovis. Whereas, as bile acids are with poor ultraviolet absorbance and high structural similarity, effective technology for identification and quality control is still lacking. Methods: In this study, high-performance liquid chromatography (HPLC) coupled with tandem mass spectrometry (LC/MS/MS) was applied in the analysis of bile acids, which effectively identified natural, artificial and in vitro cultured Calculus bovis and provide a new method for their quality control. Results: Natural, artificial and in vitro cultured Calculus bovis were differentiated by bile acids analysis. A new compound with protonated molecule at m/z 405 was found, which we called 3α, 12α-dihydroxy-7-oxo-5α-cholanic acid. This compound was discovered in in vitro cultured Calculus bovis, but almost not detected in natural and artificial Calculus bovis. A total of 13 constituents was identified. Among them, three bio-markers, including glycocholic acid, glycodeoxycholic acid and taurocholic acid (TCA) were detected in both natural and artificial Calculus bovis, but the density of TCA was different in two kinds of Calculus bovis. In addition, the characteristics of bile acids were illustrated. Conclusions: The HPLC coupled with tandem MS (LC/MS/MS) method was feasible, easy, rapid and accurate in identifying natural, artificial and in vitro cultured Calculus bovis. PMID:25829769

Maxima and Minima Without Calculus.

ERIC Educational Resources Information Center

Birnbaum, Ian

1982-01-01

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

Pulsed laser ablation of dental calculus in the near ultraviolet.

PubMed

Schoenly, Joshua E; Seka, Wolf; Rechmann, Peter

2014-02-01

Pulsed lasers emitting wavelengths near 400 nm can selectively ablate dental calculus without damaging underlying and surrounding sound dental hard tissue. Our results indicate that calculus ablation at this wavelength relies on the absorption of porphyrins endogenous to oral bacteria commonly found in calculus. Sub- and supragingival calculus on extracted human teeth, irradiated with 400-nm, 60-ns laser pulses at ≤8  J/cm2, exhibits a photobleached surface layer. Blue-light microscopy indicates this layer highly scatters 400-nm photons, whereas fluorescence spectroscopy indicates that bacterial porphyrins are permanently photobleached. A modified blow-off model for ablation is proposed that is based upon these observations and also reproduces our calculus ablation rates measured from laser profilometry. Tissue scattering and a stratified layering of absorbers within the calculus medium explain the gradual decrease in ablation rate from successive pulses. Depending on the calculus thickness, ablation stalling may occur at <5  J/cm2 but has not been observed above this fluence.

A generalized nonlocal vector calculus

NASA Astrophysics Data System (ADS)

Alali, Bacim; Liu, Kuo; Gunzburger, Max

2015-10-01

A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.

Detection, removal and prevention of calculus: Literature Review

PubMed Central

Kamath, Deepa G.; Umesh Nayak, Sangeeta

2013-01-01

Dental plaque is considered to be a major etiological factor in the development of periodontal disease. Accordingly, the elimination of supra- and sub-gingival plaque and calculus is the cornerstone of periodontal therapy. Dental calculus is mineralized plaque; because it is porous, it can absorb various toxic products that can damage the periodontal tissues. Hence, calculus should be accurately detected and thoroughly removed for adequate periodontal therapy. Many techniques have been used to identify and remove calculus deposits present on the root surface. The purpose of this review was to compile the various methods and their advantages for the detection and removal of calculus. PMID:24526823

Developing the Fundamental Theorem of Calculus. Applications of Calculus to Work, Area, and Distance Problems. [and] Atmospheric Pressure in Relation to Height and Temperature. Applications of Calculus to Atmospheric Pressure. [and] The Gradient and Some of Its Applications. Applications of Multivariate Calculus to Physics. [and] Kepler's Laws and the Inverse Square Law. Applications of Calculus to Physics. UMAP Units 323, 426, 431, 473.

ERIC Educational Resources Information Center

Lindstrom, Peter A.; And Others

This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views…

The clinical anticalculus efficacy of a tartar control whitening dentifrice for the prevention of supragingival calculus in a three-month study.

PubMed

Sowinski, J; Petrone, D M; Battista, G; Petrone, M E; Crawford, R; Patel, S; DeVizio, W; Chaknis, P; Volpe, A R; Proskin, H M

1999-01-01

The objective of this double-blind clinical study was to compare the effect of a new dentifrice (Colgate Tartar Control Plus Whitening Fluoride Toothpaste) for the prevention of supragingival calculus, with that of a commercially available calculus-inhibiting dentifrice (Crest Tartar Control Toothpaste). The study involved adult male and female subjects who had pre-qualified for participation by developing sufficient supragingival calculus (greater than 7.0 on the Volpe-Manhold Calculus Index) during an eight-week screening period. Subjects received a full oral prophylaxis, and were stratified into two treatment groups balanced for age, sex and qualifying calculus score. Subjects were instructed to brush their teeth twice daily (morning and evening) for one minute with their assigned dentifrice using a soft-bristled toothbrush. Examinations for dental calculus were performed after twelve weeks' use of the study dentifrices, using the Volpe-Manhold Calculus Index, Fifty-eight (58) subjects complied with the protocol and completed the entire study. The Colgate Tartar Control Plus Whitening group exhibited a statistically significant (p < 0.001) 34.6% reduction in mean calculus score compared to the Crest Tartar Control group.

Partial Fractions via Calculus

ERIC Educational Resources Information Center

Bauldry, William C.

2018-01-01

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

The efficacy of selective calculus ablation at 400 nm: comparison to conventional calculus removal methods

NASA Astrophysics Data System (ADS)

Schoenly, Joshua E.; Seka, Wolf; Romanos, Georgios; Rechmann, Peter

A desired outcome of scaling and root planing is the complete removal of calculus and infected root tissue and preservation of healthy cementum for rapid healing of periodontal tissues. Conventional periodontal treatments for calculus removal, such as hand instrument scaling and ultrasonic scaling, often deeply scrape the surface of the underlying hard tissue and may leave behind a smear layer. Pulsed lasers emitting at violet wavelengths (specifically, 380 to 400 nm) are a potential alternative treatment since they can selectively ablate dental calculus without ablating pristine hard tissue (i.e., enamel, cementum, and dentin). In this study, light and scanning electron microscopy are used to compare and contrast the efficacy of in vitro calculus removal for several conventional periodontal treatments (hand instruments, ultrasonic scaler, and Er:YAG laser) to calculus removal with a frequency-doubled Ti:sapphire (λ = 400 nm). After calculus removal, enamel and cementum surfaces are investigated for calculus debris and damage to the underlying hard tissue surface. Compared to the smear layer, grooves, and unintentional hard tissue removal typically found using these conventional treatments, calculus removal using the 400-nm laser is complete and selective without any removal of pristine dental hard tissue. Based on these results, selective ablation from the 400-nm laser appears to produce a root surface that would be more suitable for successful healing of periodontal tissues.

Generalized vector calculus on convex domain

NASA Astrophysics Data System (ADS)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Effect of non-functional teeth on accumulation of supra-gingival calculus in children.

PubMed

Ashkenazi, M; Miller, R; Levin, L

2012-10-01

To evaluate the occurrence of supra-gingival calculus in children aged 6-9 years with disuse conditions such as: presence of dental pain, open-bite or erupting teeth. A cohort of 327 children aged 7.64±2.12 (range: 6-9) years (45% girls) were screened for presence of supra-gingival calculus in relation to open bite, erupting teeth and dental pain. Presence of dental calculus was evaluated dichotomically in the buccal, palatinal/lingual and occlusal surfaces. Plaque index (PI) and gingival index (GI) were also evaluated. Supra-gingival calculus was found in 15.9% of the children mainly in the mandibular incisors. Children aged 6-7 years had a higher prevalence of calculus as compared to children aged 7-8 years (23% vs. 13.5%, p=0.057) or 8-9 years (23% vs. 12.4%, p=0.078), respectively. No statistical relation was found between plaque and gingival indices and presence of calculus. The prevalence of calculus among children with openbite was significantly higher than that of children without open-bite (29.4% vs. 10.7%, p=0.0006, OR=3.489). The prevalence of calculus among children with erupting teeth in their oral cavity was higher than that of children without erupting teeth (17.7% vs. 9%, respectively, p=0.119). No statistical correlation was found between presence of dental pain and calculus (15.4% vs. 15.9%; p=0.738). Accumulation of calculus in children aged 6-10 years was found mainly in the mandibular incisors, decreased with age and was correlated with open-bite.

Matrix-Gla Protein rs4236 [A/G] gene polymorphism and serum and GCF levels of MGP in patients with subgingival dental calculus.

PubMed

Doğan, Gülnihal Emrem; Demir, Turgut; Aksoy, Hülya; Sağlam, Ebru; Laloğlu, Esra; Yildirim, Abdulkadir

2016-10-01

Matrix-Gla Protein (MGP) is one of the major Gla-containing protein associated with calcification process. It also has a high affinity for Ca 2+ and hydroxyapatite. In this study we aimed to evaluate the MGP rs4236 [A/G] gene polymorphism in association with subgingival dental calculus. Also a possible relationship between MGP gene polymorphism and serum and GCF levels of MGP were examined. MGP rs4236 [A/G] gene polymorphism was investigated in 110 patients with or without subgingival dental calculus, using polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) techniques. Additionally, serum and GCF levels of MGP of the patients were compared according to subgingival dental calculus. Comparison of patients with and without subgingival dental calculus showed no statistically significant difference in MGP rs4236 [A/G] gene polymorphism (p=0.368). MGP concentrations in GCF of patients with subgingival dental calculus were statistically higher than those without subgingival dental calculus (p=0.032). However, a significant association was not observed between the genotypes of AA, AG and GG of the MGP rs4236 gene and the serum and GCF concentrations of MGP in subjects. In this study, it was found that MGP rs4236 [A/G] gene polymorphism was not to be associated with subgingival dental calculus. Also, that GCF MGP levels were detected higher in patients with subgingival dental calculus than those without subgingival dental calculus independently of polymorphism, may be the effect of adaptive mechanism to inhibit calculus formation. Copyright © 2016 Elsevier Ltd. All rights reserved.

An AP Calculus Classroom Amusement Park

ERIC Educational Resources Information Center

Ferguson, Sarah

2016-01-01

Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.…

Early Vector Calculus: A Path through Multivariable Calculus

ERIC Educational Resources Information Center

Robertson, Robert L.

2013-01-01

The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)

A Historical Perspective on Teaching and Learning Calculus

ERIC Educational Resources Information Center

Doorman, Michiel; van Maanen, Jan

2008-01-01

Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of reasoning. The calculus of Leibniz brings within the reach of an ordinary student…

Subgingival calculus imaging based on swept-source optical coherence tomography

NASA Astrophysics Data System (ADS)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Lu, Chih-Wei; Jiang, Cho-Pei; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-07-01

We characterized and imaged dental calculus using swept-source optical coherence tomography (SS-OCT). The refractive indices of enamel, dentin, cementum, and calculus were measured as 1.625 +/- 0.024, 1.534 +/- 0.029, 1.570 +/- 0.021, and 2.097 +/- 0.094, respectively. Dental calculus leads strong scattering properties, and thus, the region can be identified from enamel with SS-OCT imaging. An extracted human tooth with calculus is covered with gingiva tissue as an in vitro sample for tomographic imaging.

Dental calculus image based on optical coherence tomography

NASA Astrophysics Data System (ADS)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-03-01

In this study, the dental calculus was characterized and imaged by means of swept-source optical coherence tomography (SSOCT). The refractive indices of enamel, dentin, cementum and calculus were measured as 1.625+/-0.024, 1.534+/-0.029, 1.570+/-0.021 and 1.896+/-0.085, respectively. The dental calculus lead strong scattering property and thus the region can be identified under enamel with SSOCT imaging. An extracted human tooth with calculus was covered by gingiva tissue as in vitro sample for SSOCT imaging.

Questions Revisited: A Close Examination of Calculus of Inference and Inquiry

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.; Koga, Dennis (Technical Monitor)

2003-01-01

In this paper I examine more closely the way in which probability theory, the calculus of inference, is derived from the Boolean lattice structure of logical assertions ordered by implication. I demonstrate how the duality between the logical conjunction and disjunction in Boolean algebra is lost when deriving the probability calculus. In addition, I look more closely at the other lattice identities to verify that they are satisfied by the probability calculus. Last, I look towards developing the calculus of inquiry demonstrating that there is a sum and product rule for the relevance measure as well as a Bayes theorem. Current difficulties in deriving the complete inquiry calculus will also be discussed.

Preservation of the metaproteome: variability of protein preservation in ancient dental calculus.

PubMed

Mackie, Meaghan; Hendy, Jessica; Lowe, Abigail D; Sperduti, Alessandra; Holst, Malin; Collins, Matthew J; Speller, Camilla F

2017-01-01

Proteomic analysis of dental calculus is emerging as a powerful tool for disease and dietary characterisation of archaeological populations. To better understand the variability in protein results from dental calculus, we analysed 21 samples from three Roman-period populations to compare: 1) the quantity of extracted protein; 2) the number of mass spectral queries; and 3) the number of peptide spectral matches and protein identifications. We found little correlation between the quantity of calculus analysed and total protein identifications, as well as no systematic trends between site location and protein preservation. We identified a wide range of individual variability, which may be associated with the mechanisms of calculus formation and/or post-depositional contamination, in addition to taphonomic factors. Our results suggest dental calculus is indeed a stable, long-term reservoir of proteins as previously reported, but further systematic studies are needed to identify mechanisms associated with protein entrapment and survival in dental calculus.

Recalling Prerequisite Material in a Calculus II Course to Improve Student Success

ERIC Educational Resources Information Center

Mokry, Jeanette

2016-01-01

This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…

The Path to College Calculus: The Impact of High School Mathematics Coursework

ERIC Educational Resources Information Center

Sadler, Philip; Sonnert, Gerhard

2018-01-01

This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus-- (a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? We used a data set…

The Development and Nature of Problem-Solving among First-Semester Calculus Students

ERIC Educational Resources Information Center

Dawkins, Paul Christian; Epperson, James A. Mendoza

2014-01-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate…

Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

ERIC Educational Resources Information Center

Patel, Rita Manubhai; McCombs, Paul; Zollman, Alan

2014-01-01

Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student…

The History of the Calculus

ERIC Educational Resources Information Center

Harding, Simon; Scott, Paul

2004-01-01

Calculus is a mathematical concept that is fundamental to how we understand the world around us. Whether it is in the world of technology, finance, astronomy, sociology, medicine, calculus in one form or another can be found. This brief article describes the origins of calculus in Greece, further developments by Newton and Leibniz, and the…

Polynomial Calculus: Rethinking the Role of Calculus in High Schools

ERIC Educational Resources Information Center

Grant, Melva R.; Crombie, William; Enderson, Mary; Cobb, Nell

2016-01-01

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

Calculus ABCs: A Gateway for Freshman Calculus

ERIC Educational Resources Information Center

Fulton, Scott R.

2003-01-01

This paper describes a gateway testing program designed to ensure that students acquire basic skills in freshman calculus. Students must demonstrate they have mastered standards for "Absolutely Basic Competency"--the Calculus ABCs--in order to pass the course with a grade of C or better. We describe the background, standards, and testing program.…

Unusual Case of Calculus in Floor of Mouth: A Case Report

PubMed Central

Thosar, Nilima; Jain, Eesha S

2012-01-01

Abstract Calculus consists of mineralized bacterial plaque that forms on the surfaces of natural teeth. It is supragingival or subgingival depending upon its relation with gingival margin. The two most common locations for supragingival calculus are the buccal surfaces of maxillary molars and lingual surfaces of mandibular anterior teeth. It is very important to rule out the predisposing factor for calculus formation. In the present case of an 11-year- old female child, 1.2 × 1.5 cm large indurated mass suggestive of calculus in the left side of floor of mouth was observed. After surgical removal, along with indurated mass, an embedded root fragment was seen. Biochemical analysis of the specimen detected the calcium and phosphate ions approximately equals to the level in calculus. Thus, we diagnosed it as a calculus. Oral hygiene instructions and regular follow-up was advised. How to cite this article: Bahadure RN, Thosar N, Jain ES. Unusual Case of Calculus in Floor of Mouth: A Case Report. Int J Clin Pediatr Dent 2012;5(3):223-225. PMID:25206174

Investigation of In vitro Mineral forming bacterial isolates from supragingival calculus.

PubMed

Baris, O; Demir, T; Gulluce, M

2017-12-01

Although it is known that bacterial mechanisms are involved in dental calculus formation, which is a predisposing factor in periodontal diseases, there have been few studies of such associations, and therefore, information available is limited. The purpose of this study was to isolate and identify aerobic bacteria responsible for direct calcification from supragingival calculus samples. The study was conducted using supragingival calculus samples from patients with periodontal disease, which was required as part of conventional treatment. Isolations were performed by sampling the supragingival calculus with buffer and inoculating the samples on media on which crystallization could be observed. The 16S recombinant DNA of the obtained pure cultures was then amplified and sequenced. A few bacterial species that have not previously been associated with mineralization or identified on bacterial plaque or calculus were detected. The bacteria that caused mineralization an aerobic environment are identified as Neisseria flava, Aggregatibacter segnis, Streptococcus tigurinus, and Morococcus cerebrosus. These findings proved that bacteria potentially play a role in the etiopathology of supragingival calculus. The association between the effects of the identified bacteria on periodontal diseases and calculus formation requires further studies.

Dental calculus formation in children and adolescents undergoing hemodialysis.

PubMed

Martins, Carla; Siqueira, Walter Luiz; Oliveira, Elizabeth; Nicolau, José; Primo, Laura Guimarães

2012-10-01

This study aimed to determine whether dental calculus formation is really higher among patients with chronic kidney disease undergoing hemodialysis than among controls. Furthermore, the study evaluated correlations between dental calculus formation and dental plaque, variables that are related to renal disease and/or saliva composition. The Renal Group was composed of 30 patients undergoing hemodialysis, whereas the Healthy Group had 30 clinically healthy patients. Stimulated whole saliva and parotid saliva were collected. Salivary flow rate and calcium and phosphate concentrations were determined. In the Renal Group the saliva collection was carried out before and after a hemodialysis session. Patients from both groups received intraoral exams, oral hygiene instructions, and dental scaling. Three months later, the dental calculus was measured by the Volpe-Manhold method to determine the rate of dental calculus formation. The Renal Group presented a higher rate of dental calculus formation (p < 0.01). Correlation was observed between rate of dental calculus formation and whole saliva flow rate in the Renal Group after a hemodialysis session (r = 0.44, p < 0.05). The presence of dental calculus was associated with phosphate concentration in whole saliva from the Renal Group (p < 0.05). In conclusion, patients undergoing hemodialysis presented accelerated dental calculus formation, probably due to salivary variables.

The Case for Biocalculus: Design, Retention, and Student Performance

PubMed Central

Eaton, Carrie Diaz; Highlander, Hannah Callender

2017-01-01

Calculus is one of the primary avenues for initial quantitative training of students in all science, technology, engineering, and mathematics fields, but life science students have been found to underperform in the traditional calculus setting. As a result, and because of perceived lack of its contribution to the understanding of biology, calculus is being actively cut from biology program requirements at many institutions. Here, we present an alternative: a model for learning mathematics that sees the partner disciplines as crucial to student success. We equip faculty with information to engage in dialogue within and between disciplinary departments involved in quantitative education. This includes presenting a process for interdisciplinary development and implementation of biology-oriented Calculus I courses at two institutions with different constituents, goals, and curricular constraints. When life science students enrolled in these redesigned calculus courses are compared with life science students enrolled in traditional calculus courses, students in the redesigned calculus courses learn calculus concepts and skills as well as their traditional course peers; however, the students in the redesigned courses experience more authentic life science applications and are more likely to stay and succeed in the course than their peers who are enrolled in traditional courses. Therefore, these redesigned calculus courses hold promise in helping life science undergraduate students attain Vision and Change recommended competencies. PMID:28450445

Improving student learning in calculus through applications

NASA Astrophysics Data System (ADS)

Young, C. Y.; Georgiopoulos, M.; Hagen, S. C.; Geiger, C. L.; Dagley-Falls, M. A.; Islas, A. L.; Ramsey, P. J.; Lancey, P. M.; Straney, R. A.; Forde, D. S.; Bradbury, E. E.

2011-07-01

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.

The development and nature of problem-solving among first-semester calculus students

NASA Astrophysics Data System (ADS)

Dawkins, Paul Christian; Mendoza Epperson, James A.

2014-08-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem-solving performance, we observe that current instruction requires ongoing refinement to help students develop multi-register fluency and the ability to model quantitatively, as is called for in current US standards for mathematical instruction.

In vitro performance of DIAGNOdent laser fluorescence device for dental calculus detection on human tooth root surfaces.

PubMed

Rams, Thomas E; Alwaqyan, Abdulaziz Y

2017-10-01

This study assessed the reproducibility of a red diode laser device, and its capability to detect dental calculus in vitro on human tooth root surfaces. On each of 50 extracted teeth, a calculus-positive and calculus-free root surface was evaluated by two independent examiners with a low-power indium gallium arsenide phosphide diode laser (DIAGNOdent) fitted with a periodontal probe-like sapphire tip and emitting visible red light at 655 nm wavelength. Laser autofluorescence intensity readings of examined root surfaces were scored on a 0-99 scale, with duplicate assessments performed using the laser probe tip directed both perpendicular and parallel to evaluated tooth root surfaces. Pearson correlation coefficients of untransformed measurements, and kappa analysis of data dichotomized with a >40 autofluorescence intensity threshold, were calculated to assess intra- and inter-examiner reproducibility of the laser device. Mean autofluorescence intensity scores of calculus-positive and calculus-free root surfaces were evaluated with the Student's t -test. Excellent intra- and inter-examiner reproducibility was found for DIAGNOdent laser autofluorescence intensity measurements, with Pearson correlation coefficients above 94%, and kappa values ranging between 0.96 and 1.0, for duplicate readings taken with both laser probe tip orientations. Significantly higher autofluorescence intensity values were measured when the laser probe tip was directed perpendicular, rather than parallel, to tooth root surfaces. However, calculus-positive roots, particularly with calculus in markedly-raised ledges, yielded significantly greater mean DIAGNOdent laser autofluorescence intensity scores than calculus-free surfaces, regardless of probe tip orientation. DIAGNOdent autofluorescence intensity values >40 exhibited a stronger association with calculus (36.6 odds ratio) then measurements of ≥5 (20.1 odds ratio) when the laser probe tip was advanced parallel to root surfaces. Excellent intra- and inter-examiner reproducibility of autofluorescence intensity measurements was obtained with the DIAGNOdent laser fluorescence device on human tooth roots. Calculus-positive root surfaces exhibited significantly greater DIAGNOdent laser autofluorescence than calculus-free tooth roots, even with the laser probe tip directed parallel to root surfaces. These findings provide further in vitro validation of the potential utility of a DIAGNOdent laser fluorescence device for identifying dental calculus on human tooth root surfaces.

Crystalline structure of pulverized dental calculus induces cell death in oral epithelial cells.

PubMed

Ziauddin, S M; Yoshimura, A; Montenegro Raudales, J L; Ozaki, Y; Higuchi, K; Ukai, T; Kaneko, T; Miyazaki, T; Latz, E; Hara, Y

2018-06-01

Dental calculus is a mineralized deposit attached to the tooth surface. We have shown that cellular uptake of dental calculus triggers nucleotide-binding oligomerization domain-like receptor family pyrin domain-containing 3 (NLRP3) inflammasome activation, leading to the processing of the interleukin-1β precursor into its mature form in mouse and human phagocytes. The activation of the NLRP3 inflammasome also induced a lytic form of programmed cell death, pyroptosis, in these cells. However, the effects of dental calculus on other cell types in periodontal tissue have not been investigated. The aim of this study was to determine whether dental calculus can induce cell death in oral epithelial cells. HSC-2 human oral squamous carcinoma cells, HOMK107 human primary oral epithelial cells and immortalized mouse macrophages were exposed to dental calculus or 1 of its components, hydroxyapatite crystals. For inhibition assays, the cells were exposed to dental calculus in the presence or absence of cytochalasin D (endocytosis inhibitor), z-YVAD-fmk (caspase-1 inhibitor) or glyburide (NLRP3 inflammasome inhibitor). Cytotoxicity was determined by measuring lactate dehydrogenase (LDH) release and staining with propidium iodide. Tumor necrosis factor-α production was quantified by enzyme-linked immunosorbent assay. Oral epithelial barrier function was examined by permeability assay. Dental calculus induced cell death in HSC-2 cells, as judged by LDH release and propidium iodide staining. Dental calculus also induced LDH release from HOMK107 cells. Following heat treatment, dental calculus lost its capacity to induce tumor necrosis factor-α in mouse macrophages, but could induce LDH release in HSC-2 cells, indicating a major role of inorganic components in cell death. Hydroxyapatite crystals also induced cell death in both HSC-2 and HOMK107 cells, as judged by LDH release, indicating the capacity of crystal particles to induce cell death. Cell death induced by dental calculus was significantly inhibited by cytochalasin D, z-YVAD-fmk and glyburide, indicating NLRP3 inflammasome involvement. In permeability assays, dental calculus attenuated the barrier function of HSC-2 cell monolayers. Dental calculus induces pyroptotic cell death in human oral epithelial cells and the crystalline structure plays a major role in this process. Oral epithelial cell death induced by dental calculus might be important for the etiology of periodontitis. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

A Transition Course from Advanced Placement to College Calculus

ERIC Educational Resources Information Center

Lucas, Timothy A.; Spivey, Joseph

2011-01-01

In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…

Improving Calculus II and III through the Redistribution of Topics

ERIC Educational Resources Information Center

George, C. Yousuf; Koetz, Matt; Lewis, Heather A.

2016-01-01

Three years ago our mathematics department rearranged the topics in second and third semester calculus, moving multivariable calculus to the second semester and series to the third semester. This paper describes the new arrangement of topics, and how it could be adapted to calculus curricula at different schools. It also explains the benefits we…

On the Presentation of Pre-Calculus and Calculus Topics: An Alternate View

ERIC Educational Resources Information Center

Davydov, Aleksandr; Sturm-Beiss, Rachel

2008-01-01

The orders of presentation of pre-calculus and calculus topics, and the notation used, deserve careful study as they affect clarity and ultimately students' level of understanding. We introduce an alternate approach to some of the topics included in this sequence. The suggested alternative is based on years of teaching in colleges within and…

Computer Managed Instruction Homework Modules for Calculus I.

ERIC Educational Resources Information Center

Goodman-Petrushka, Sharon; Roitberg, Yael

This booklet contains 11 modules (290 multiple-choice items) designed for use in the first course of a three-course calculus sequence using the textbook "Calculus with Analytic Geometry" (Dennis G. Zill). In each module, relevant sections of the textbook are identified for users. It can, however, be used in conjunction with any calculus textbook.…

Subgingival calculus imaging based on swept-source optical coherence tomography.

PubMed

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Lu, Chih-Wei; Jiang, Cho-Pei; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-07-01

We characterized and imaged dental calculus using swept-source optical coherence tomography (SS-OCT). The refractive indices of enamel, dentin, cementum, and calculus were measured as 1.625 ± 0.024, 1.534 ± 0.029, 1.570 ± 0.021, and 2.097 ± 0.094, respectively. Dental calculus leads strong scattering properties, and thus, the region can be identified from enamel with SS-OCT imaging. An extracted human tooth with calculus is covered with gingiva tissue as an in vitro sample for tomographic imaging.

A new proof of the generalized Hamiltonian–Real calculus

PubMed Central

Gao, Hua; Mandic, Danilo P.

2016-01-01

The recently introduced generalized Hamiltonian–Real (GHR) calculus comprises, for the first time, the product and chain rules that makes it a powerful tool for quaternion-based optimization and adaptive signal processing. In this paper, we introduce novel dual relationships between the GHR calculus and multivariate real calculus, in order to provide a new, simpler proof of the GHR derivative rules. This further reinforces the theoretical foundation of the GHR calculus and provides a convenient methodology for generic extensions of real- and complex-valued learning algorithms to the quaternion domain.

Calculus detection technologies: where do we stand now?

PubMed Central

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data. PMID:25870667

Calculus detection technologies: where do we stand now?

PubMed

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data.

Comparative clinical efficacy of three toothpastes in the control of supragingival calculus formation.

PubMed

Kraivaphan, Petcharat; Amornchat, Cholticha

2017-01-01

The purpose of this double-blind, parallel clinical study was to assess clinical efficacy in supragingival calculus formation reduction using Abhaibhubejhr Herbal Toothpaste compared to Colgate Total and Colgate Cavity Protection toothpastes. A total of 150 subjects participated in the pretest phase. All subjects were given oral soft/hard tissue evaluation, calculus examination using Volpe-Manhold calculus, and whole mouth oral prophylaxis. They received noncalculus control fluoride toothpaste and a soft-bristled toothbrush to brush for 1 min two times daily for 8 weeks. After which, subjects were given a test phase oral soft/hard tissue evaluation and calculus examination and were randomized into one of the three toothpaste groups. All subjects in the test phase received a whole mouth oral prophylaxis and were given their assigned toothpaste and a soft-bristled toothbrush to brush for 1 min two times a day for 12 weeks. Thereafter, subjects were assessed for their oral soft/hard tissue and calculus formation. Mean Volpe-Manhold calculus index scores for the Cavity Protection, Abhaibhubejhr, and Total toothpaste groups were 0.78, 0.62, and 0.48, respectively, at the 12-week test phase evaluation. Abhaibhubejhr and Total toothpaste groups show 20.51% and 38.46% significantly less calculus formation than the Cavity Protection toothpaste group ( P < 0.05). Total toothpaste group also show 22.58% significantly less calculus formation than the Abhaibhubejhr toothpaste group ( P < 0.05). The use of Colgate Total toothpaste over a 12-week period was clinically more effective than either Abhaibhubejhr or Colgate Cavity Protection toothpastes in controlling supragingival calculus formation.

Endoscopic vs. tactile evaluation of subgingival calculus.

PubMed

Osborn, Joy B; Lenton, Patricia A; Lunos, Scott A; Blue, Christine M

2014-08-01

Endoscopic technology has been developed to facilitate imagery for use during diagnostic and therapeutic phases of periodontal care. The purpose of this study was to compare the level of subgingival calculus detection using a periodontal endoscope with that of conventional tactile explorer in periodontitis subjects. A convenience sample of 26 subjects with moderate periodontitis in at least 2 quadrants was recruited from the University of Minnesota School of Dentistry to undergo quadrant scaling and root planing. One quadrant from each subject was randomized for tactile calculus detection alone and the other quadrant for tactile detection plus the Perioscope ™ (Perioscopy Inc., Oakland, Cali). A calculus index on a 0 to 3 score was performed at baseline and at 2 post-scaling and root planing visits. Sites where calculus was detected at visit 1 were retreated. T-tests were used to determine within-subject differences between Perioscope™ and tactile measures, and changes in measures between visits. Significantly more calculus was detected using the Perioscope™ vs. tactile explorer for all 3 subject visits (p<0.005). Mean changes (reduction) in calculus detection from baseline to visit 1 were statistically significant for both the Perioscope™ and tactile quadrants (p<0.0001). However, further reductions in calculus detection from visit 1 to visit 2 was only significant for the Perioscope™ quadrant (p<0.025), indicating that this methodology was able to more precisely detect calculus at this visit. It was concluded that the addition of a visual component to calculus detection via the Perioscope™ was most helpful in the re-evaluation phase of periodontal therapy. Copyright © 2014 The American Dental Hygienists’ Association.

A comparison of dental ultrasonic technologies on subgingival calculus removal: a pilot study.

PubMed

Silva, Lidia Brión; Hodges, Kathleen O; Calley, Kristin Hamman; Seikel, John A

2012-01-01

This pilot study compared the clinical endpoints of the magnetostrictive and piezoelectric ultrasonic instruments on calculus removal. The null hypothesis stated that there is no statistically significant difference in calculus removal between the 2 instruments. A quasi-experimental pre- and post-test design was used. Eighteen participants were included. The magnetostrictive and piezoelectric ultrasonic instruments were used in 2 assigned contra-lateral quadrants on each participant. A data collector, blind to treatment assignment, assessed the calculus on 6 predetermined tooth sites before and after ultrasonic instrumentation. Calculus size was evaluated using ordinal measurements on a 4 point scale (0, 1, 2, 3). Subjects were required to have size 2 or 3 calculus deposit on the 6 predetermined sites. One clinician instrumented the pre-assigned quadrants. A maximum time of 20 minutes of instrumentation was allowed with each technology. Immediately after instrumentation, the data collector then conducted the post-test calculus evaluation. The repeated analysis of variance (ANOVA) was used to analyze the pre- and post-test calculus data (p≤0.05). The null hypothesis was accepted indicating that there is no statistically significant difference in calculus removal when comparing technologies (p≤0.05). Therefore, under similar conditions, both technologies removed the same amount of calculus. This research design could be used as a foundation for continued research in this field. Future studies include implementing this study design with a larger sample size and/or modifying the study design to include multiple clinicians who are data collectors. Also, deposit removal with periodontal maintenance patients could be explored.

Science 101: How Do We Use Calculus in Science?

ERIC Educational Resources Information Center

Robertson, Bill

2014-01-01

How is calculus used in science? That might seem like an odd question to answer in a magazine intended primarily for elementary school teachers. After all, how much calculus gets used in elementary science? Here the author guesses that quite a few readers of this column do not know a whole lot about calculus and have not taken a course in…

An Analysis of College Mathematics Departments' Credit Granting Policies for Students with High School Calculus Experience

ERIC Educational Resources Information Center

Laurent, Theresa A.

2009-01-01

The purpose of this study was to investigate higher education mathematics departments' credit granting policies for students with high school calculus experience. The number of students taking calculus in high school has more than doubled since 1982 (NCES, 2007) and it is estimated that approximately 530,000 students took a calculus course in high…

A Study of Calculus Instructors' Perceptions of Approximation as a Unifying Thread of the First-Year Calculus

ERIC Educational Resources Information Center

Sofronas, Kimberly S.; DeFranco, Thomas C.; Swaminathan, Hariharan; Gorgievski, Nicholas; Vinsonhaler, Charles; Wiseman, Brianna; Escolas, Samuel

2015-01-01

This paper discusses findings from a research study designed to investigate calculus instructors' perceptions of approximation as a central concept and possible unifying thread of the first-year calculus. The study also examines the role approximation plays in participants' self-reported instructional practices. A survey was administered to 279…

What Does It Mean for a Student to Understand the First-Year Calculus? Perspectives of 24 Experts

ERIC Educational Resources Information Center

Sofronas, Kimberly S.; DeFranco, Thomas C.; Vinsonhaler, Charles; Gorgievski, Nicholas; Schroeder, Larissa; Hamelin, Chris

2011-01-01

This article presents the views of 24 nationally recognized authorities in the field of mathematics, and in particular the calculus, on student understanding of the first-year calculus. A framework emerged that includes four overarching end goals for understanding of the first-year calculus: (a) mastery of the fundamental concepts and-or skills of…

Examining related influential factors for dental calculus scaling utilization among people with disabilities in Taiwan, a nationwide population-based study.

PubMed

Lai, Hsien-Tang; Kung, Pei-Tseng; Su, Hsun-Pi; Tsai, Wen-Chen

2014-09-01

Limited studies with large samples have been conducted on the utilization of dental calculus scaling among people with physical or mental disabilities. This study aimed to investigate the utilization of dental calculus scaling among the national disabled population. This study analyzed the utilization of dental calculus scaling among the disabled people, using the nationwide data between 2006 and 2008. Descriptive analysis and logistic regression were performed to analyze related influential factors for dental calculus scaling utilization. The dental calculus scaling utilization rate among people with physical or mental disabilities was 16.39%, and the annual utilization frequency was 0.2 times. Utilization rate was higher among the female and non-aboriginal samples. Utilization rate decreased with increased age and disability severity while utilization rate increased with income, education level, urbanization of residential area and number of chronic illnesses. Related influential factors for dental calculus scaling utilization rate were gender, age, ethnicity (aboriginal or non-aboriginal), education level, urbanization of residence area, income, catastrophic illnesses, chronic illnesses, disability types, and disability severity significantly influenced the dental calculus scaling utilization rate. Copyright © 2014 Elsevier Ltd. All rights reserved.

Dental calculus detection using the VistaCam.

PubMed

Shakibaie, Fardad; Walsh, Laurence J

2016-12-01

The VistaCam® intra-oral camera system (Dürr Dental, Bietigheim-Bissingen, Germany) is a fluorescence system using light emitting diodes that produce a 405-nm violet light. This wavelength has potential application for detection of dental calculus based on red emissions from porphyrin molecules. This study assessed the digital scores obtained for both supragingival and subgingival calculus on 60 extracted teeth and compared these with lesions of dental caries. It has also examined the effect of saliva and blood on the fluorescence readings for dental calculus. VistaCam fluorescence scores for both supragingival (1.7-3.3) and subgingival calculus (1.3-2.4) were higher than those for sound root surfaces (0.9-1.1) and dental caries (0.9-2.2) ( p  < .05). The readings for calculus samples were not affected by the presence of saliva or blood. These results suggest that the use of violet light fluorescence could be a possible adjunct to clinical examination for deposits of dental calculus.

Preservation of the metaproteome: variability of protein preservation in ancient dental calculus

PubMed Central

Mackie, Meaghan; Hendy, Jessica; Lowe, Abigail D.; Sperduti, Alessandra; Holst, Malin; Collins, Matthew J.; Speller, Camilla F.

2017-01-01

ABSTRACT Proteomic analysis of dental calculus is emerging as a powerful tool for disease and dietary characterisation of archaeological populations. To better understand the variability in protein results from dental calculus, we analysed 21 samples from three Roman-period populations to compare: 1) the quantity of extracted protein; 2) the number of mass spectral queries; and 3) the number of peptide spectral matches and protein identifications. We found little correlation between the quantity of calculus analysed and total protein identifications, as well as no systematic trends between site location and protein preservation. We identified a wide range of individual variability, which may be associated with the mechanisms of calculus formation and/or post-depositional contamination, in addition to taphonomic factors. Our results suggest dental calculus is indeed a stable, long-term reservoir of proteins as previously reported, but further systematic studies are needed to identify mechanisms associated with protein entrapment and survival in dental calculus. PMID:29098079

Understanding Calculus beyond Computations: A Descriptive Study of the Parallel Meanings and Expectations of Teachers and Users of Calculus

ERIC Educational Resources Information Center

Ferguson, Leann J.

2012-01-01

Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…

Bacterial Viability within Dental Calculus: An Untrodden, Inquisitive Clinico-Patho- Microbiological Research.

PubMed

Gupta, Swati; Jain, P K; Kumra, Madhumani; Rehani, Shweta; Mathias, Yulia; Gupta, Ramakant; Mehendiratta, Monica; Chander, Anil

2016-07-01

Chronic inflammatory periodontal diseases i.e. gingivitis and periodontitis are one of the most common afflictions faced by human beings. Dental plaque, which is a pool of pathogenic microorganisms, remains to be current mainstay in etiopathogenesis. Dental calculus, which is a mineralized product of this plaque remains ignored and is considered merely as an ash heap of minor significance. However, the intriguing array in disease etiopathogenesis bulldozed researchers to suspect the role of calculus in disease chrysalis but still the viability of bacteria inside calculus and thus its pathogenicity remains an intricacy; the answer to which lies in the Pandora's Box. The present study was undertaken to investigate the viability of bacteria within dental calculus along with their identification. Also, to classify dental calculus on the basis of mineralization and to observe the variation of viable microflora found in dental calculus with the extent of mineralization and disease severity. A total of 60 samples were obtained, by harvesting two samples of supragingival calculus from each patient having chronic inflammatory periodontal disease. These samples were divided into two groups (Group A and Group B). Samples of Group A were kept non-irradiated and samples of Group B were exposed to UV radiation. The samples were categorized into less, moderately and highly mineralized according to the force required for crushing them. All the crushed calculus samples were then divided into three parts. These were used for dark-field microscopy, gram staining and bacterial cultures. Bacterial identification of the cultures obtained was also carried out by performing various biochemical assays. The present study revealed the presence of motile spirochaetes within the samples under dark-field microscope. Gram staining revealed presence of numerous gram positive cocci and gram negative bacilli. Bacterial cultures showed growth of variety of aerobic and capnophilic microorganisms. The present study concludes the presence of viable aerobic and capnophilic bacteria inside dental calculus which may reside within the lacunae and channels in the calculus.

Successful enrichment and recovery of whole mitochondrial genomes from ancient human dental calculus.

PubMed

Ozga, Andrew T; Nieves-Colón, Maria A; Honap, Tanvi P; Sankaranarayanan, Krithivasan; Hofman, Courtney A; Milner, George R; Lewis, Cecil M; Stone, Anne C; Warinner, Christina

2016-06-01

Archaeological dental calculus is a rich source of host-associated biomolecules. Importantly, however, dental calculus is more accurately described as a calcified microbial biofilm than a host tissue. As such, concerns regarding destructive analysis of human remains may not apply as strongly to dental calculus, opening the possibility of obtaining human health and ancestry information from dental calculus in cases where destructive analysis of conventional skeletal remains is not permitted. Here we investigate the preservation of human mitochondrial DNA (mtDNA) in archaeological dental calculus and its potential for full mitochondrial genome (mitogenome) reconstruction in maternal lineage ancestry analysis. Extracted DNA from six individuals at the 700-year-old Norris Farms #36 cemetery in Illinois was enriched for mtDNA using in-solution capture techniques, followed by Illumina high-throughput sequencing. Full mitogenomes (7-34×) were successfully reconstructed from dental calculus for all six individuals, including three individuals who had previously tested negative for DNA preservation in bone using conventional PCR techniques. Mitochondrial haplogroup assignments were consistent with previously published findings, and additional comparative analysis of paired dental calculus and dentine from two individuals yielded equivalent haplotype results. All dental calculus samples exhibited damage patterns consistent with ancient DNA, and mitochondrial sequences were estimated to be 92-100% endogenous. DNA polymerase choice was found to impact error rates in downstream sequence analysis, but these effects can be mitigated by greater sequencing depth. Dental calculus is a viable alternative source of human DNA that can be used to reconstruct full mitogenomes from archaeological remains. Am J Phys Anthropol 160:220-228, 2016. © 2016 The Authors American Journal of Physical Anthropology Published by Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Successful enrichment and recovery of whole mitochondrial genomes from ancient human dental calculus

PubMed Central

Ozga, Andrew T.; Nieves‐Colón, Maria A.; Honap, Tanvi P.; Sankaranarayanan, Krithivasan; Hofman, Courtney A.; Milner, George R.; Lewis, Cecil M.; Stone, Anne C.

2016-01-01

ABSTRACT Objectives Archaeological dental calculus is a rich source of host‐associated biomolecules. Importantly, however, dental calculus is more accurately described as a calcified microbial biofilm than a host tissue. As such, concerns regarding destructive analysis of human remains may not apply as strongly to dental calculus, opening the possibility of obtaining human health and ancestry information from dental calculus in cases where destructive analysis of conventional skeletal remains is not permitted. Here we investigate the preservation of human mitochondrial DNA (mtDNA) in archaeological dental calculus and its potential for full mitochondrial genome (mitogenome) reconstruction in maternal lineage ancestry analysis. Materials and Methods Extracted DNA from six individuals at the 700‐year‐old Norris Farms #36 cemetery in Illinois was enriched for mtDNA using in‐solution capture techniques, followed by Illumina high‐throughput sequencing. Results Full mitogenomes (7–34×) were successfully reconstructed from dental calculus for all six individuals, including three individuals who had previously tested negative for DNA preservation in bone using conventional PCR techniques. Mitochondrial haplogroup assignments were consistent with previously published findings, and additional comparative analysis of paired dental calculus and dentine from two individuals yielded equivalent haplotype results. All dental calculus samples exhibited damage patterns consistent with ancient DNA, and mitochondrial sequences were estimated to be 92–100% endogenous. DNA polymerase choice was found to impact error rates in downstream sequence analysis, but these effects can be mitigated by greater sequencing depth. Discussion Dental calculus is a viable alternative source of human DNA that can be used to reconstruct full mitogenomes from archaeological remains. Am J Phys Anthropol 160:220–228, 2016. © 2016 The Authors American Journal of Physical Anthropology Published by Wiley Periodicals, Inc. PMID:26989998

Comparative clinical efficacy of three toothpastes in the control of supragingival calculus formation

PubMed Central

Kraivaphan, Petcharat; Amornchat, Cholticha

2017-01-01

Objectives: The purpose of this double-blind, parallel clinical study was to assess clinical efficacy in supragingival calculus formation reduction using Abhaibhubejhr Herbal Toothpaste compared to Colgate Total and Colgate Cavity Protection toothpastes. Materials and Methods: A total of 150 subjects participated in the pretest phase. All subjects were given oral soft/hard tissue evaluation, calculus examination using Volpe-Manhold calculus, and whole mouth oral prophylaxis. They received noncalculus control fluoride toothpaste and a soft-bristled toothbrush to brush for 1 min two times daily for 8 weeks. After which, subjects were given a test phase oral soft/hard tissue evaluation and calculus examination and were randomized into one of the three toothpaste groups. All subjects in the test phase received a whole mouth oral prophylaxis and were given their assigned toothpaste and a soft-bristled toothbrush to brush for 1 min two times a day for 12 weeks. Thereafter, subjects were assessed for their oral soft/hard tissue and calculus formation. Results: Mean Volpe-Manhold calculus index scores for the Cavity Protection, Abhaibhubejhr, and Total toothpaste groups were 0.78, 0.62, and 0.48, respectively, at the 12-week test phase evaluation. Abhaibhubejhr and Total toothpaste groups show 20.51% and 38.46% significantly less calculus formation than the Cavity Protection toothpaste group (P < 0.05). Total toothpaste group also show 22.58% significantly less calculus formation than the Abhaibhubejhr toothpaste group (P < 0.05). Conclusion: The use of Colgate Total toothpaste over a 12-week period was clinically more effective than either Abhaibhubejhr or Colgate Cavity Protection toothpastes in controlling supragingival calculus formation. PMID:28435373

Selective ablation of sub- and supragingival calculus with a frequency-doubled Alexandrite laser

NASA Astrophysics Data System (ADS)

Rechmann, Peter; Hennig, Thomas

1995-05-01

In a preceding trial the absorption characteristics of subgingival calculus were calculated using fluorescence emission spectroscopy (excitation laser: N2-laser, wavelength 337 nm, pulse duration 4 ns). Subgingival calculus seems to contain chromophores absorbing in the ultraviolet spectral region up to 420 nm. The aim of the actual study was the ablation of sub- and supragingival calculus using a frequency doubled Alexandrite-laser (wavelength 377 nm, pulse duration 100 ns, repetition rate 110 Hz). Extracted human teeth presenting sub- and supragingival calculus were irradiated perpendicular to their axis with a laser fluence of 1 Jcm-2. Using a standard application protocol calculus was irradiated at the enamel surface, at the junction between enamel and root, and at the root surface (located on dentin or on cementum). During the irradiation procedure an effective water cooling-system was engaged. For light microscopical investigations undecalcified histological sections were prepared after treatment. The histological sections revealed that a selective and total removal of calculus is possible at all locations without ablation of healthy enamel, dentin or cementum. Even low fluences provide us with a high effectiveness for the ablation of calculus. Thus, based on different absorption characteristics and ablation thresholds, engaging a frequency doubled Alexandrite-laser a fast and, even more, a selective ablation of sub- and supragingival calculus is possible without adverse side effects to the surrounding tissues. Even more, microbial dental plaque can be perfectly removed.

Fluorescence-based calculus detection using a 405-nm excitation wavelength

NASA Astrophysics Data System (ADS)

Brede, O.; Schelle, F.; Krueger, S.; Oehme, B.; Dehn, C.; Frentzen, M.; Braun, A.

2011-03-01

The aim of this study was to assess the difference of fluorescence signals of cement and calculus using a 405 nm excitation wavelength. A total number of 20 freshly extracted teeth was used. The light source used for this study was a blue LED with a wavelength of 405nm. For each tooth the spectra of calculus and cementum were measured separately. Fluorescence light was collimated into an optical fibre and spectrally analyzed using an echelle spectrometer (aryelle 200, Lasertechnik Berlin, Germany) with an additionally bandpass (fgb 67, Edmund Industrial Optics, Karlsruhe, Germany). From these 40 measurements the median values were calculated over the whole spectrum, leading to two different median spectra, one for calculus and one for cementum. For further statistical analysis we defined 8 areas of interest (AOI) in wavelength regions, showing remarkable differences in signal strength. In 7 AOIs the intensity of the calculus spectrum differed statistically significant from the intensity of the cementum spectrum (p < 0.05). A spectral difference could be shown between calculus and cement between 600nm and 700nm. Thus, we can conclude that fluorescence of calculus shows a significant difference to the fluorescence of cement. A differentiation over the intensity is possible as well as over the spectrum. Using a wavelength of 405nm, it is possible to distinguish between calculus and cement. These results could be used for further devices to develop a method for feedback controlled calculus removal.

Taking a Quantum Leap in Cyber Deterrence

DTIC Science & Technology

2010-02-17

calculus that weighs the cost and benefit of an action. 76 According to John Mearsheimer, that decision calculus is ―a function of the costs and...frame an adversary‘s rationale and decision calculus . 82 Understanding a group‘s rationale helps frame a strategy for deterrence. Emanuel Adler...only remaining option. Mearsheimer‘s decision calculus described above indicates that if the cost of an attack is high, or the probability of

Measuring Teacher Immediacy and Communication Competence on Student Achievement in Calculus: A Sequential Explanatory Mixed Method Design

ERIC Educational Resources Information Center

Barclay, Allen C.

2012-01-01

On a national level, data indicate that about 40 percent of students in calculus courses finish with a grade of D or F, drop the course, or withdraw (Reinholz, 2009). This high failure rate has led to research studies investigating the teaching of calculus at the national level (House, 1995). Calculus courses have a history of high failure rates,…

Complete staghorn calculus in polycystic kidney disease: infection is still the cause

PubMed Central

2013-01-01

Background Kidney stones in patients with autosomal dominant polycystic kidney disease are common, regarded as the consequence of the combination of anatomic abnormality and metabolic risk factors. However, complete staghorn calculus is rare in polycystic kidney disease and predicts a gloomy prognosis of kidney. For general population, recent data showed metabolic factors were the dominant causes for staghorn calculus, but for polycystic kidney disease patients, the cause for staghorn calculus remained elusive. Case presentation We report a case of complete staghorm calculus in a polycystic kidney disease patient induced by repeatedly urinary tract infections. This 37-year-old autosomal dominant polycystic kidney disease female with positive family history was admitted in this hospital for repeatedly upper urinary tract infection for 3 years. CT scan revealed the existence of a complete staghorn calculus in her right kidney, while there was no kidney stone 3 years before, and the urinary stone component analysis showed the composition of calculus was magnesium ammonium phosphate. Conclusion UTI is an important complication for polycystic kidney disease and will facilitate the formation of staghorn calculi. As staghorn calculi are associated with kidney fibrosis and high long-term renal deterioration rate, prompt control of urinary tract infection in polycystic kidney disease patient will be beneficial in preventing staghorn calculus formation. PMID:24070202

Complete staghorn calculus in polycystic kidney disease: infection is still the cause.

PubMed

Mao, Zhiguo; Xu, Jing; Ye, Chaoyang; Chen, Dongping; Mei, Changlin

2013-08-01

Kidney stones in patients with autosomal dominant polycystic kidney disease are common, regarded as the consequence of the combination of anatomic abnormality and metabolic risk factors. However, complete staghorn calculus is rare in polycystic kidney disease and predicts a gloomy prognosis of kidney. For general population, recent data showed metabolic factors were the dominant causes for staghorn calculus, but for polycystic kidney disease patients, the cause for staghorn calculus remained elusive. We report a case of complete staghorm calculus in a polycystic kidney disease patient induced by repeatedly urinary tract infections. This 37-year-old autosomal dominant polycystic kidney disease female with positive family history was admitted in this hospital for repeatedly upper urinary tract infection for 3 years. CT scan revealed the existence of a complete staghorn calculus in her right kidney, while there was no kidney stone 3 years before, and the urinary stone component analysis showed the composition of calculus was magnesium ammonium phosphate. UTI is an important complication for polycystic kidney disease and will facilitate the formation of staghorn calculi. As staghorn calculi are associated with kidney fibrosis and high long-term renal deterioration rate, prompt control of urinary tract infection in polycystic kidney disease patient will be beneficial in preventing staghorn calculus formation.

Miniature endoscopic optical coherence tomography for calculus detection.

PubMed

Kao, Meng-Chun; Lin, Chun-Li; Kung, Che-Yen; Huang, Yi-Fung; Kuo, Wen-Chuan

2015-08-20

The effective treatment of periodontitis involves the detection and removal of subgingival dental calculus. However, subgingival calculus is more difficult to detect than supragingival calculus because it is firmly attached to root surfaces within periodontal pockets. To achieve a smooth root surface, clinicians often remove excessive amounts of root structure because of decreased visibility. In addition, enamel pearl, a rare type of ectopic enamel formation on the root surface, can easily be confused with dental calculus in the subgingival environment. In this study, we developed a fiber-probe swept-source optical coherence tomography (SSOCT) technique and combined it with the quantitative measurement of an optical parameter [standard deviation (SD) of the optical coherence tomography (OCT) intensity] to differentiate subgingival calculus from sound enamel, including enamel pearl. Two-dimensional circumferential images were constructed by rotating the miniprobe (0.9 mm diameter) while acquiring image lines, and the adjacent lines in each rotation were stacked to generate a three-dimensional volume. In OCT images, compared to sound enamel and enamel pearls, dental calculus showed significant differences (P<0.001) in SD values. Finally, the receiver operating characteristic curve had a high capacity (area under the curve=0.934) for discriminating between healthy regions (including enamel pearl) and dental calculus.

An evaluation of a pre-scaling gel (SofScale) on the ease of supragingival calculus removal.

PubMed

Smith, S R; Foyle, D M; Daniels, J

1994-09-01

SofScale is a pre-scaling gel, containing disodium EDTA and sodium lauryl sulphate, which is claimed to soften calculus and therefore facilitate its removal. 31 subjects were treated in a double blind randomised placebo controlled split mouth study to evaluate this product. Test or placebo gels were applied to the lingual surfaces of the mandibular teeth for 4 min and the time taken to complete the removal of supragingival calculus recorded. The operator recorded on which side the calculus was considered easier to remove and the patient indicated how comfortable the scaling had been. The mean calculus index was 1.99 for the SofScale group and 1.97 for the placebo. The mean time taken to complete scaling was 5.31 min for both groups. Using the Student t-test, there were no statistically significant differences (p > 0.7) between either the calculus index or time taken to complete the scaling between the groups. The operator did not consider SofScale to facilitate calculus removal and patients did not find calculus removal more comfortable when SofScale had been used. There was no increased sensitivity in the SofScale group following scaling. The results of this study do not support the use of SofScale as an adjunct to scaling.

Use of the feed additive sodium hexametaphosphate to prevent dental calculus in squirrel monkeys (Saimiri spp.).

PubMed

Brady, A G; Williams, L E; Haught, D; Abee, C R

2000-03-01

Dental calculus and associated periodontal disease are serious clinical problems in captive squirrel monkeys. Calculus begins to appear as early as 2 years of age, with subsequent development of periodontal disease, dental abscessation, tooth loss and other sequelae. When used as a feed additive, sodium hexametaphosphate (HMP) retards the growth of calculus on previously cleaned teeth in rhesus monkeys, lemurs, and other species. We wanted to determine whether HMP would reduce dental calculus in squirrel monkeys (Saimiri spp.) whose teeth had not been pre-cleaned. The study animals were divided into two groups. One received a standard diet; the other received an identical diet containing the HMP additive at a concentration effective in other primate and non-primate species that had received dental cleaning prior to treatment with HMP. Teeth were graded for extent of calculus formation at the start of the study and at 3 and 6 months during HMP treatment. We compared the results from the two groups both by total score per animal and according to tooth type (e.g., incisors versus incisors in test and control groups). At the end of 6 months, dental calculus did not differ significantly between the experimental groups. Therefore, we conclude that HMP is ineffective in squirrel monkeys with preexisting dental calculus.

Real-time detection of dental calculus by blue-LED-induced fluorescence spectroscopy.

PubMed

Qin, Y L; Luan, X L; Bi, L J; Lü, Z; Sheng, Y Q; Somesfalean, G; Zhou, C N; Zhang, Z G

2007-05-25

Successful periodontal therapy requires sensitive techniques to discriminate dental calculus from healthy teeth. The aim of the present study was to develop a fluorescence-based procedure to enable real-time detection and quantification of dental calculus. Thirty human teeth--15 teeth with sub- and supragingival calculus and 15 healthy teeth--covered with a layer of physiological saline solution or blood were illuminated by a focused blue LED light source of 405 nm. Autofluorescence spectra recorded along a randomly selected line stretching over the crown-neck-root area of each tooth were utilized to evaluate a so called calculus parameter R, which was selected to define a relationship between the integrated intensities specific for healthy teeth and for calculus in the 477-497 nm (S(A)) and 628-685 nm (S(B)) wavelength regions, respectively. Statistical analysis was performed and a cut-off threshold of R=0.2 was found to distinguish dental calculus from healthy teeth with 100% sensitivity and specificity under various experimental conditions. The results of the spectral evaluation were confirmed by clinical and histological findings. Automated real-time detection and diagnostics for clinical use were implemented by a corresponding software program written in Visual Basic language. The method enables cost-effective and reliable calculus detection, and can be further developed for imaging applications.

Selective ablation of dental calculus with a frequency-doubled Alexandrite laser

NASA Astrophysics Data System (ADS)

Rechmann, Peter; Hennig, Thomas

1996-01-01

The aim of the study was the selective removal of dental calculus by means of pulsed lasers. In a first approach the optical characteristics of subgingival calculus were calculated using fluorescence emission spectroscopy (excitation laser: N2-laser, wavelength 337 nm, pulse duration 4 ns). Subgingival calculus seems to absorb highly in the ultraviolet spectral region up to 420 nm. According to these measurements a frequency doubled Alexandrite-laser (wavelength 377 nm, pulse duration 100 ns, repetition rate 110 Hz) was used to irradiate calculus located on enamel, at the cementum enamel junction and on the root surface (located on dentin or on cementum). Irradiation was performed perpendicular to the root surface with a laser fluence of 1 Jcm-2. During the irradiation procedure an effective water cooling-system was engaged. Histological investigations were done on undecalcified sections. As a result, engaging low fluences allows a fast and strictly selective removal of subgingival calculus. Even more the investigations revealed that supragingival calculus can be removed in a strictly selective manner engaging a frequency doubled Alexandrite-laser. No adverse side effects to the surrounding tissues could be found.

Comparative study on major bioactive components in natural, artificial and in-vitro cultured Calculus Bovis.

PubMed

Yan, Shi-Kai; Wu, Yan-Wen; Liu, Run-Hui; Zhang, Wei-Dong

2007-01-01

Major bioactive components in various Calculus Bovis, including natural, artificial and in-vitro cultured Calculus Bovis, were comparatively studied. An approach of high-performance liquid chromatography coupled with ultraviolet and evaporative light scattering detections (HPLC/UV/ELSD) was established to simultaneously determinate six bioactive components thereof, including five bile acids (cholic acid, deoxycholic acid, ursodeoxycholic, chenodeoxycholic acid, hyodeoxycholic acid) and bilirubin. ELSD and UV detector were applied to detect bile acids and bilirubin respectively. The assay was performed on a C(18) column with water-acetonitrile gradient elution and the investigated constituents were authenticated by comparing retention times and mass spectra with those of reference compounds. The proposed method was applied to analyze twenty-one Calculus Bovis extraction samples, and produced data with acceptable linearity, precision, repeatability and accuracy. The result indicated the variations among Calculus Bovis samples under different developmental conditions. Artificial and in-vitro cultured Calculus Bovis, especially in-vitro cultured ones, which contain total bioactive constituents no less than natural products and have the best batch-to-batch uniformity, suffice to be used as substitutes of natural Calculus Bovis.

Putting Differentials Back into Calculus

ERIC Educational Resources Information Center

Dray, Tevian; Manogue, Corrine A.

2010-01-01

We argue that the use of differentials in introductory calculus courses is useful and provides a unifying theme, leading to a coherent view of the calculus. Along the way, we meet several interpretations of differentials, some better than others.

Study Modules for Calculus-Based General Physics. [Includes Modules 1 and 2: Dimensions and Vector Addition; Rectilinear Motion; plus a Trigonometry and Calculus Review].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1998-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Initialization, conceptualization, and application in the generalized (fractional) calculus.

PubMed

Lorenzo, Carl F; Hartley, Tom T

2007-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Association between chronic kidney disease and urinary calculus by stone location: a population-based study.

PubMed

Keller, Joseph J; Chen, Yi-Kuang; Lin, Herng-Ching

2012-12-01

Study Type--Disease prevalence study (cohort design) Level of Evidence 2a. What's known on the subject? and What does the study add? Several studies have estimated the potential association of urinary calculus (UC) with chronic kidney disease (CKD). However, previous literature focusing on this issue tended to evaluate the impact of kidney stones alone on incident CKD, with no studies having been conducted investigating the association between CKD and stone formation in other portions of the urological system. We found that patients with CKD were consistently more likely than comparison subjects to have been previously diagnosed with kidney calculus (odds ratio [OR] 2.10, 95% confidence interval [CI] 1.95-2.27), ureter calculus (OR 1.68, 95% CI 1.51-1.85), bladder calculus (OR 1.49, 95% CI 1.13-1.98), and unspecified calculus (OR 1.89, 95% CI 1.74-2.06). We concluded that there was an association between CKD and UC regardless of stone location. • To explore the association of chronic kidney disease (CKD) with prior kidney calculus, ureter calculus, and bladder calculus using a population-based dataset in Taiwan. Several studies have estimated the potential association of urinary calculus (UC) with CKD. However, previous literature focusing on this issue tended to evaluate the impact of kidney stones alone on incident CKD, with no studies having been conducted investigating the association between CKD and stone formation in other portions of the urological system. • We identified 21,474 patients who received their first-time diagnosis of CKD between 2001 and 2009. • The 21,474 controls were frequency-matched with cases for sex, age group, and index year. • We used conditional logistic regression analyses to compute the odds ratio (OR) and corresponding 95% confidence interval (CI) as an estimation of association between CKD and having been previously diagnosed with UC. • The results show that compared with controls, the OR of prior UC for cases was 1.91 (95% CI 1.81-2.01, P < 0.001) after adjusting for potential confounders. • Furthermore, cases were consistently more likely than controls to have been previously diagnosed with kidney calculus (OR 2.10, 95% CI 1.95-2.27), ureter calculus (OR 1.68, 95% CI 1.51-1.85), bladder calculus (OR 1.49, 95% CI 1.13-1.98), and unspecified UC (OR 1.89, 95% CI 1.74-2.06). • We concluded that there was an association between ckd and UC regardless of stone location. © 2012 BJU INTERNATIONAL.

Raw beef bones as chewing items to reduce dental calculus in Beagle dogs.

PubMed

Marx, F R; Machado, G S; Pezzali, J G; Marcolla, C S; Kessler, A M; Ahlstrøm, Ø; Trevizan, L

2016-01-01

Evaluate the effect of raw bovine cortical bone (CB) (medullary bone cross-sectioned) and marrow or epiphyseal 'spongy' bone (SB) as chew items to reduce dental calculus in adult dogs. Eight 3-year-old Beagle dogs were observed in two study periods. In the first study, the dogs each received a piece of bovine femur CB (122 ± 17 g) daily and in the second study, a piece of bovine femur SB (235 ± 27 g). The first study lasted 12 days and the second 20 days. Dental calculus was evaluated using image integration software. At the start of the studies, dental calculus covered 42.0% and 38.6% of the dental arcade areas, respectively. In study one, the chewing reduced the established dental calculus area to 27.1% (35.5% reduction) after 3 days and after 12 days the dental calculus covering was reduced to 12.3% (70.6% reduction). In study two, the dental calculus covered 16.8% (56.5% reduction) after 3 days, 7.1% (81.6% reduction) after 12 days and 4.7% (87.8% reduction) after 20 days. The CB remained largely intact after 24 h, but SB was reduced to smaller pieces and in some cases totally consumed after 24 h. No complications such as tooth fractures, pieces of bone stuck between teeth or intestinal obstructions were observed during the studies. Chewing raw bovine bones was an effective method of removing dental calculus in dogs. The SB bones removed dental calculus more efficiently in the short term. © 2016 Australian Veterinary Association.

The Legendre transform in geometric calculus

NASA Astrophysics Data System (ADS)

McClellan, Gene E.

2013-10-01

This paper explores the extension of the Legendre transform from scalar calculus to geometric calculus. In physics, the Legendre transform provides a change of variables to express equations of motion or other physical relationships in terms of the most convenient dynamical quantities for a given experimental or theoretical analysis. In classical mechanics and in field theory, the Legendre transform generates the Hamiltonian function of a system from the Lagrangian function or vice versa. In thermodynamics, the Legendre transform allows thermodynamic relationships to be written in terms of alternative sets of independent variables. In this paper, we review the properties of the Legendre transform in scalar calculus and show how an analogous transformation with similar properties may be constructed in geometric calculus.

Calculus for a New Century: A Pump, Not a Filter. Papers Presented at a Colloquium (Washington, D.C., October 28-29, 1987). MAA Notes Number 8.

ERIC Educational Resources Information Center

Steen, Lynn Arthur, Ed.

This document, intended as a resource for calculus reform, contains 75 separate contributions, comprising a very diverse set of opinions about the shape of calculus for a new century. The authors agree on the forces that are reshaping calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory,…

Correlation of Salivary Statherin and Calcium Levels with Dental Calculus Formation: A Preliminary Study.

PubMed

Pateel, Deepak Gowda Sadashivappa; Gunjal, Shilpa; Math, Swarna Y; Murugeshappa, Devarasa Giriyapura; Nair, Sreejith Muraleedharan

2017-01-01

Salivary constituents have a wide range of functions including oral calcium homeostasis. Salivary proteins such as statherin inhibit crystal growth of calcium phosphate in supersaturated solutions and interact with several oral bacteria to adsorb on hydroxyapatite. Concurrently, saliva, which is supersaturated with respect to calcium phosphates, is the driving force for plaque mineralization and formation of calculus. Thus, the aim of the present study was to estimate and correlate salivary statherin and calcium concentration to the dental calculus formation. A cross-sectional study was conducted to assess the relationship between salivary statherin, calcium, and dental calculus among 70 subjects, aged 20-55 years. Subjects were divided into 3 groups based on the calculus scores as interpreted by Calculus Index which was followed by collection of whole saliva using Super•SAL™. Salivary calcium levels were assessed by calorimetric method using Calcium Assay kit (Cayman Chemical, Michigan, USA) and statherin levels by using ELISA Kit (Cusabio Biotech). Statherin levels showed a weak negative correlation with the calcium levels and with calculus formation. The mean salivary statherin and calcium concentration were found to be 0.96  μ g/ml and 3.87 mg/ml, respectively. Salivary statherin levels differed significantly among the three groups ( p < 0.05). Our preliminary data indicates that statherin could possibly play a role in the formation of dental calculus.

Prevention of lingual calculus formation with daily use of 6% H2O2/2% pyrophosphate whitening strips.

PubMed

Farrell, S; Barker, M L; Gerlach, R W; Putt, M S; Milleman, J L

2009-01-01

This randomized controlled clinical trial was conducted to evaluate whether daily use of a hydrogen peroxide/ pyrophosphate-containing antitartar whitening strip might safely yield clinical reductions in post-prophylaxis calculus accumulation. A three-month, randomized controlled trial was conducted to compare calculus accumulation with a daily 6% hydrogen peroxide/pyrophosphate strip versus regular brushing. After an eight-week run-in phase to identify calculus formers, a prophylaxis was administered, and 77 subjects were randomly assigned to daily strip or brushing only groups. All subjects received an anticavity dentifrice (Crest Cavity Protection) and manual brush for use throughout the three-month study; for subjects assigned to the experimental group, strip application was once daily for five minutes on the facial and lingual surfaces of the mandibular teeth. Efficacy was measured as mm calculus (VMI) before prophylaxis and after six and 12 weeks of treatment, while safety was assessed from examination and interview. Subjects ranged in age from 21-87 years, with groups balanced (p > 0.26) on pertinent demographic and behavioral parameters, and pre-prophylaxis calculus baseline mean scores (16.0 mm). At Week 6, calculus accumulation was lower in the strip group, with adjusted mean (SE) lingual VMI of 12.0 (0.87) for the strip group and 17.0 (0.88) for the brushing control. At Week 12, calculus accumulation was lower in the strip group, with adjusted mean (SE) lingual VMI of 14.3 (0.85) for the strip group and 17.2 (0.86) for the brushing control. Treatments differed significantly (p < 0.02) on calculus accumulation at both time points. A total of three subjects (8%) in the strip group and two subjects (5%) in the brushing control had mild oral irritation or tooth sensitivity during treatment; no one discontinued early due to an adverse event. Daily use of hydrogen peroxide whitening strips with pyrophosphate reduced calculus formation by up to 29% versus regular brushing, without meaningful adverse events.

Calculus removal on a root cement surface by ultrashort laser pulses

NASA Astrophysics Data System (ADS)

Kraft, Johan F.; Vestentoft, Kasper; Christensen, Bjarke H.; Løvschall, Henrik; Balling, Peter

2008-01-01

Ultrashort-pulse-laser ablation of dental calculus (tartar) and cement is performed on root surfaces. The investigation shows that the threshold fluence for ablation of calculus is a factor of two to three times smaller than that of a healthy root cement surface. This indicates that ultrashort laser pulses may provide an appropriate tool for selective removal of calculus with minimal damage to the underlying root cement. Future application of an in situ profiling technique allows convenient on-line monitoring of the ablation process.

Formal Modeling of Multi-Agent Systems using the Pi-Calculus and Epistemic Logic

NASA Technical Reports Server (NTRS)

Rorie, Toinette; Esterline, Albert

1998-01-01

Multi-agent systems have become important recently in computer science, especially in artificial intelligence (AI). We allow a broad sense of agent, but require at least that an agent has some measure of autonomy and interacts with other agents via some kind of agent communication language. We are concerned in this paper with formal modeling of multi-agent systems, with emphasis on communication. We propose for this purpose to use the pi-calculus, an extension of the process algebra CCS. Although the literature on the pi-calculus refers to agents, the term is used there in the sense of a process in general. It is our contention, however, that viewing agents in the AI sense as agents in the pi-calculus sense affords significant formal insight. One formalism that has been applied to agents in the AI sense is epistemic logic, the logic of knowledge. The success of epistemic logic in computer science in general has come in large part from its ability to handle concepts of knowledge that apply to groups. We maintain that the pi-calculus affords a natural yet rigorous means by which groups that are significant to epistemic logic may be identified, encapsulated, structured into hierarchies, and restructured in a principled way. This paper is organized as follows: Section 2 introduces the pi-calculus; Section 3 takes a scenario from the classical paper on agent-oriented programming [Sh93] and translates it into a very simple subset of the n-calculus; Section 4 then shows how more sophisticated features of the pi-calculus may bc brought into play; Section 5 discusses how the pi-calculus may be used to define groups for epistemic logic; and Section 6 is the conclusion.

Composition and distribution of elements and ultrastructural topography of a human cardiac calculus.

PubMed

Cheng, Ching-Li; Chang, Hsiao-Huang; Huang, Pei-Jung; Chu, Yu-Ting; Lin, Shan-Yang

2013-04-01

Trace elements (TEs) may contribute to the formation of calculi or stones or be involved in the aetiopathogenesis of stone diseases. The compositions and spatial distribution of elements from the inner nucleus to outer crust of the cardiac calculus were investigated by energy-dispersive X-ray fluorescence (EDXRF) spectrometer. The surface topograph, distribution map of elements, elemental and chemical compositions were also determined by environmental scanning electron microscope (ESEM)-energy-dispersive X-ray (EDX) analysis. Twenty-five elements were identifiable from 18 positions on the cardiac calculus by EDXRF spectrometer, in which the highest concentrations of toxic TEs (Ni, Pt, Hg, Sn, Pb, W, Au, Al, Si) and higher levels of essential TEs (Ca, Sr, Cr, P) were detected. A moderate positive Pearson's correlation between TEs concentrations of Mg, Ca or P and location differences from centre to periphery in the cardiac calculus was observed. A positive correlation was also found for Ca/Zn and Ca/Cu, indicating the gradual increase of calcium concentration from inner nucleus to outer crust of cardiac calculus. The drop-like nodules/crystals on the surface of petrous part of cardiac calculus were observed from ESEM analysis. ESEM-EDX analysis determined the calculus to be predominantly composed of calcium hydroxyapatite and cholesterol, as indicated by the petrous surface and drop-like nodules/crystals, respectively. This composition was confirmed using a portable Raman analyser. The spatial distribution analysis indicated a gradual increase in Mg, P and Ca concentrations from the inner nucleus to the outer crust of the cardiac calculus. The major chemical compositions of calcium hydroxyapatite and cholesterol were detected on this cardiac calculus.

Study of orthophosphate, pyrophosphate, and pyrophosphatase in saliva with reference to calculus formation and inhibition.

PubMed

Pradeep, A R; Agarwal, Esha; P, Arjun Raju; Rao, M S Narayana; Faizuddin, Mohamed

2011-03-01

A large amount of calculus may hamper the efficacy of daily oral hygiene and thereby accelerate plaque formation. Salivary concentrations of orthophosphate and pyrophosphate are important in preventing calculus formation. Activity of orthophosphate, pyrophosphate, and pyrophosphatase was studied in whole saliva in calculus-forming groups and plaque-forming groups. The material for this study consists of 60 healthy individuals (age range: 15 to 30 years; mean age: 22 years). Depending on calculus index score, individuals were divided into four groups, each of 15 patients: Group 1, calculus index score 0 to 0.6; Group 2, calculus index score 0.7 to 1.8; Group 3, calculus index score 1.9 to 3; and Group 4, plaque group where index varied from 0 to 3. The saliva was collected and biochemically analyzed for concentration of orthophosphate, pyrophosphate, and pyrophosphatase. The mean values of orthophosphate in Groups 1, 2, 3, and 4 were 0.2559, 1.3639, 1.7311, and 0.1868 mM, respectively. The mean values of pyrophosphate in Groups 1, 2, 3, and 4 were 0.3258, 0.1091, 0.0314, and 0.3860 mM, respectively. The mean values of pyrophosphatase in Groups 1, 2, 3, and 4 were 10.7937, 15.4249, 27.2900, and 7.5427 units/ml, respectively. A holistic approach toward the control of periodontal disease should include antiplaque and anticalculus agents. The results are conclusive that the components orthophosphate, pyrophosphate, and pyrophosphatase present in saliva have a very significant role to play in formation and inhibition of calculus. This study reinforces the idea of using pyrophosphate and newer bisphosphonates as potential anticalculus agents.

The Case for Biocalculus: Design, Retention, and Student Performance.

PubMed

Eaton, Carrie Diaz; Highlander, Hannah Callender

2017-01-01

Calculus is one of the primary avenues for initial quantitative training of students in all science, technology, engineering, and mathematics fields, but life science students have been found to underperform in the traditional calculus setting. As a result, and because of perceived lack of its contribution to the understanding of biology, calculus is being actively cut from biology program requirements at many institutions. Here, we present an alternative: a model for learning mathematics that sees the partner disciplines as crucial to student success. We equip faculty with information to engage in dialogue within and between disciplinary departments involved in quantitative education. This includes presenting a process for interdisciplinary development and implementation of biology-oriented Calculus I courses at two institutions with different constituents, goals, and curricular constraints. When life science students enrolled in these redesigned calculus courses are compared with life science students enrolled in traditional calculus courses, students in the redesigned calculus courses learn calculus concepts and skills as well as their traditional course peers; however, the students in the redesigned courses experience more authentic life science applications and are more likely to stay and succeed in the course than their peers who are enrolled in traditional courses. Therefore, these redesigned calculus courses hold promise in helping life science undergraduate students attain Vision and Change recommended competencies. © 2017 C. D. Eaton and H. C. Highlander. CBE—Life Sciences Education © 2017 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

Site specific mineral composition and microstructure of human supra-gingival dental calculus.

PubMed

Hayashizaki, Junko; Ban, Seiji; Nakagaki, Haruo; Okumura, Akihiko; Yoshii, Saori; Robinson, Colin

2008-02-01

Dental calculus has been implicated in the aetiology of several periodontal conditions. Its prevention and removal are therefore desirable clinical goals. While it is known that calculus is very variable in chemical composition, crystallinity and crystallite size little is known about site specific variability within a dentition and between individuals. With this in mind, a study was undertaken to investigate the comparative site specific nature and composition of human dental supra-gingival dental calculus obtained from 66 male patients visiting for their dental check-up using fluorescent X-ray spectroscopy, X-ray diffractometry and Fourier transform infrared spectroscopy. The supra-gingival dental calculus formed on the lingual surfaces of lower anterior teeth and the buccal surfaces of upper molar teeth were classified into four types based on calcium phosphate phases present. There was significant difference in composition of the crystal phase types between lower and upper teeth (p<0.01). There was no significant difference in crystal size between dental calculus on anterior or molar teeth of all samples. The degree of crystallinity of dental calculus formed on the upper molar teeth was higher than that formed on the lower anterior teeth (p<0.01). The CO(3)(2-) contents in dental calculus formed on the lower anterior teeth were higher than on upper molar teeth (p<0.05) which might explain the difference in crystallinity. Magnesium and Si contents and Ca:P ratio on the other hand showed no significant difference between lower and upper teeth. It was concluded that the crystal phases, crystallinity and CO(3)(2-) contents of human dental supra-gingival dental calculus is related to its location in the mouth.

Testicular calculus: A rare case.

PubMed

Sen, Volkan; Bozkurt, Ozan; Demır, Omer; Tuna, Burcin; Yorukoglu, Kutsal; Esen, Adil

2015-01-01

Testicular calculus is an extremely rare case with unknown etiology and pathogenesis. To our knowledge, here we report the third case of testicular calculus. A 31-year-old man was admitted to our clinic with painful solid mass in left testis. After diagnostic work-up for a possible testicular tumour, he underwent inguinal orchiectomy and histopathologic examination showed a testicular calculus. Case hypothesis: Solid testicular lesions in young adults generally correspond to testicular cancer. Differential diagnosis should be done carefully. Future implications: In young adults with painful and solid testicular mass with hyperechogenic appearance on scrotal ultrasonography, testicular calculus must be kept in mind in differential diagnosis. Further reports on this topic may let us do more clear recommendations about the etiology and treatment of this rare disease.

A Logical Process Calculus

NASA Technical Reports Server (NTRS)

Cleaveland, Rance; Luettgen, Gerald; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

This paper presents the Logical Process Calculus (LPC), a formalism that supports heterogeneous system specifications containing both operational and declarative subspecifications. Syntactically, LPC extends Milner's Calculus of Communicating Systems with operators from the alternation-free linear-time mu-calculus (LT(mu)). Semantically, LPC is equipped with a behavioral preorder that generalizes Hennessy's and DeNicola's must-testing preorder as well as LT(mu's) satisfaction relation, while being compositional for all LPC operators. From a technical point of view, the new calculus is distinguished by the inclusion of: (1) both minimal and maximal fixed-point operators and (2) an unimple-mentability predicate on process terms, which tags inconsistent specifications. The utility of LPC is demonstrated by means of an example highlighting the benefits of heterogeneous system specification.

Visual Thinking and Gender Differences in High School Calculus

ERIC Educational Resources Information Center

Haciomeroglu, Erhan Selcuk; Chicken, Eric

2012-01-01

This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…

The Integration of Biology into Calculus Courses

ERIC Educational Resources Information Center

Comar, Timothy D.

2008-01-01

This article discusses the incorporation of biological content into existing calculus courses without significantly changing the courses. This is exemplified by the common laboratory course taken by students in all first semester calculus courses at Benedictine University. Several biologically oriented projects are implemented in this laboratory…

Unisex Math: Narrowing the Gender Gap.

ERIC Educational Resources Information Center

Tapia, Martha; Marsh, George E., II

This study examined gender differences in attitudes toward mathematics of undergraduate students. The Attitudes Toward Mathematics Instrument (ATMI) was administered to students enrolled in introductory mathematics classes (Pre-Calculus, Calculus, and Business Calculus) at two Southeast universities, one a large state university and the other one…

A giant dumbbell shaped vesico-prostatic urethral calculus: a case report and review of literature.

PubMed

Prabhuswamy, Vinod Kumar; Tiwari, Rahul; Krishnamoorthy, Ramakrishnan

2013-01-01

Calculi in the urethra are an uncommon entity. Giant calculi in prostatic urethra are extremely rare. The decision about treatment strategy of calculi depends upon the size, shape, and position of the calculus and the status of the urethra. If the stone is large and immovable, it may be extracted via the perineal or the suprapubic approach. In most of the previous reported cases, giant calculi were extracted via the transvesical approach and external urethrotomy. A 38-year-old male patient presented with complaints of lower urinary tract symptoms. Further investigations showed a giant urethral calculus secondary to stricture of bulbo-membranous part of the urethra. Surgical removal of calculus was done via transvesical approach. Two calculi were found and extracted. One was a huge dumbbell calculus and the other was a smaller round calculus. This case was reported because of the rare size and the dumbbell nature of the stone. Giant urethral calculi are better managed by open surgery.

A Giant Dumbbell Shaped Vesico-Prostatic Urethral Calculus: A Case Report and Review of Literature

PubMed Central

Prabhuswamy, Vinod Kumar; Tiwari, Rahul; Krishnamoorthy, Ramakrishnan

2013-01-01

Calculi in the urethra are an uncommon entity. Giant calculi in prostatic urethra are extremely rare. The decision about treatment strategy of calculi depends upon the size, shape, and position of the calculus and the status of the urethra. If the stone is large and immovable, it may be extracted via the perineal or the suprapubic approach. In most of the previous reported cases, giant calculi were extracted via the transvesical approach and external urethrotomy. A 38-year-old male patient presented with complaints of lower urinary tract symptoms. Further investigations showed a giant urethral calculus secondary to stricture of bulbo-membranous part of the urethra. Surgical removal of calculus was done via transvesical approach. Two calculi were found and extracted. One was a huge dumbbell calculus and the other was a smaller round calculus. This case was reported because of the rare size and the dumbbell nature of the stone. Giant urethral calculi are better managed by open surgery. PMID:23762742

Estimation and quantification of human DNA in dental calculus: A pilot study.

PubMed

Singh, Udita; Goel, Saurabh

2017-01-01

Identification using DNA has proved its accuracy multiple times in the field of forensic investigations. Investigators usually rely on either teeth or bone as the DNA reservoirs. However, there are instances where the skeletal or dental remains are not available or not preserved properly. Moreover, due to religious beliefs, the family members of the dead do not allow the investigating team to damage the remains for the sole purpose of identification. To investigate the presence of human DNA in dental calculus and to quantify the amount, if present. This prospective single-blinded pilot study included twenty subjects selected from the patients visiting a dental college. The samples of dental calculus were collected from the thickest portion of calculus deposited on the lingual surfaces of mandibular incisors. These samples were decontaminated and subjected to gel electrophoresis for DNA extraction. DNA was found in 85% cases. The amount of DNA varied from 21 to 37 μg/ml of dental calculus. Dental calculus is a rich reservoir of human DNA.

Backpropagation and ordered derivatives in the time scales calculus.

PubMed

Seiffertt, John; Wunsch, Donald C

2010-08-01

Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.

Colloquium: Fractional calculus view of complexity: A tutorial

NASA Astrophysics Data System (ADS)

West, Bruce J.

2014-10-01

The fractional calculus has been part of the mathematics and science literature for 310 years. However, it is only in the past decade or so that it has drawn the attention of mainstream science as a way to describe the dynamics of complex phenomena with long-term memory, spatial heterogeneity, along with nonstationary and nonergodic statistics. The most recent application encompasses complex networks, which require new ways of thinking about the world. Part of the new cognition is provided by the fractional calculus description of temporal and topological complexity. Consequently, this Colloquium is not so much a tutorial on the mathematics of the fractional calculus as it is an exploration of how complex phenomena in the physical, social, and life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions such as differentiability are discarded and the ordinary calculus is replaced with the fractional calculus. Exemplars considered include the fractional differential equations describing the dynamics of viscoelastic materials, turbulence, foraging, and phase transitions in complex social networks.

Two- and three-dimensional CT measurements of urinary calculi length and width: a comparative study.

PubMed

Lidén, Mats; Thunberg, Per; Broxvall, Mathias; Geijer, Håkan

2015-04-01

The standard imaging procedure for a patient presenting with renal colic is unenhanced computed tomography (CT). The CT measured size has a close correlation to the estimated prognosis for spontaneous passage of a ureteral calculus. Size estimations of urinary calculi in CT images are still based on two-dimensional (2D) reformats. To develop and validate a calculus oriented three-dimensional (3D) method for measuring the length and width of urinary calculi and to compare the calculus oriented measurements of the length and width with corresponding 2D measurements obtained in axial and coronal reformats. Fifty unenhanced CT examinations demonstrating urinary calculi were included. A 3D symmetric segmentation algorithm was validated against reader size estimations. The calculus oriented size from the segmentation was then compared to the estimated size in axial and coronal 2D reformats. The validation showed 0.1 ± 0.7 mm agreement against reference measure. There was a 0.4 mm median bias for 3D estimated calculus length compared to 2D (P < 0.001), but no significant bias for 3D width compared to 2D. The length of a calculus in axial and coronal reformats becomes underestimated compared to 3D if its orientation is not aligned to the image planes. Future studies aiming to correlate calculus size with patient outcome should use a calculus oriented size estimation. © The Foundation Acta Radiologica 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

Reflections on Our First Calculus Undergraduate Teaching Assistant

ERIC Educational Resources Information Center

Deshler, Jessica M.

2016-01-01

This article describes some reflections from the first Calculus I undergraduate teaching assistant in our department as she explored the various ways in which she was able to support both novice and experienced Calculus teachers and the effect of her experience on her academic and career plans.

Calculus Demonstrations Using MATLAB

ERIC Educational Resources Information Center

Dunn, Peter K.; Harman, Chris

2002-01-01

The note discusses ways in which technology can be used in the calculus learning process. In particular, five MATLAB programs are detailed for use by instructors or students that demonstrate important concepts in introductory calculus: Newton's method, differentiation and integration. Two of the programs are animated. The programs and the…

A Snapshot of the Calculus Classroom

ERIC Educational Resources Information Center

Weathers, Tony D.; Latterell, Carmen M.

2003-01-01

Essentially a focus group to discuss textbook related issues, a meeting of calculus instructors from a wide variety of environments was convened and sponsored by McGraw Hill to provide feedback on the current state of the calculus classroom. This paper provides a description of the group's discussions.

Improving the Instruction of Infinite Series

ERIC Educational Resources Information Center

Lindaman, Brian; Gay, A. Susan

2012-01-01

Calculus instructors struggle to teach infinite series, and students have difficulty understanding series and related concepts. Four instructional strategies, prominently used during the calculus reform movement, were implemented during a 3-week unit on infinite series in one class of second-semester calculus students. A description of each…

Interrater Agreement on Subgingival Calculus Detection Following Scaling.

ERIC Educational Resources Information Center

Pippin, David J.; Feil, Philip

1992-01-01

Two studies investigated interrater agreement among 10 clinical dental examiners who scored residual subgingival calculus after student scaling on 4,160 real and 92 manikin tooth surfaces. Interrater reliability was low. Results suggest a need in periodontics for effective examiner calibration methods and objective subgingival calculus detection…

Imagine Yourself in This Calculus Classroom

ERIC Educational Resources Information Center

Bryan, Luajean

2007-01-01

The efforts to attract students to precalculus, trigonometry, and calculus classes became more successful at the author's school when projects-based classes were offered. Data collection from an untethered hot air balloon flight for calculus students was planned to maximize enrollment. The data were analyzed numerically, graphically, and…

Hands-On Calculus

ERIC Educational Resources Information Center

Sutherland, Melissa

2006-01-01

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and…

Calculus Instructors' and Students' Discourses on the Derivative

ERIC Educational Resources Information Center

Park, Jungeun

2011-01-01

Recently, there has been an increasing interest in collegiate mathematics education, especially teaching and learning calculus (e.g., Oehrtman, Carlson, & Thompson, 2008; Speer, Smith, & Horvath, 2010). Of many calculus concepts, the derivative is known as a difficult concept for students to understand because it involves various concepts…

Advanced Algebra and Calculus. High School Mathematics Curricula. Instructor's Guide.

ERIC Educational Resources Information Center

Natour, Denise M.

This manual is an instructor's guide for the utilization of the "CCA High School Mathematics Curricula: Advanced Algebra and Calculus" courseware developed by the Computer-based Education Research Laboratory (CERL). The curriculum comprises 34 algebra lessons within 12 units and 15 calculus lessons that are computer-based and require…

Differentiated Instruction in a Calculus Curriculum for College Students in Taiwan

ERIC Educational Resources Information Center

Chen, Jing-Hua; Chen, Yi-Chou

2018-01-01

Objectives: To explore differentiated instruction within a calculus curriculum. For college students to learn concentration, motivation and the impact of academic achievement; explore the attitudes and ideas of students on differentiated instruction within a calculus curriculum; build up the diversity of mathematics education within varied…

A Cross-National Study of Calculus

ERIC Educational Resources Information Center

Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen

2015-01-01

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan…

Teaching the Calculus

ERIC Educational Resources Information Center

Sauerheber, Richard D.

2012-01-01

Methods of teaching the Calculus are presented in honour of Sir Isaac Newton, by discussing an extension of his original proofs and discoveries. The methods, requested by Newton to be used that reflect the historical sequence of the discovered Fundamental Theorems, allow first-time students to grasp quickly the basics of the Calculus from its…

The Calculus of a Vase

ERIC Educational Resources Information Center

Scherger, Nicole

2012-01-01

Of the most universal applications in integral calculus are those involved with finding volumes of solids of revolution. These profound problems are typically taught with traditional approaches of the disk and shell methods, after which most calculus curriculums will additionally cover arc length and surfaces of revolution. Even in these visibly…

Calculus and Success in a Business School

ERIC Educational Resources Information Center

Kim, Dong-gook; Garcia, Fernando; Dey, Ishita

2012-01-01

Many business schools or colleges require calculus as a prerequisite for certain classes or for continuing to upper division courses. While there are many studies investigating the relationship between performance in calculus and performance in a single course, such as economics, statistics, and finance, there are very few studies investigating…

An Introductory Calculus-Based Mechanics Investigation

ERIC Educational Resources Information Center

Allen, Bradley

2017-01-01

One challenge for the introductory physics teacher is incorporating calculus techniques into the laboratory setting. It can be difficult to strike a balance between presenting an experimental task for which calculus is essential and making the mathematics accessible to learners who may be apprehensive about applying it. One-dimensional kinematics…

How Students Use Physics to Reason about Calculus Tasks

ERIC Educational Resources Information Center

Marrongelle, Karen A.

2004-01-01

The present research study investigates how undergraduate students in an integrated calculus and physics class use physics to help them solve calculus problems. Using Zandieh's (2000) framework for analyzing student understanding of derivative as a starting point, this study adds detail to her "paradigmatic physical" context and begins to address…

The Basic Principle of Calculus?

ERIC Educational Resources Information Center

Hardy, Michael

2011-01-01

A simple partial version of the Fundamental Theorem of Calculus can be presented on the first day of the first-year calculus course, and then relied upon repeatedly in assigned problems throughout the course. With that experience behind them, students can use the partial version to understand the full-fledged Fundamental Theorem, with further…

Calculus Instructors' Responses to Prior Knowledge Errors

ERIC Educational Resources Information Center

Talley, Jana Renee

2009-01-01

This study investigates the responses to prior knowledge errors that Calculus I instructors make when assessing students. Prior knowledge is operationalized as any skill or understanding that a student needs to successfully navigate through a Calculus I course. A two part qualitative study consisting of student exams and instructor interviews was…

Resequencing Calculus

ERIC Educational Resources Information Center

Dwyer, Dave; Gruenwald, Mark; Stickles, Joe; Axtell, Mike

2018-01-01

Resequencing Calculus is a project that has reordered the typical delivery of Calculus material to better serve the needs of STEM majors. Funded twice by the National Science Foundation, this project has produced a three-semester textbook that has been piloted at numerous institutions, large and small, public and private. This paper describes the…

Transitioning from Introductory Calculus to Formal Limit Conceptions

ERIC Educational Resources Information Center

Nagle, Courtney

2013-01-01

The limit concept is a fundamental mathematical notion both for its practical applications and its importance as a prerequisite for later calculus topics. Past research suggests that limit conceptualizations promoted in introductory calculus are far removed from the formal epsilon-delta definition of limit. In this article, I provide an overview…

Utilizing Microsoft Mathematics in Teaching and Learning Calculus

ERIC Educational Resources Information Center

Oktaviyanthi, Rina; Supriani, Yani

2015-01-01

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students' achievement and the effects of the use of Microsoft…

Experimental Design: Utilizing Microsoft Mathematics in Teaching and Learning Calculus

ERIC Educational Resources Information Center

Oktaviyanthi, Rina; Supriani, Yani

2015-01-01

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students' achievement and the effects of the use of Microsoft…

Aspects of Calculus for Preservice Teachers

ERIC Educational Resources Information Center

Fothergill, Lee

2011-01-01

The purpose of this study was to compare the perspectives of faculty members who had experience teaching undergraduate calculus and preservice teachers who had recently completed student teaching in regards to a first semester undergraduate calculus course. An online survey was created and sent to recent student teachers and college mathematics…

An Excel-Aided Method for Teaching Calculus-Based Business Mathematics

ERIC Educational Resources Information Center

Liang, Jiajuan; Martin, Linda

2008-01-01

Calculus-based business mathematics is a required quantitative course for undergraduate business students in most AACSB accredited schools or colleges of business. Many business students, however, have relatively weak mathematical background or even display math-phobia when presented with calculus problems. Because of the popularity of Excel, its…

Calculus in High School--At What Cost?

ERIC Educational Resources Information Center

Sorge, D. H.; Wheatley, G. H.

1977-01-01

Evidence on the decline in preparation of entering calculus students and the relationship to high school preparation is presented, focusing on the trend toward the de-emphasis of trigonometry and analytic geometry in favor of calculus. Data on students' perception of the adequacy of their preparation are also presented. (Author/MN)

Advanced Placement Mathematics Calculus, Grade 12 Curriculum Guide.

ERIC Educational Resources Information Center

Scharf, John; And Others

This document is a guide to the advanced placement program in calculus for grade 12 in the city schools in Warren, Ohio. The program covers analytic geometry, differential and integral calculus of algebraic functions, elementary transcendental functions, and applications of differentiation and integration. The philosophy and aims of the program…

DIFFERENTIAL AND INTEGRAL CALCULUS. A TENTATIVE CURRICULUM GUIDE.

ERIC Educational Resources Information Center

BRANT, VINCENT; GERARDI, WILLIAM

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…

Student Achievement in College Calculus, Louisiana State University 1967-1968.

ERIC Educational Resources Information Center

Scannicchio, Thomas Henry

An investigation of freshmen achievement in an introductory calculus course was performed on the basis of high school mathematics background to find predictors of college calculus grades. Overall high school academic achievement, overall high school mathematics achievement, number of high school mathematics units, pattern of college preparatory…

Recursive sequences in first-year calculus

NASA Astrophysics Data System (ADS)

Krainer, Thomas

2016-02-01

This article provides ready-to-use supplementary material on recursive sequences for a second-semester calculus class. It equips first-year calculus students with a basic methodical procedure based on which they can conduct a rigorous convergence or divergence analysis of many simple recursive sequences on their own without the need to invoke inductive arguments as is typically required in calculus textbooks. The sequences that are accessible to this kind of analysis are predominantly (eventually) monotonic, but also certain recursive sequences that alternate around their limit point as they converge can be considered.

Class dependency of fuzzy relational database using relational calculus and conditional probability

NASA Astrophysics Data System (ADS)

Deni Akbar, Mohammad; Mizoguchi, Yoshihiro; Adiwijaya

2018-03-01

In this paper, we propose a design of fuzzy relational database to deal with a conditional probability relation using fuzzy relational calculus. In the previous, there are several researches about equivalence class in fuzzy database using similarity or approximate relation. It is an interesting topic to investigate the fuzzy dependency using equivalence classes. Our goal is to introduce a formulation of a fuzzy relational database model using the relational calculus on the category of fuzzy relations. We also introduce general formulas of the relational calculus for the notion of database operations such as ’projection’, ’selection’, ’injection’ and ’natural join’. Using the fuzzy relational calculus and conditional probabilities, we introduce notions of equivalence class, redundant, and dependency in the theory fuzzy relational database.

Extending Maxwell's equations for dielectric materials using analytical principles from viscoelasticity based on the fractional calculus

NASA Astrophysics Data System (ADS)

Wharmby, Andrew William

Existing fractional calculus models having a non-empirical basis used to describe constitutive relationships between stress and strain in viscoelastic materials are modified to employ all orders of fractional derivatives between zero and one. Parallels between viscoelastic and dielectric theory are drawn so that these modified fractional calculus based models for viscoelastic materials may be used to describe relationships between electric flux density and electric field intensity in dielectric materials. The resulting fractional calculus based dielectric relaxation model is tested using existing complex permittivity data in the radio-frequency bandwidth of a wide variety of homogeneous materials. The consequences that the application of this newly developed fractional calculus based dielectric relaxation model has on Maxwell's equations are also examined through the effects of dielectric dissipation and dispersion.

Evidence for calcifying nanoparticles in gingival crevicular fluid and dental calculus in periodontitis.

PubMed

Zhang, Song-Mei; Tian, Fei; Jiang, Xin-Quan; Li, Jing; Xu, Chun; Guo, Xiao-Kui; Zhang, Fu-Qiang

2009-09-01

Calcifying nanoparticles (CNPs), also known as nanobacteria, can produce carbonate apatite on their cell walls and initiate pathologic calcification. The objective of this study was to determine whether CNPs are present in the gingival crevicular fluid (GCF) from subjects with periodontal disease and whether they can induce the pathologic calcification of primary cultured human gingival epithelial cells. GCF and dental calculus samples were collected from 10 subjects with gingivitis and 10 subjects with chronic periodontitis. CNPs in GCF and calculus filtrates were detected with nanocapture enzyme-linked immunosorbent assay kits. The CNPs in cultures of dental calculus filtrates were also identified using immunofluorescence staining, transmission electron microscopy (TEM), and chemical analysis. Pathologic changes in the CNP-treated gingival epithelial cells were observed with TEM, alizarin red staining, and disk-scanning confocal microscopy. CNPs were found in GCF samples from two subjects with chronic periodontitis. Based on chemical analysis, the surface-associated material from CNPs isolated and cultured from calculus has a composition similar to dental calculus. The pathologic calcification of CNP-treated gingival epithelial cells was also observed. Self-replicating calcifying nanoparticles can be cultured and identified from dental calculus. This raises the issue of whether CNPs contribute to the pathogenesis of periodontitis.

Dental hygiene faculty calibration in the evaluation of calculus detection.

PubMed

Garland, Kandis V; Newell, Kathleen J

2009-03-01

The purpose of this pilot study was to explore the impact of faculty calibration training on intra- and interrater reliability regarding calculus detection. After IRB approval, twelve dental hygiene faculty members were recruited from a pool of twenty-two for voluntary participation and randomized into two groups. All subjects provided two pre- and two posttest scorings of calculus deposits on each of three typodonts by recording yes or no indicating if they detected calculus. Accuracy and consistency of calculus detection were evaluated using an answer key. The experimental group received three two-hour training sessions to practice a prescribed exploring sequence and technique for calculus detection. Participants immediately corrected their answers, received feedback from the trainer, and reconciled missed areas. Intra- and interrater reliability (pre- and posttest) was determined using Cohen's Kappa and compared between groups using repeated measures (split-plot) ANOVA. The groups did not differ from pre- to posttraining (intrarater reliability p=0.64; interrater reliability p=0.20). Training had no effect on reliability levels for simulated calculus detection in this study. Recommendations for future studies of faculty calibration when evaluating students include using patients for assessing rater reliability, employing larger samples at multiple sites, and assessing the impact on students' attitudes and learning outcomes.

Alpha-synuclein is present in dental calculus but not altered in Parkinson's disease patients in comparison to controls.

PubMed

Schmid, Sabrina; Goldberg-Bockhorn, Eva; Schwarz, Silke; Rotter, Nicole; Kassubek, Jan; Del Tredici, Kelly; Pinkhardt, Elmar; Otto, Markus; Ludolph, Albert C; Oeckl, Patrick

2018-06-01

In autopsy cases staged for sporadic Parkinson's disease (PD), the neuropathology is characterized by a preclinical phase that targets the enteric nervous system of the gastrointestinal tract (GIT). Therefore, the ENS might be a source of potential (presymptomatic) PD biomarkers. In this clinically based study, we examined the alpha-synuclein (αSyn) concentration in an easily accessible protein storage medium of the GIT, dental calculus, in 21/50 patients with PD and 28/50 age- and gender-matched controls using ELISA. αSyn was detectable in dental calculus and the median concentration in the control patients was 8.6 pg/mg calculus (interquartile range 2.6-13.1 pg/mg). αSyn concentrations were significantly influenced by blood contamination and samples with a hemoglobin concentration of > 4000 ng/mL were excluded. There was no significant difference of αSyn concentrations in the dental calculus of PD patients (5.76 pg/mg, interquartile range 2.91-9.74 pg/mg) compared to those in controls (p = 0.40). The total αSyn concentration in dental calculus is not a suitable biomarker for sporadic PD. Disease-related variants such as oligomeric or phosphorylated αSyn in calculus might prove to be more specific.

The comparative clinical efficacy of pyrophosphate/triclosan, copolymer/triclosan and zinc citrate/triclosan dentifrices for the reduction of supragingival calculus formation.

PubMed

Fairbrother, K J; Kowolik, M J; Curzon, M E; Müller, I; McKeown, S; Hill, C M; Hannigan, C; Bartizek, R D; White, D J

1997-01-01

Three triclosan-containing "multi-benefit" dentifrices were compared for clinical efficacy in reducing supragingival calculus formation following a dental prophylaxis. A total of 544 subjects completed a double-blind parallel-group clinical study using the Volpe-Manhold Index (VMI) to record severity and occurrence of supragingival calculus. The study design included a pre-test period where the calculus formation rate was measured in subjects brushing with a placebo dentifrice. Following a prophylaxis, subjects were stratified for age, gender and VMI scores and assigned to one of four treatments: 1) a dentifrice containing 5.0% soluble pyrophosphate/0.145% fluoride as NaF/silica abrasive/0.28% triclosan (hereafter PPi/TCS-comparable to Crest Complete dentifrice, Procter & Gamble, UK); 2) a commercial dentifrice containing 2.0% Gantrez acid copolymer/ 0.145% fluoride as NaF/silica abrasive/0.30% triclosan (hereafter Gan/TCS-Colgate Total dentifrice, Colgate-Palmolive Company, UK); 3) a commercial dentifrice containing 0.5% zinc citrate trihydrate/0.15% fluoride as sodium monofluorophosphate/silica abrasive/0.20% triclosan (hereafter Zn/TCS-Mentadent P dentifrice, Unilever, UK); and 4) a control dentifrice comprised of 0.145% fluoride as NaF/silica abrasive (hereafter Control). Subjects were instructed to use their assigned dentifrice at least twice per day and to brush as they do normally. Supragingival calculus formation was assesed at two and four months using site-specific and whole-mouth VMI indices for both calculus severity and occurrence. Following four months of use, the PPi/TCS dentifrice provided statistically significant reductions in calculus severity (22-23%) and occurrence (15%) as compared with the Control dentifrice. The Zn/TCS dentifrice also provided significant reductions in calculus severity (17-19%) and occurrence (12-13%) as compared with the Control. The Gan/TCS produced no statistically significant reductions in calculus formation (occurrence or severity) compared with the Control. The PPi/TCS dentifrice provided statistically significant reductions in calculus severity (15-21%) and occurrence (12-16%) as compared with the Gan/TCS dentifrice. These results support the clinical effectiveness of PPi/TCS and Zn/TCS dentifrices for the reduction of supragingival dental calculus formation following a dental prophylaxis.

A randomized controlled clinical study of the effect of daily intake of Ascophyllum nodosum alga on calculus, plaque, and gingivitis.

PubMed

van Dijken, Jan W V; Koistinen, S; Ramberg, Per

2015-07-01

The aim of this study is to evaluate, in a randomized controlled cross-over study, the effect of daily intake of the alga Ascophyllum nodosum on supragingival calculus, plaque formation, and gingival health over a 6-month period. Sixty-one adults with moderate to heavy calculus formation since their last yearly recall visit participated. In a randomized order over two 6-month periods, they swallowed two capsules daily, comprising a total of 500 mg dried marine alga powder (Ascophyllum nodosum, ProDen PlaqueOff®) or two negative control tablets. During the study, the participants maintained their regular oral habits. Their teeth were professionally cleaned at the start of each period and after the 6-month registrations. A wash out period of 1 month separated the two 6-month periods. Supragingival calculus (Volpe Manhold), gingivitis (Löe and Silness), gingival bleeding (Ainamo and Bay), and plaque (Quigley-Hein) were registered at screening and at the end of the two periods. Differences in oral health between the test and control periods were analyzed using a paired t test and Wilcoxon signed rank test. Fifty-five participants completed the study. After the alga intake, the mean calculus reduction was 52% compared to the control (p < 0.0001). Fifty-two participants showed less calculus formation in the alga group than in the control group. Plaque (p = 0.008) and gingival bleeding (p = 0.02) were also significantly less in the alga group. However, no significant difference was found between the groups for gingivitis (p = 0.13). The alga intake significantly reduced the formation of supragingival calculus and plaque and occurrence of gingival bleeding. The alga has a systemic effect on oral health. Daily intake of the alga Ascophyllum nodosum as an adjunct to customary oral hygiene showed a major reduction of supragingival calculus formation and reduced plaque formation. In addition, the calculus in the alga group was characterized by a more porous and less solid structure and was easier to remove than the calculus in the control group.

Abdominal fat distribution on computed tomography predicts ureteric calculus fragmentation by shock wave lithotripsy.

PubMed

Juan, Hsu-Cheng; Lin, Hung-Yu; Chou, Yii-Her; Yang, Yi-Hsin; Shih, Paul Ming-Chen; Chuang, Shu-Mien; Shen, Jung-Tsung; Juan, Yung-Shun

2012-08-01

To assess the effects of abdominal fat on shock wave lithotripsy (SWL). We used pre-SWL unenhanced computed tomography (CT) to evaluate the impact of abdominal fat distribution and calculus characteristics on the outcome of SWL. One hundred and eighty-five patients with a solitary ureteric calculus treated with SWL were retrospectively reviewed. Each patient underwent unenhanced CT within 1 month before SWL treatment. Treatment outcomes were evaluated 1 month later. Unenhanced CT parameters, including calculus surface area, Hounsfield unit (HU) density, abdominal fat area and skin to calculus distance (SSD) were analysed. One hundred and twenty-eight of the 185 patients were found to be calculus-free following treatment. HU density, total fat area, visceral fat area and SSD were identified as significant variables on multivariate logistic regression analysis. The receiver-operating characteristic analyses showed that total fat area, para/perirenal fat area and visceral fat area were sensitive predictors of SWL outcomes. This study revealed that higher quantities of abdominal fat, especially visceral fat, are associated with a lower calculus-free rate following SWL treatment. Unenhanced CT is a convenient technique for diagnosing the presence of a calculus, assessing the intra-abdominal fat distribution and thereby helping to predict the outcome of SWL. • Unenhanced CT is now widely used to assess ureteric calculi. • The same CT protocol can provide measurements of abdominal fat distribution. • Ureteric calculi are usually treated by shock wave lithotripsy (SWL). • Greater intra-abdominal fat stores are generally associated with poorer SWL results.

Attendance and Attainment in a Calculus Course

ERIC Educational Resources Information Center

Meulenbroek, Bernard; van den Bogaard, Maartje

2013-01-01

In this paper the relationship between attendance and attainment in a standard calculus course is investigated. Calculus could in principle be studied without attending lectures due to the wealth of material available (in hardcopy and online). However, in this study we will show that the pass rate of students attending classes regularly (>75%…

A Study of Students' Readiness to Learn Calculus

ERIC Educational Resources Information Center

Carlson, Marilyn P.; Madison, Bernard; West, Richard D.

2015-01-01

The Calculus Concept Readiness (CCR) instrument assesses foundational understandings and reasoning abilities that have been documented to be essential for learning calculus. The CCR Taxonomy describes the understandings and reasoning abilities assessed by CCR. The CCR is a 25-item multiple-choice instrument that can be used as a placement test for…

Evaluating the Use of Learning Objects for Improving Calculus Readiness

ERIC Educational Resources Information Center

Kay, Robin; Kletskin, Ilona

2010-01-01

Pre-calculus concepts such as working with functions and solving equations are essential for students to explore limits, rates of change, and integrals. Yet many students have a weak understanding of these key concepts which impedes performance in their first year university Calculus course. A series of online learning objects was developed to…

Initialized Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

The AP Calculus Exam Reading Experience: Implications for Teacher Classroom Practice and Student Comprehension

ERIC Educational Resources Information Center

Corcoran, Mimi

2017-01-01

This dissertation explores the views and experiences of high school calculus teachers and college mathematics professors on the professional development which occurs at the annual national AP Calculus exam grading. This professional development experience comes in several forms: the exam briefing sessions, the actual reading of the exams, the…

Undergraduate Course and Curriculum Development Program and Calculus and the Bridge to Calculus Program: 1993 Awards.

ERIC Educational Resources Information Center

National Science Foundation, Arlington, VA. Div. of Undergraduate Education.

The Undergraduate Course and Curriculum Development Program of the National Science Foundation supports the development of courses in all disciplines to improve the quality of undergraduate courses and curricula in science, mathematics, engineering, and technology. The purpose of the program in Curriculum Development in Mathematics: Calculus and…

Calculus in the Middle School?

ERIC Educational Resources Information Center

Barger, Rita H.; McCoy, Ann C.

2010-01-01

This article presents an example of how middle school teachers can lay a foundation for calculus. Although many middle school activities connect directly to calculus concepts, the authors have decided to look in depth at only one: the concept of change. They will show how teachers can lead their students to see and appreciate the calculus…

An Exploration of Definition and Procedural Fluency in Integral Calculus

ERIC Educational Resources Information Center

Grundmeier, Todd A.; Hansen, Jennifer; Sousa, Emily

2006-01-01

A survey was administered to calculus students who had previously been exposed to a course on integral calculus. The purpose of the survey was to explore students' understanding of the definition of a definite integral, their abilities to evaluate definite integrals, and their graphical interpretations of definite integrals. The analysis of…

The Use of Technology and Visualization in Calculus Instruction

ERIC Educational Resources Information Center

Samuels, Jason

2010-01-01

This study was inspired by a history of student difficulties in calculus, and innovation in response to those difficulties. The goals of the study were fourfold. First, to design a mathlet for students to explore local linearity. Second, to redesign the curriculum of first semester calculus around the use of technology, an emphasis on…

Problem Posing at All Levels in the Calculus Classroom

ERIC Educational Resources Information Center

Perrin, John Robert

2007-01-01

This article explores the use of problem posing in the calculus classroom using investigative projects. Specially, four examples of student work are examined, each one differing in originality of problem posed. By allowing students to explore actual questions that they have about calculus, coming from their own work or class discussion, or…

Coordinating Multiple Representations in a Reform Calculus Textbook

ERIC Educational Resources Information Center

Chang, Briana L.; Cromley, Jennifer G.; Tran, Nhi

2015-01-01

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

Calculus Challenges: An Active Learning Approach

ERIC Educational Resources Information Center

Crawford, Pam; Moseley, Daniel; Nancarrow, Mike; Ward, Erika

2018-01-01

One of the greatest challenges facing students new to calculus is the ability to persevere in the face of failure. Whether the student is choosing an integration technique or a series test, calculus is often the first course in mathematics where the path to the solution is not prescribed in an algorithmic way. At Jacksonville University we…

Descartes' Calculus of Subnormals: What Might Have Been

ERIC Educational Resources Information Center

Boudreaux, Gregory Mark; Walls, Jess E.

2013-01-01

Rene Descartes' method for finding tangents (equivalently, subnormals) depends on geometric and algebraic properties of a family of circles intersecting a given curve. It can be generalized to establish a calculus of subnormals, an alternative to the calculus of Newton and Leibniz. Here we prove subnormal counterparts of the well-known…

On Flipping the Classroom in Large First Year Calculus Courses

ERIC Educational Resources Information Center

Jungic, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy

2015-01-01

Over the course of two years, 2012-2014, we have implemented a "flipping" the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of…

A Methodology in the Teaching Process of Calculus and Its Motivation.

ERIC Educational Resources Information Center

Vasquez-Martinez, Claudio-Rafael

The development of calculus and science by being permanent, didactic, demands on one part an analytical, deductive study and on another an application of methods, rhochrematics, resources, within calculus, which allows to dialectically conform knowledge in its different phases and to test the results. For the purpose of this study, the motivation…

Inversion exercises inspired by mechanics

NASA Astrophysics Data System (ADS)

Groetsch, C. W.

2016-02-01

An elementary calculus transform, inspired by the centroid and gyration radius, is introduced as a prelude to the study of more advanced transforms. Analysis of the transform, including its inversion, makes use of several key concepts from basic calculus and exercises in the application and inversion of the transform provide practice in the use of technology in calculus.

The Association of Precollege Use of Calculators with Student Performance in College Calculus

ERIC Educational Resources Information Center

Mao, Yi; White, Tyreke; Sadler, Philip M.; Sonnert, Gerhard

2017-01-01

This study investigates how the use of calculators during high school mathematics courses is associated with student performance in introductory college calculus courses in the USA. Data were drawn from a nationally representative sample of 7087 students enrolled in college calculus at 134 colleges and universities. They included information about…

The Development of Prerequisite Notions for an Introductory Conception of a Functional Limit

ERIC Educational Resources Information Center

Nagle, Courtney Rose

2012-01-01

The limit concept plays a foundational role in calculus, appearing in the definitions of the two main ideas of introductory calculus, derivatives and integrals. Previous research has focused on three stages of students' development of limit ideas: the premathematical stage, the introductory calculus stage, and the transition from introductory…

Discrete fractional solutions of a Legendre equation

NASA Astrophysics Data System (ADS)

Yılmazer, Resat

2018-01-01

One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.

Calculus: An Active Approach with Projects.

ERIC Educational Resources Information Center

Hilbert, Steve; And Others

Ithaca College, in New York, has developed and tested a projects-based first-year calculus course over the last 3 years which uses the graphs of functions and physical phenomena to illustrate and motivate the major concepts of calculus and to introduce students to mathematical modeling. The course curriculum is designed to: (1) emphasize on the…

Student Created Calculus Movies Using Computers and the TI-92.

ERIC Educational Resources Information Center

Sher, Lawrence; Wilkinson, Patricia

The Mathematics Department at Borough of Manhattan Community College (BMCC) (New York) has been actively involved since 1988 in a serious and successful program to improve instruction, understanding, and retention for women and minority students in calculus courses. One result of this work has been students creating calculus animations using…

Analyzing Conceptual Gains in Introductory Calculus with Interactively-Engaged Teaching Styles

ERIC Educational Resources Information Center

Thomas, Matthew

2013-01-01

This dissertation examines the relationship between an instructional style called Interactive-Engagement (IE) and gains on a measure of conceptual knowledge called the Calculus Concept Inventory (CCI). The data comes from two semesters of introductory calculus courses (Fall 2010 and Spring 2011), consisting of a total of 482 students from the…

Educating about Sustainability while Enhancing Calculus

ERIC Educational Resources Information Center

Pfaff, Thomas J.

2011-01-01

We give an overview of why it is important to include sustainability in mathematics classes and provide specific examples of how to do this for a calculus class. We illustrate that when students use "Excel" to fit curves to real data, fundamentally important questions about sustainability become calculus questions about those curves. (Contains 5…

Commentary on A General Curriculum in Mathematics for Colleges.

ERIC Educational Resources Information Center

Committee on the Undergraduate Program in Mathematics, Berkeley, CA.

This document constitutes a complete revision of the report of the same name first published in 1965. A new list of basic courses is described, consisting of Calculus I, Calculus II, Elementary Linear Algebra, Multivariable Calculus I, Linear Algebra, and Introductory Modern Algebra. Commentaries outline the content and spirit of these courses in…

Online Homework in Calculus I: Friend or Foe?

ERIC Educational Resources Information Center

Halcrow, Cheryl; Dunnigan, Gerri

2012-01-01

This article describes a quantitative and qualitative assessment from a study done on the possible effectiveness of including an online homework component in first-semester calculus. Two instructors, each teaching two sections of Calculus I, agreed to treat one of their sections as an experimental group and the other as a control group. Students…

Modelling the Landing of a Plane in a Calculus Lab

ERIC Educational Resources Information Center

Morante, Antonio; Vallejo, Jose A.

2012-01-01

We exhibit a simple model of a plane landing that involves only basic concepts of differential calculus, so it is suitable for a first-year calculus lab. We use the computer algebra system Maxima and the interactive geometry software GeoGebra to do the computations and graphics. (Contains 5 figures and 1 note.)

Coordinating Multiple Representations in a Reform Calculus Textbook

ERIC Educational Resources Information Center

Chang, Briana L.; Cromley, Jennifer G.; Tran, Nhi

2016-01-01

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

Plaque, gingival bleeding and calculus formation after supragingival scaling with and without polishing: a randomised clinical trial.

PubMed

Zanatta, Fabricio Batistin; Pinto, Tatiana Militz; Kantorski, Karla Zanini; Rösing, Cassiano Kuchenbecker

2011-01-01

The aim of this study was to compare the effect of polishing after scaling and root planing on supragingival plaque, calculus formation, and gingival bleeding. The study was designed as a split-mouth randomised clinical trial. Seventy-six patients were submitted to supragingival scaling on the six mandibular anterior teeth with manual curettes until a smooth surface was achieved. Subsequently, quadrants were randomly selected to be polished (test) or not (control) with a rubber cup and pumice. One, two and three weeks following treatment, a blinded examiner evaluated the visible plaque index, gingival bleeding index and the presence of supragingival calculus on the lingual tooth surfaces. The results showed that unpolished surfaces exhibited higher mean percentages of visible plaque in the third week. No statistically significant differences were observed between unpolished and polished sites related to gingival bleeding. Calculus formation was higher on unpolished sites than on polished sites at 2 and 3 weeks. Dental polishing after supragingival scaling contributed to reducing plaque and calculus formation. Polishing exerts an inhibitory effect on plaque and calculus formation.

Light and scanning electron microscope investigations comparing calculus removal using an Er:YAG laser and a frequency-doubled alexandrite laser

NASA Astrophysics Data System (ADS)

Rechmann, Peter; Hennig, Thomas; Sadegh, Hamid M. M.; Goldin, Dan S.

1997-05-01

With respect to lasers emitting within the mid-IR spectral domain fiber applicators are being developed. Intended is the use of these lasers in periodontal therapy and their application inside the gingival pocket. Aim of the study presented here is to compare the effect of an Er:YAG laser on dental calculus with the results following irradiation with a frequency doubled Alexandrite laser. The surface of freshly extracted wisdom teeth and of extracted teeth suffering from severe periodontitis were irradiated with both laser wavelengths using a standardized application protocol. Calculus on the enamel surface, at the enamel cementum junction and on the root surface was irradiated. For light microscope investigations undecalcified histological sections were prepared after treatment. For the scanning electron microscope teeth were dried in alcohol and sputtered with gold. Investigations revealed that with both laser systems calculus can be removed. Using the frequency doubled Alexandrite laser selective removal of calculus is possible while engaging the Er:YAG laser even at lowest energies necessary for calculus removal healthy cementum is ablated without control.

On flipping first-semester calculus: a case study

NASA Astrophysics Data System (ADS)

Petrillo, Joseph

2016-05-01

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are 'flipping' (or inverting) their classrooms. By flipping, we mean administering course content outside of the classroom and replacing the traditional in-class lectures with discussion, practice, group work, and other elements of active learning. This paper presents the major results from a three-year study of a flipped, first-semester calculus course at a small, comprehensive, American university with a well-known engineering programme. The data we have collected help quantify the positive and substantial effects of our flipped calculus course on failure rates, scores on the common final exam, student opinion of calculus, teacher impact on measurable outcomes, and success in second-semester calculus. While flipping may not be suitable for every teacher, every student, and in every situation, this report provides some evidence that it may be a viable option for those seeking an alternative to the traditional lecture model.

Dental calculus: the calcified biofilm and its role in disease development.

PubMed

Akcalı, Aliye; Lang, Niklaus P

2018-02-01

Dental calculus represents the first fossilized record of bacterial communities as a testimony of evolutionary biology. The development of dental calculus is a dynamic process that starts with a nonmineralized biofilm which eventually calcifies. Nonmineralized dental biofilm entraps particles from the oral cavity, including large amounts of oral bacteria, human proteins, viruses and food remnants, and preserves their DNA. The process of mineralization involves metabolic activities of the bacterial colonies and strengthens the attachment of nonmineralized biofilms to the tooth surface. From a clinical point of view, dental calculus always harbors a living, nonmineralized biofilm, jeopardizing the integrity of the dento-gingival or implanto-mucosal unit. This narrative review presents a brief historical overview of dental calculus formation and its clinical relevance in modern periodontal practice. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Characterization of calculus migration during Ho:YAG laser lithotripsy by high speed camera using suspended pendulum method

NASA Astrophysics Data System (ADS)

Zhang, Jian James; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Chia, Ray W. J.; Hasenberg, Tom

2014-03-01

Calculus migration is a common problem during ureteroscopic laser lithotripsy procedure to treat urolithiasis. A conventional experimental method to characterize calculus migration utilized a hosting container (e.g. a "V" grove or a test tube). These methods, however, demonstrated large variation and poor detectability, possibly attributing to friction between the calculus and the container on which the calculus was situated. In this study, calculus migration was investigated using a pendulum model suspended under water to eliminate the aforementioned friction. A high speed camera was used to study the movement of the calculus which covered zero order (displacement), 1st order (speed) and 2nd order (acceleration). A commercialized, pulsed Ho:YAG laser at 2.1 um, 365-um core fiber, and calculus phantom (Plaster of Paris, 10×10×10mm cube) were utilized to mimic laser lithotripsy procedure. The phantom was hung on a stainless steel bar and irradiated by the laser at 0.5, 1.0 and 1.5J energy per pulse at 10Hz for 1 second (i.e., 5, 10, and 15W). Movement of the phantom was recorded by a high-speed camera with a frame rate of 10,000 FPS. Maximum displacement was 1.25+/-0.10, 3.01+/-0.52, and 4.37+/-0.58 mm for 0.5, 1, and 1.5J energy per pulse, respectively. Using the same laser power, the conventional method showed <0.5 mm total displacement. When reducing the phantom size to 5×5×5mm (1/8 in volume), the displacement was very inconsistent. The results suggested that using the pendulum model to eliminate the friction improved sensitivity and repeatability of the experiment. Detailed investigation on calculus movement and other causes of experimental variation will be conducted as a future study.

Investigation into the optimum beam shape and fluence for selective ablation of dental calculus at lambda = 400 nm.

PubMed

Schoenly, Joshua E; Seka, Wolf; Rechmann, Peter

2010-01-01

A frequency-doubled Ti:sapphire laser is shown to selectively ablate dental calculus. The optimal transverse shape of the laser beam, including its variability under water-cooling, is determined for selective ablation of dental calculus. Intensity profiles under various water-cooling conditions were optically observed. The 400-nm laser was coupled into a multimode optical fiber using an f = 2.5-cm lens and light-shaping diffuser. Water-cooling was supplied coaxially around the fiber. Five human tooth samples (four with calculus and one pristine) were irradiated perpendicular to the tooth surface while the tooth was moved back and forth at 0.3 mm/second, varying between 20 and 180 iterations. The teeth were imaged before and after irradiation using light microscopy with a flashing blue light-emitting diode (LED). An environmental scanning electron microscope imaged each tooth after irradiation. High-order super-Gaussian intensity profiles are observed at the output of a fiber coiled around a 4-in. diameter drum. Super-Gaussian beams have a more-homogenous fluence distribution than Gaussian beams and have a higher energy efficiency for selective ablation. Coaxial water-cooling does not noticeably distort the intensity distribution within 1 mm from the optical fiber. In contrast, lasers focused to a Gaussian cross section (< or =50-microm diameter) without fiber propagation and cooled by a water spray are heavily distorted and may lead to variable ablation. Calculus is preferentially ablated at high fluences (> or =2 J/cm(2)); below this fluence, stalling occurs because of photo-bleaching of the calculus. Healthy dental hard tissue is not removed at fluences < or =3 J/cm(2). Supplying laser light to a tooth using an optical fiber with coaxial water-cooling is determined to be the most appropriate method when selectively removing calculus with a frequency-doubled Ti:sapphire laser. Fluences over 2 J/cm(2) are required to remove calculus efficiently since photo-bleaching stalls calculus removal below that value.

Investigation Into the Optimum Beam Shape and Fluence for Selective Ablation of Dental Calculus at lambda = 400 nm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schoenly, J.E.; Seka. W.; Rechmann, P.

A frequency-doubled Ti:sapphire laser is shown to selectively ablate dental calculus. The optimal transverse shape of the laser beam, including its variability under water-cooling, is determined for selective ablation of dental calculus. Intensity profiles under various water-cooling conditions were optically observed. The 400-nm laser was coupled into a multimode optical fiber using an f = 2.5-cm lens and light-shaping diffuser. Water-cooling was supplied coaxially around the fiber. Five human tooth samples (four with calculus and one pristine) were irradiated perpendicular to the tooth surface while the tooth was moved back and forth at 0.3 mm/second, varying between 20 and 180more » iterations. The teeth were imaged before and after irradiation using light microscopy with a flashing blue light-emitting diode (LED). An environmental scanning electron microscope imaged each tooth after irradiation. High-order super-Gaussian intensity profiles are observed at the output of a fiber coiled around a 4-in. diameter drum. Super-Gaussian beams have a morehomogenous fluence distribution than Gaussian beams and have a higher energy efficiency for selective ablation. Coaxial water-cooling does not noticeably distort the intensity distribution within 1 mm from the optical fiber. In contrast, lasers focused to a Gaussian cross section (<=50-mm diameter) without fiber propagation and cooled by a water spray are heavily distorted and may lead to variable ablation. Calculus is preferentially ablated at high fluences (>= 2 J/cm^2); below this fluence, stalling occurs because of photo-bleaching of the calculus. Healthy dental hard tissue is not removed at fluences <=3 J/cm^2. Supplying laser light to a tooth using an optical fiber with coaxial water-cooling is determined to be the most appropriate method when selectively removing calculus with a frequency-doubled Ti:sapphire laser. Fluences over 2 J/cm^2 are required to remove calculus efficiently since photo-bleaching stalls calculus removal below that value.« less

Dual-Energy Computed Tomography Gemstone Spectral Imaging: A Novel Technique to Determine Human Cardiac Calculus Composition.

PubMed

Cheng, Ching-Li; Chang, Hsiao-Huang; Ko, Shih-Chi; Huang, Pei-Jung; Lin, Shan-Yang

2016-01-01

Understanding the chemical composition of any calculus in different human organs is essential for choosing the best treatment strategy for patients. The purpose of this study was to assess the capability of determining the chemical composition of a human cardiac calculus using gemstone spectral imaging (GSI) mode on a single-source dual-energy computed tomography (DECT) in vitro. The cardiac calculus was directly scanned on the Discovery CT750 HD FREEdom Edition using GSI mode, in vitro. A portable fiber-optic Raman spectroscopy was also applied to verify the quantitative accuracy of the DECT measurements. The results of spectral DECT measurements indicate that effective Z values in 3 designated positions located in this calculus were 15.02 to 15.47, which are close to values of 15.74 to 15.86, corresponding to the effective Z values of calcium apatite and hydroxyapatite. The Raman spectral data were also reflected by the predominant Raman peak at 960 cm for hydroxyapatite and the minor peak at 875 cm for calcium apatite. A potential single-source DECT with GSI mode was first used to examine the morphological characteristics and chemical compositions of a giant human cardiac calculus, in vitro. The CT results were consistent with the Raman spectral data, suggesting that spectral CT imaging techniques could be accurately used to diagnose and characterize the compositional materials in the cardiac calculus.

Giant ureteric and staghorn calculi in a young adult Nigerian male: a case report.

PubMed

Gali, B M; Ali, A; Ibrahim, A G; Bakari, A; Minoza, K

2010-01-01

Ureteric calculi are usually small and solitary.The term giant has been applied to ureteric calculi that aremore than five cms in length and/or 50g or more in weight. These are uncommon and may present with few or no urological symptoms and might be ignored or be missed. To present a rare case of a giant left ureteric calculus associated with an ipsilateral staghorn calculus. A 31-year-old Nigerian male presented with recurrent left abdominal pain, dysuria, urinary frequency, and fever which had been on for 10 years. Patient was clinically evaluated. He had plain abdominal X-rays, abdominal ultrasonography and intravenous urography. He had to undergo nephrouterorectomy. Patient took analgesics and antibiotics purchased from patent chemist shops for relief of symptoms by himself. He was fit except for a hard cylindrical mass felt arising from the pelvis. Abdomino-pelvic ultrasound scan, plain abdominal X-ray and Intravenous urogram showed a giant ureteric calculus with an ipsilateral staghorn calculus in a nonfunctioning hydronephrotic left kidney. There was no evidence of underlying anatomic or metabolic abnormalities. He had left nephroureterectomy. The ureteric calculus measured 10.5 x 3.0cm and weighed 20.1gm. Giant ureteric calculi are rare. The association giant ureteric calculus with an ipsilateral staghorn renal calculus without underlying anatomic abnormalities appear not have been reported earlier.

Improving Student Success in Calculus I Using a Co-Requisite Calculus I Lab

ERIC Educational Resources Information Center

Vestal, Sharon Schaffer; Brandenburger, Thomas; Furth, Alfred

2015-01-01

This paper describes how one university mathematics department was able to improve student success in Calculus I by requiring a co-requisite lab for certain groups of students. The groups of students required to take the co-requisite lab were identified by analyzing student data, including Math ACT scores, ACT Compass Trigonometry scores, and…

Areas and Volumes in Pre-Calculus

ERIC Educational Resources Information Center

Jarrett, Joscelyn A.

2008-01-01

This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

Effects of Clicker Use on Calculus Students' Mathematics Anxiety

ERIC Educational Resources Information Center

Batchelor, John

2015-01-01

This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught…

The Role of Cognitive Ability and Preferred Mode of Processing in Students' Calculus Performance

ERIC Educational Resources Information Center

Haciomeroglu, Erhan Selcuk

2015-01-01

The present study sought to design calculus tasks to determine students' preference for visual or analytic processing as well as examine the role of preferred mode of processing in calculus performance and its relationship to spatial ability and verbal-logical reasoning ability. Data were collected from 150 high school students who were enrolled…

Using Dynamic Tools to Develop an Understanding of the Fundamental Ideas of Calculus

ERIC Educational Resources Information Center

Verzosa, Debbie; Guzon, Angela Fatima; De Las Peñas, Ma. Louise Antonette N.

2014-01-01

Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the…

Instructional Experiences That Align with Conceptual Understanding in the Transition from High School Mathematics to College Calculus

ERIC Educational Resources Information Center

Wade, Carol H.; Sonnert, Gerhard; Sadler, Philip M.; Hazari, Zahra

2017-01-01

Using data from the first National study on high school preparation for college calculus success, the Factors Influencing College Success in Mathematics (FICSMath) project, this article connects student high school instructional experiences to college calculus performance. The findings reported here reveal that students were better prepared for…

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendices; Index.

Promoting Students' Ability to Think Conceptually in Calculus

ERIC Educational Resources Information Center

Zerr, Ryan J.

2010-01-01

An overview is given of three conceptual lessons that can be incorporated into any first-semester calculus class. These lessons were developed to help promote calculus students' ability to think conceptually, in particular with regard to the role that infinity plays in the subject. A theoretical basis for the value of these lessons is provided,…

Preparatory Year Program Courses as Predictors of First Calculus Course Grade

ERIC Educational Resources Information Center

Yushau, B; Omar, M. H

2007-01-01

This study investigates the effect of the preparatory year program courses on the first calculus course (Calculus I) at King Fahd University of Petroleum and Minerals (KFUPM). The data consists of more than 2,000 bilingual Arab university students studying in the English language, tracked over seven semesters. These students represent over 70% of…

Relativistic Kinetics from the Bondi "K"-Calculus

ERIC Educational Resources Information Center

Dasgupta, Ananda

2007-01-01

The Bondi K-calculus is a delightful method that has been used to provide rich insights into relativistic kinematics. In this paper, we will try to show how several important results of relativistic kinetics can be derived simply by using this approach. In addition, we will also indicate how the K-calculus can be used to simplify certain…

Studies in Mathematics, Volume XV. Calculus and Science.

ERIC Educational Resources Information Center

Twersky, Victor

This book is designed to illustrate how one general method of calculus is used in many different sciences and how different methods of calculus have furthered the development of essentially one field of science. The material is written so that it could serve as a math-science supplement for many courses. Chapters included are: (1) Introduction;…

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendix.

Fluorescence spectroscopy of dental calculus

NASA Astrophysics Data System (ADS)

Bakhmutov, D.; Gonchukov, S.; Sukhinina, A.

2010-05-01

The aim of the present study was to investigate the fluorescence properties of dental calculus in comparison with the properties of adjacent unaffected tooth structure using both lasers and LEDs in the UV-visible range for fluorescence excitation. The influence of calculus color on the informative signal is demonstrated. The optimal spectral bands of excitation and registration of the fluorescence are determined.

Implementing Projects in Calculus on a Large Scale at the University of South Florida

ERIC Educational Resources Information Center

Fox, Gordon A.; Campbell, Scott; Grinshpan, Arcadii; Xu, Xiaoying; Holcomb, John; Bénéteau, Catherine; Lewis, Jennifer E.; Ramachandran, Kandethody

2017-01-01

This paper describes the development of a program of project-based learning in Calculus courses at a large urban research university. In this program, students developed research projects in consultation with a faculty advisor in their major, and supervised by their calculus instructors. Students wrote up their projects in a prescribed format…

Improving Student Learning of Calculus Topics via Modified Just-in-Time Teaching Methods

ERIC Educational Resources Information Center

Natarajan, Rekha; Bennett, Andrew

2014-01-01

Although the use of traditional just-in-time teaching techniques has long been viewed positively by students and instructors in undergraduate calculus courses, past studies in this area have not addressed gains in student achievement with respect to specific calculus topics. This paper investigates the latter by administering modified just-in-time…

Calculus: A Computer Oriented Presentation, Part 1 [and] Part 2.

ERIC Educational Resources Information Center

Stenberg, Warren; Walker, Robert J.

Parts one and two of a one-year computer-oriented calculus course (without analytic geometry) are presented. The ideas of calculus are introduced and motivated through computer (i.e., algorithmic) concepts. An introduction to computing via algorithms and a simple flow chart language allows the book to be self-contained, except that material on…

Towards the Development of an Automated Learning Assistant for Vector Calculus: Integration over Planar Regions

ERIC Educational Resources Information Center

Yaacob, Yuzita; Wester, Michael; Steinberg, Stanly

2010-01-01

This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a…

Disappearing renal calculus.

PubMed

Cui, Helen; Thomas, Johanna; Kumar, Sunil

2013-04-10

We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging.

Tablet PC: A Preliminary Report on a Tool for Teaching Calculus

ERIC Educational Resources Information Center

Gorgievski, Nicholas; Stroud, Robert; Truxaw, Mary; DeFranco, Thomas

2005-01-01

This study examined students' perceptions of the Tablet PC as an instructional tool for teaching Calculus. A thirteen item survey was developed by the researchers and administered to 103 students in an introductory Calculus course at a large university in the Northeast of the United States. The purpose of this survey was to collect data regarding…

On flipping the classroom in large first year calculus courses

NASA Astrophysics Data System (ADS)

Jungić, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy

2015-05-01

Over the course of two years, 2012--2014, we have implemented a 'flipping' the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of both instructors and students.

Resequencing Skills and Concepts in Applied Calculus Using the Computer as a Tool.

ERIC Educational Resources Information Center

Heid, M. Kathleen

1988-01-01

During the first 12 weeks of an applied calculus course, two classes of college students studied calculus concepts using graphical and symbol-manipulation computer programs to perform routine manipulations. Three weeks were spent on skill development. Students showed better understanding of concepts and performed almost as well on routine skills.…

Teaching Children How to Include the Inversion Principle in Their Reasoning about Quantitative Relations

ERIC Educational Resources Information Center

Nunes, Terezinha; Bryant, Peter; Evans, Deborah; Bell, Daniel; Barros, Rossana

2012-01-01

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research…

A case-control study on the association between bladder cancer and prior bladder calculus.

PubMed

Chung, Shiu-Dong; Tsai, Ming-Chieh; Lin, Ching-Chun; Lin, Herng-Ching

2013-03-15

Bladder calculus is associated with chronic irritation and inflammation. As there is substantial documentation that inflammation can play a direct role in carcinogenesis, to date the relationship between stone formation and bladder cancer (BC) remains unclear. This study aimed to examine the association between BC and prior bladder calculus using a population-based dataset. This case-control study included 2,086 cases who had received their first-time diagnosis of BC between 2001 and 2009 and 10,430 randomly selected controls without BC. Conditional logistic regressions were employed to explore the association between BC and having been previously diagnosed with bladder calculus. Of the sampled subjects, bladder calculus was found in 71 (3.4%) cases and 105 (1.1%) controls. Conditional logistic regression analysis revealed that the odds ratio (OR) of having been diagnosed with bladder calculus before the index date for cases was 3.42 (95% CI = 2.48-4.72) when compared with controls after adjusting for monthly income, geographic region, hypertension, diabetes, coronary heart disease, and renal disease, tobacco use disorder, obesity, alcohol abuse, and schistosomiasis, bladder outlet obstruction, and urinary tract infection. We further analyzed according to sex and found that among males, the OR of having been previously diagnosed with bladder calculus for cases was 3.45 (95% CI = 2.39-4.99) that of controls. Among females, the OR was 3.05 (95% CI = 1.53-6.08) that of controls. These results add to the evidence surrounding the conflicting reports regarding the association between BC and prior bladder calculus and highlight a potential target population for bladder cancer screening.

[Melamine related urinary calculus and acute renal failure in infants].

PubMed

Sun, Ning; Shen, Ying; Sun, Qiang; Li, Xu-ran; Jia, Li-qun; Zhang, Gui-ju; Zhang, Wei-ping; Chen, Zhi; Fan, Jian-feng; Jiang, Ye-ping; Feng, Dong-chuan; Zhang, Rui-feng; Zhu, Xiao-yu; Xiao, Hong-zhan

2008-11-01

To summarize clinical characteristics, diagnosis and treatment of infants with urinary calculus and acute renal failure developed after being fed with melamine tainted formula milk. Data of infant patients with urinary calculus and acute renal failure due to melamine tainted formula milk admitted to the Beijing Children's Hospital affiliated to the Capital Medical University and the Xuzhou Children's Hospital in 2008 were used to analyze the epidemiological characteristics, clinical manifestations, image features as well as effects of 4 types of therapies. All the 34 infants with urinary calculus were complicated with acute renal failure, their blood urea nitrogen (BUN) was (24.1 +/- 8.2) mmol/L and creatinine (Cr) was (384.2 +/- 201.2) micromol/L. The chemical analysis on the urinary calculus sampled from 14 of the infants showed that the calculus contained melamine and acidum uricum. The time needed for the four types of therapies for returning Cr to normal was (3.5 +/- 1.9) d for cystoscopy group, (2.7 +/- 1.1) d for lithotomy group, (3.8 +/- 2.3) d for dialysis group, and (2.7 +/- 1.6) d for medical treatment group, which had no statistically significant difference (P = 0.508). Renal failure of all the 34 infants was relieved within 1 to 7 days, averaging (3.0 +/- 1.8) d. Melamine tainted formula milk may cause urinary calculus and obstructive acute renal failure. It is suggested that firstly the patients with urinary calculus complicated with acute renal failure should be treated with dialysis or medication to correct electrolyte disturbances, in particular hyperkalemia, and then relieve the obstruction with available medical and surgical methods as soon as possible. It is observed that the short term prognosis is satisfactory.

Potential of shock waves to remove calculus and biofilm.

PubMed

Müller, Philipp; Guggenheim, Bernhard; Attin, Thomas; Marlinghaus, Ernst; Schmidlin, Patrick R

2011-12-01

Effective calculus and biofilm removal is essential to treat periodontitis. Sonic and ultrasonic technologies are used in several scaler applications. This was the first feasibility study to assess the potential of a shock wave device to remove calculus and biofilms and to kill bacteria. Ten extracted teeth with visible subgingival calculus were treated with either shock waves for 1 min at an energy output of 0.4 mJ/mm(2) at 3 Hz or a magnetostrictive ultrasonic scaler at medium power setting for 1 min, which served as a control. Calculus was determined before and after treatment planimetrically using a custom-made software using a grey scale threshold. In a second experiment, multispecies biofilms were formed on saliva-preconditioned bovine enamel discs during 64.5 h. They were subsequently treated with shock waves or the ultrasonic scaler (N = 6/group) using identical settings. Biofilm detachment and bactericidal effects were then assessed. Limited efficiency of the shock wave therapy in terms of calculus removal was observed: only 5% of the calculus was removed as compared to 100% when ultrasound was used (P ≤ 0.0001). However, shock waves were able to significantly reduce adherent bacteria by three orders of magnitude (P ≤ 0.0001). The extent of biofilm removal by the ultrasonic device was statistically similar. Only limited bactericidal effects were observed using both methods. Within the limitations of this preliminary study, the shock wave device was not able to reliably remove calculus but had the potential to remove biofilms by three log steps. To increase the efficacy, technical improvements are still required. This novel noninvasive intervention, however, merits further investigation.

Surgical removal of a large vaginal calculus formed after a tension-free vaginal tape procedure.

PubMed

Zilberlicht, Ariel; Feiner, Benjamin; Haya, Nir; Auslender, Ron; Abramov, Yoram

2016-11-01

Vaginal calculus is a rare disorder which has been reported in association with urethral diverticulum, urogenital sinus anomaly, bladder exstrophy and the tension-free vaginal tape (TVT) procedure. We report a 42-year-old woman who presented with persistent, intractable urinary tract infection (UTI) following a TVT procedure. Cystoscopy demonstrated an eroded tape with the formation of a bladder calculus, and the patient underwent laser cystolithotripsy and cystoscopic resection of the tape. Following this procedure, her UTI completely resolved and she remained asymptomatic for several years. Seven years later she presented with a solid vaginal mass. Pelvic examination followed by transvaginal ultrasonography and magnetic resonance imaging demonstrated a large vaginal calculus located at the lower third of the anterior vaginal wall adjacent to the bladder neck. This video presents the transvaginal excision and removal of the vaginal calculus.

Rare calcium oxalate monohydrate calculus attached to the wall of the renal pelvis.

PubMed

Grases, Felix; Costa-Bauza, Antonia; Prieto, Rafael M; Saus, Carlos; Servera, Antonio; García-Miralles, Reyes; Benejam, Joan

2011-04-01

Most renal calculi can be classified using well-established criteria in a manner that reflects both composition and fine structure under specific pathophysiological conditions. However, when a large patient population is considered, rare renal calculi invariably appear, some of which have never been classified; careful study is required to establish stone etiology in such cases. The patient in the present case report formed two types of calculi. One was attached on the wall of the renal pelvis near the ureter and part of the calculus was embedded inside pelvic renal tissue. The calculus developed on an ossified calcification located in the pelvis tissue. Current knowledge on the development of calcification in soft tissues suggests a pre-existing injury as an inducer of its development. A mechanism of calculus formation is proposed. The second stone was a typical jack-stone calculus. © 2011 The Japanese Urological Association.

Adiabatic elimination for systems with inertia driven by compound Poisson colored noise.

PubMed

Li, Tiejun; Min, Bin; Wang, Zhiming

2014-02-01

We consider the dynamics of systems driven by compound Poisson colored noise in the presence of inertia. We study the limit when the frictional relaxation time and the noise autocorrelation time both tend to zero. We show that the Itô and Marcus stochastic calculuses naturally arise depending on these two time scales, and an extra intermediate type occurs when the two time scales are comparable. This leads to three different limiting regimes which are supported by numerical simulations. Furthermore, we establish that when the resulting compound Poisson process tends to the Wiener process in the frequent jump limit the Itô and Marcus calculuses, respectively, tend to the classical Itô and Stratonovich calculuses for Gaussian white noise, and the crossover type calculus tends to a crossover between the Itô and Stratonovich calculuses. Our results would be very helpful for understanding relevant experiments when jump type noise is involved.

Success in Introductory Calculus: The Role of High School and Pre-Calculus Preparation

ERIC Educational Resources Information Center

Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles

2017-01-01

Calculus at the college level has significant potential to serve as a pump for increasing the number of students majoring in STEM fields. It is a foundation course for all STEM majors and, if mastered well, should provide students with a positive and successful first-year experience and gateway into more advanced courses. Studies have shown that a…

Development of Curriculum Units as Basic Course for Calculus Provided for Freshmen with Low Academic Achievement

ERIC Educational Resources Information Center

Lue, Yuang-Tswong

2015-01-01

This study was to design, develop, and investigate instructional units for freshmen with low academic achievement to learn before they study calculus. Because the concepts, skills, and theories of function are fundamental for the calculus course but the below average students were not familiar with the basic knowledge and ability in function when…

Improving Student Success in Calculus at Seattle University

ERIC Educational Resources Information Center

Carter, J. D.; Helliwell, D.; Henrich, Allison; Principe, M.; Sloughter, J. M.

2016-01-01

Finding ways to improve student success in calculus is a critically important step on the path to supporting students who are pursuing degrees in STEM fields. Far too many students fail calculus 1 and are pushed to drop their majors in technical fields. One way of addressing this issue is by following a program that was pioneered at University of…

An Evaluative Calculus Project: Applying Bloom's Taxonomy to the Calculus Classroom

ERIC Educational Resources Information Center

Karaali, Gizem

2011-01-01

In education theory, Bloom's taxonomy is a well-known paradigm to describe domains of learning and levels of competency. In this article I propose a calculus capstone project that is meant to utilize the sixth and arguably the highest level in the cognitive domain, according to Bloom et al.: evaluation. Although one may assume that mathematics is…

Incorporating Inquiry-Based Learning in the Calculus Sequence: A Most Challenging Endeavour

ERIC Educational Resources Information Center

McLoughlin, M. Padraig M. M.

2009-01-01

A course in the Calculus sequence is arguably the most difficult course in which inquiry-based learning (IBL) can be achieved with any degree of success within the curriculum in part due to: (1) the plethora of majors taking Calculus to which the sequence relates to their majors in what is considered an "applied" manner; and (2) the…

Evaluating Views of Lecturers on the Consistency of Teaching Content with Teaching Approach: Traditional versus Reform Calculus

ERIC Educational Resources Information Center

Sevimli, Eyup

2016-01-01

This study aims to evaluate the consistency of teaching content with teaching approaches in calculus on the basis of lecturers' views. In this sense, the structures of the examples given in two commonly used calculus textbooks, both in traditional and reform classrooms, are compared. The content analysis findings show that the examples in both…

A Useful Demonstration of Calculus in a Physics High School Laboratory

ERIC Educational Resources Information Center

Alvarez, Gustavo; Schulte, Jurgen; Stockton, Geoffrey; Wheeler, David

2018-01-01

The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an…

Disappearing renal calculus

PubMed Central

Cui, Helen; Thomas, Johanna; Kumar, Sunil

2013-01-01

We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging. PMID:23580676

Calculus, Part 3, Student's Text, Unit No. 70. Revised Edition.

ERIC Educational Resources Information Center

Beck, A.; And Others

This is part three of a three-part SMSG calculus text for high school students. One of the goals of the text is to present calculus as a mathematical discipline as well as presenting its practical uses. The authors emphasize the importance of being able to interpret the concepts and theory in terms of models to which they apply. The text…

Students' Conceptual Knowledge of Limits in Calculus: A Two-Part Constructivist Case Study

ERIC Educational Resources Information Center

Adams, Margaret Smolinka

2013-01-01

This case study investigated students' conceptual knowledge of limits in calculus by implementing semi-structured interviews. The constructivist learning principles of Piaget and Inhelder as well as theories of understanding by Skemp guided the study. In Phase I, a pilot study was conducted with 15 students from a Calculus III class. By using…

Fluorescence detection of dental calculus

NASA Astrophysics Data System (ADS)

Gonchukov, S.; Biryukova, T.; Sukhinina, A.; Vdovin, Yu

2010-11-01

This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 - 645 nm and 340 - 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy.

Revised Bloom's taxonomy and integral calculus: unpacking the knowledge dimension

NASA Astrophysics Data System (ADS)

Radmehr, Farzad; Drake, Michael

2017-11-01

In this paper, the knowledge dimension for Revised Bloom's taxonomy (RBT) is unpacked for integral calculus. As part of this work, the 11 subtypes of the knowledge dimension are introduced, and through document analysis of chapter 4 of the RBT handbook, these subtypes are defined. Then, by consulting materials frequently used for teaching integral calculus, each subtype is exemplified. The developed dimension may enable or enhance opportunities for dialogue between lecturers, teachers, and researchers about how to develop and align educational objectives, teaching activities, and assessments in integral calculus, or how metacognition and metacognitive knowledge could be used to support teaching and learning.

Representing and reasoning about program in situation calculus

NASA Astrophysics Data System (ADS)

Yang, Bo; Zhang, Ming-yi; Wu, Mao-nian; Xie, Gang

2011-12-01

Situation calculus is an expressive tool for modeling dynamical system in artificial intelligence, changes in a dynamical world is represented naturally by the notions of action, situation and fluent in situation calculus. Program can be viewed as a discrete dynamical system, so it is possible to model program with situation calculus. To model program written in a smaller core programming language CL, notion of fluent is expanded for representing value of expression. Together with some functions returning concerned objects from expressions, a basic action theory of CL programming is constructed. Under such a theory, some properties of program, such as correctness and termination can be reasoned about.

Dental calculus evidence of Taï Forest Chimpanzee plant consumption and life history transitions

NASA Astrophysics Data System (ADS)

Power, Robert C.; Salazar-García, Domingo C.; Wittig, Roman M.; Freiberg, Martin; Henry, Amanda G.

2015-10-01

Dental calculus (calcified dental plaque) is a source of multiple types of data on life history. Recent research has targeted the plant microremains preserved in this mineralised deposit as a source of dietary and health information for recent and past populations. However, it is unclear to what extent we can interpret behaviour from microremains. Few studies to date have directly compared the microremain record from dental calculus to dietary records, and none with long-term observation dietary records, thus limiting how we can interpret diet, food acquisition and behaviour. Here we present a high-resolution analysis of calculus microremains from wild chimpanzees (Pan troglodytes verus) of Taï National Park, Côte d’Ivoire. We test microremain assemblages against more than two decades of field behavioural observations to establish the ability of calculus to capture the composition of diet. Our results show that some microremain classes accumulate as long-lived dietary markers. Phytolith abundance in calculus can reflect the proportions of plants in the diet, yet this pattern is not true for starches. We also report microremains can record information about other dietary behaviours, such as the age of weaning and learned food processing techniques like nut-cracking.

Dental calculus evidence of Taï Forest Chimpanzee plant consumption and life history transitions.

PubMed

Power, Robert C; Salazar-García, Domingo C; Wittig, Roman M; Freiberg, Martin; Henry, Amanda G

2015-10-19

Dental calculus (calcified dental plaque) is a source of multiple types of data on life history. Recent research has targeted the plant microremains preserved in this mineralised deposit as a source of dietary and health information for recent and past populations. However, it is unclear to what extent we can interpret behaviour from microremains. Few studies to date have directly compared the microremain record from dental calculus to dietary records, and none with long-term observation dietary records, thus limiting how we can interpret diet, food acquisition and behaviour. Here we present a high-resolution analysis of calculus microremains from wild chimpanzees (Pan troglodytes verus) of Taï National Park, Côte d'Ivoire. We test microremain assemblages against more than two decades of field behavioural observations to establish the ability of calculus to capture the composition of diet. Our results show that some microremain classes accumulate as long-lived dietary markers. Phytolith abundance in calculus can reflect the proportions of plants in the diet, yet this pattern is not true for starches. We also report microremains can record information about other dietary behaviours, such as the age of weaning and learned food processing techniques like nut-cracking.

Near-ultraviolet removal rates for subgingival dental calculus at different irradiation angles.

PubMed

Schoenly, Joshua E; Seka, Wolf D; Rechmann, Peter

2011-07-01

The laser ablation rate of subgingival dental calculus irradiated at a 400-nm-wavelength, 7.4-mJ pulse energy, and 85- and 20-deg irradiation angles is measured using laser triangulation. Three-dimensional images taken before and after irradiation create a removal map with 6-μm axial resolution. Fifteen human teeth with subgingival calculus are irradiated in vitro under a cooling water spray with an ∼300-μm-diam, tenth-order super-gaussian beam. The average subgingival calculus removal rates for irradiation at 85 and 20 deg are 11.1±3.6 and 11.5±5.9 μm∕pulse, respectively, for depth removal and 4.5±1.7×10(5) and 4.8±2.3×10(5) μm(3)∕pulse, respectively, for volume removal. The ablation rate is constant at each irradiation site but varies between sites because of the large differences in the physical and optical properties of calculus. Comparison of the average depth- and volume-removal rates does not reveal any dependence on the irradiation angle and is likely due to the surface topology of subgingival calculus samples that overshadows any expected angular dependence.

Kinetics of canine dental calculus crystallization: an in vitro study on the influence of inorganic components of canine saliva.

PubMed

Borah, Ballav M; Halter, Timothy J; Xie, Baoquan; Henneman, Zachary J; Siudzinski, Thomas R; Harris, Stephen; Elliott, Matthew; Nancollas, George H

2014-07-01

This work identifies carbonated hydroxyapatite (CAP) as the primary component of canine dental calculus, and corrects the long held belief that canine dental calculus is primarily CaCO3 (calcite). CAP is known to be the principal crystalline component of human dental calculus, suggesting that there are previously unknown similarities in the calcification that occurs in these two unique oral environments. In vitro kinetic experiments mimicking the inorganic components of canine saliva have examined the mechanisms of dental calculus formation. The solutions were prepared so as to mimic the inorganic components of canine saliva; phosphate, carbonate, and magnesium ion concentrations were varied individually to investigate the roll of these ions in controlling the nature of the phases that is nucleated. To date, the inorganic components of the canine oral systems have not been investigated at concentrations that mimic those in vivo. The mineral composition of the synthetic calculi grown under these conditions closely resembled samples excised from canines. This finding adds new information about calculus formation in humans and canines, and their sensitivity to chemicals used to treat these conditions. Copyright © 2014 Elsevier Inc. All rights reserved.

Near-ultraviolet removal rates for subgingival dental calculus at different irradiation angles

NASA Astrophysics Data System (ADS)

Schoenly, Joshua E.; Seka, Wolf D.; Rechmann, Peter

2011-07-01

The laser ablation rate of subgingival dental calculus irradiated at a 400-nm-wavelength, 7.4-mJ pulse energy, and 85- and 20-deg irradiation angles is measured using laser triangulation. Three-dimensional images taken before and after irradiation create a removal map with 6-μm axial resolution. Fifteen human teeth with subgingival calculus are irradiated in vitro under a cooling water spray with an ~300-μm-diam, tenth-order super-Gaussian beam. The average subgingival calculus removal rates for irradiation at 85 and 20 deg are 11.1+/-3.6 and 11.5+/-5.9 μm/pulse, respectively, for depth removal and 4.5+/-1.7×105 and 4.8+/-2.3×105 μm3/pulse, respectively, for volume removal. The ablation rate is constant at each irradiation site but varies between sites because of the large differences in the physical and optical properties of calculus. Comparison of the average depth- and volume-removal rates does not reveal any dependence on the irradiation angle and is likely due to the surface topology of subgingival calculus samples that overshadows any expected angular dependence.

Two-parameter asymptotics in magnetic Weyl calculus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lein, Max

2010-12-15

This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter {epsilon}, the case of small coupling {lambda} to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols aremore » proven as (i) {epsilon}<< 1 and {lambda}<< 1, (ii) {epsilon}<< 1 and {lambda}= 1, as well as (iii) {epsilon}= 1 and {lambda}<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.« less

On power series expansions of the S-resolvent operator and the Taylor formula

NASA Astrophysics Data System (ADS)

Colombo, Fabrizio; Gantner, Jonathan

2016-12-01

The S-functional calculus is based on the theory of slice hyperholomorphic functions and it defines functions of n-tuples of not necessarily commuting operators or of quaternionic operators. This calculus relays on the notion of S-spectrum and of S-resolvent operator. Since most of the properties that hold for the Riesz-Dunford functional calculus extend to the S-functional calculus, it can be considered its non commutative version. In this paper we show that the Taylor formula of the Riesz-Dunford functional calculus can be generalized to the S-functional calculus. The proof is not a trivial extension of the classical case because there are several obstructions due to the non commutativity of the setting in which we work that have to be overcome. To prove the Taylor formula we need to introduce a new series expansion of the S-resolvent operators associated to the sum of two n-tuples of operators. This result is a crucial step in the proof of our main results, but it is also of independent interest because it gives a new series expansion for the S-resolvent operators. This paper is addressed to researchers working in operator theory and in hypercomplex analysis.

Calculus domains modelled using an original bool algebra based on polygons

NASA Astrophysics Data System (ADS)

Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.

2016-08-01

Analytical and numerical computer based models require analytical definitions of the calculus domains. The paper presents a method to model a calculus domain based on a bool algebra which uses solid and hollow polygons. The general calculus relations of the geometrical characteristics that are widely used in mechanical engineering are tested using several shapes of the calculus domain in order to draw conclusions regarding the most effective methods to discretize the domain. The paper also tests the results of several CAD commercial software applications which are able to compute the geometrical characteristics, being drawn interesting conclusions. The tests were also targeting the accuracy of the results vs. the number of nodes on the curved boundary of the cross section. The study required the development of an original software consisting of more than 1700 computer code lines. In comparison with other calculus methods, the discretization using convex polygons is a simpler approach. Moreover, this method doesn't lead to large numbers as the spline approximation did, in that case being required special software packages in order to offer multiple, arbitrary precision. The knowledge resulted from this study may be used to develop complex computer based models in engineering.

Dental calculus evidence of Taï Forest Chimpanzee plant consumption and life history transitions

PubMed Central

Power, Robert C.; Salazar-García, Domingo C.; Wittig, Roman M.; Freiberg, Martin; Henry, Amanda G.

2015-01-01

Dental calculus (calcified dental plaque) is a source of multiple types of data on life history. Recent research has targeted the plant microremains preserved in this mineralised deposit as a source of dietary and health information for recent and past populations. However, it is unclear to what extent we can interpret behaviour from microremains. Few studies to date have directly compared the microremain record from dental calculus to dietary records, and none with long-term observation dietary records, thus limiting how we can interpret diet, food acquisition and behaviour. Here we present a high-resolution analysis of calculus microremains from wild chimpanzees (Pan troglodytes verus) of Taï National Park, Côte d’Ivoire. We test microremain assemblages against more than two decades of field behavioural observations to establish the ability of calculus to capture the composition of diet. Our results show that some microremain classes accumulate as long-lived dietary markers. Phytolith abundance in calculus can reflect the proportions of plants in the diet, yet this pattern is not true for starches. We also report microremains can record information about other dietary behaviours, such as the age of weaning and learned food processing techniques like nut-cracking. PMID:26481858

[Does carbonate originate from carbonate-calcium crystal component of the human urinary calculus?].

PubMed

Yuzawa, Masayuki; Nakano, Kazuhiko; Kumamaru, Takatoshi; Nukui, Akinori; Ikeda, Hitoshi; Suzuki, Kazumi; Kobayashi, Minoru; Sugaya, Yasuhiro; Morita, Tatsuo

2008-09-01

It gives important information in selecting the appropriate treatment for urolithiasis to confirm the component of urinary calculus. Presently component analysis of the urinary calculus is generally performed by infrared spectroscopy which is employed by companies providing laboratory testing services in Japan. The infrared spectroscopy determines the molecular components from the absorption spectra in consequence of atomic vibrations. It has the drawback that an accurate crystal structure cannot be analyzed compared with the X-ray diffraction method which analyzes the crystal constituent based on the diffraction of X-rays on crystal lattice. The components of the urinary calculus including carbonate are carbonate apatite and calcium carbonate such as calcite. Although the latter is reported to be very rare component in human urinary calculus, the results by infrared spectroscopy often show that calcium carbonate is included in calculus. The infrared spectroscopy can confirm the existence of carbonate but cannot determine whether carbonate is originated from carbonate apatite or calcium carbonate. Thus, it is not clear whether calcium carbonate is included in human urinary calculus component in Japan. In this study, we examined human urinary calculus including carbonate by use of X-ray structural analysis in order to elucidate the origin of carbonate in human urinary calculus. We examined 17 human calculi which were reported to contain calcium carbonate by infrared spectroscopy performed in the clinical laboratory. Fifteen calculi were obtained from urinary tract, and two were from gall bladder. The stones were analyzed by X-ray powder method after crushed finely. The reports from the clinical laboratory showed that all urinary culculi consisted of calcium carbonate and calcium phosphate, while the gallstones consisted of calcium carbonate. But the components of all urinary calculi were revealed to be carbonate apatite by X-ray diffraction. The components of gallstones were shown to be calcium carbonate (one calcite and the other aragonite) not only by infrared spectroscopy but by X-ray diffraction. It was shown that component analysis of the calculus could be more accurately performed by adding X-ray diffraction method to infrared spectroscopy. It was shown that calcium carbonate existed in a gallstone. As for the carbonate in human urinary calculi, present study showed that it was not calcium carbonate origin but carbonate apatite origin.

Calculus migration characterization during Ho:YAG laser lithotripsy by high-speed camera using suspended pendulum method.

PubMed

Zhang, Jian James; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Chia, Ray W J; Hasenberg, Thomas

2017-07-01

Calculus migration is a common problem during ureteroscopic laser lithotripsy procedure to treat urolithiasis. A conventional experimental method to characterize calculus migration utilized a hosting container (e.g., a "V" grove or a test tube). These methods, however, demonstrated large variation and poor detectability, possibly attributed to the friction between the calculus and the container on which the calculus was situated. In this study, calculus migration was investigated using a pendulum model suspended underwater to eliminate the aforementioned friction. A high-speed camera was used to study the movement of the calculus which covered zero order (displacement), first order (speed), and second order (acceleration). A commercialized, pulsed Ho:YAG laser at 2.1 μm, a 365-μm core diameter fiber, and a calculus phantom (Plaster of Paris, 10 × 10 × 10 mm 3 ) was utilized to mimic laser lithotripsy procedure. The phantom was hung on a stainless steel bar and irradiated by the laser at 0.5, 1.0, and 1.5 J energy per pulse at 10 Hz for 1 s (i.e., 5, 10, and 15 W). Movement of the phantom was recorded by a high-speed camera with a frame rate of 10,000 FPS. The video data files are analyzed by MATLAB program by processing each image frame and obtaining position data of the calculus. With a sample size of 10, the maximum displacement was 1.25 ± 0.10, 3.01 ± 0.52, and 4.37 ± 0.58 mm for 0.5, 1, and 1.5 J energy per pulse, respectively. Using the same laser power, the conventional method showed <0.5 mm total displacement. When reducing the phantom size to 5 × 5 × 5 mm 3 (one eighth in volume), the displacement was very inconsistent. The results suggested that using the pendulum model to eliminate the friction improved sensitivity and repeatability of the experiment. A detailed investigation on calculus movement and other causes of experimental variation will be conducted as a future study.

Effect of Ramadan fasting on urinary risk factors for calculus formation.

PubMed

Miladipour, Amir Hossein; Shakhssalim, Nasser; Parvin, Mahmoud; Azadvari, Mohaddeseh

2012-01-01

Even though dehydration could aggravate formation of urinary calculi, the effects of fluid and food restriction on calculus formation is not thoroughly defined. The purpose of this study is to evaluate the effects of fluid and food restriction in Ramadan fasting on urinary factors in kidney and urinary calculus formation. Fifty-seven men aged 30 to 55 years old, including 37 recurrent calcium calculus formers and 20 with no history of kidney calculi were evaluated for blood tests, ultrasonography investigations, urinalysis, urine culture, and also 24-hour urine collection test. Metabolites including calcium, oxalate, citrate, uric acid, magnesium, phosphate, potassium, sodium, and creatinine were measured before and during Ramadan fasting. The values of calculus-precipitating solutes as well as inhibitory factors were documented thoroughly. Total excretion of calcium, phosphate, and magnesium in 24-hour urine and also urine volume during fasting were significantly lower than those in the nonfasting period. Urine concentration of calcium during fasting was significantly lower than nonfasting (P < .001). Urine concentrations of uric acid, citrate, phosphate, sodium, and potassium during fasting were significantly higher than nonfasting. Uric acid supersaturation was accentuated, and calcium phosphate supersaturation was decreased significantly during fasting. There was no significant increase in calcium oxalate supersaturation during the fasting period. Fasting during Ramadan has different effects on total excretion and concentrations of urinary precipitate and inhibitory factors contributing to calculus formation. We did not find enough evidence in favor of increased risks of calculus formation during Ramadan fasting.

[Giant prostatic calculus with neurogenic bladder disease and prostate diverticulum: a case report and review of the literature].

PubMed

Li, Xiao-Shi; Quan, Chang-Yi; Li, Gang; Cai, Qi-Liang; Hu, Bin; Wang, Jiu-Wei; Niu, Yuan-Jie

2013-02-01

To study the etiology, clinical manifestation, diagnosis and treatment of giant prostatic calculus with neurogenic bladder disease and prostate diverticulum. We retrospectively analyzed the clinical data of a case of giant prostatic calculus with neurogenic bladder disease and prostate diverticulum and reviewed the relevant literature. The patient was a 37-year-old man, with urinary incontinence for 22 years and intermittent dysuria with frequent micturition for 9 years, aggravated in the past 3 months. He had received surgery for spina bifida and giant vesico-prostatic calculus. The results of preoperative routine urinary examination were as follows: WBC 17 -20/HPF, RBC 12 - 15/HPF. KUB, IVU and pelvic CT revealed spina bifida occulta, neurogenic bladder and giant prostatic calculus. The patient underwent TURP and transurethral lithotripsy with holmium-YAG laser. The prostatic calculus was carbonate apatite in composition. Urinary dynamic images at 2 weeks after surgery exhibited significant improvement in the highest urine flow rate and residual urine volume. Seventeen months of postoperative follow-up showed dramatically improved urinary incontinence and thicker urine stream. Prostate diverticulum with prostatic giant calculus is very rare, and neurogenic bladder may play a role in its etiology. Cystoscopy is an accurate screening method for its diagnosis. For the young patients and those who wish to retain sexual function, TURP combined with holmium laser lithotripsy can be employed, and intraoperative rectal examination should be taken to ensure complete removal of calculi.

Drinking water composition and incidence of urinary calculus: introducing a new index.

PubMed

Basiri, Abbas; Shakhssalim, Nasser; Khoshdel, Ali Reza; Pakmanesh, Hamid; Radfar, Mohammad Hadi

2011-01-01

INTRODUCTION. We searched for a pathophysiologically based feature of major water electrolytes, which may define water quality better than the water hardness, respecting urinary calculus formation. MATERIALS AND METHODS. Utilizing a multistage stratified sampling, 2310 patients were diagnosed in the imaging centers of the provincial capitals in Iran between 2007 and 2008. These were composed of 1755 patients who were settled residents of 24 provincial capitals. Data on the regional drinking water composition, obtained from an accredited registry, and their relationships with the region's incidence of urinary calculi were evaluated by metaregression models. The stone risk index (defined as the ratio of calcium to magnesium-bicarbonate product in drinking water) was used to assess the risk of calculus formation. RESULTS. No correlation was found between the urinary calculus incidence and the amount of calcium, bicarbonate, or the total hardness of the drinking water. In contrast, water magnesium had a marginally significant nonlinear inverse relationship with the incidence of the disease in the capitals (R(2) = 26%, P = .05 for a power model). The stone risk index was associated nonlinearly with the calculus incidence (R(2) = 28.4%, P = .04). CONCLUSIONS. Urinary calculus incidence was inversely related with drinking water magnesium content. We introduced a new index constructed on the foundation of a pathophysiologically based formula; the stone risk index had a strong positive association with calculus incidence. This index can have therapeutic and preventive applications, yet to be confirmed by clinical trials.

High levels of heavy metal accumulation in dental calculus of smokers: a pilot inductively coupled plasma mass spectrometry study.

PubMed

Yaprak, E; Yolcubal, I; Sinanoğlu, A; Doğrul-Demiray, A; Guzeldemir-Akcakanat, E; Marakoğlu, I

2017-02-01

Various trace elements, including toxic heavy metals, may exist in dental calculus. However, the effect of environmental factors on heavy metal composition of dental calculus is unknown. Smoking is a major environmental source for chronic toxic heavy metal exposition. The aim of this study is to compare toxic heavy metal accumulation levels in supragingival dental calculus of smokers and non-smokers. A total of 29 supragingival dental calculus samples were obtained from non-smoker (n = 14) and smoker (n = 15) individuals. Subjects with a probability of occupational exposure were excluded from the study. Samples were analyzed by inductively coupled plasma mass spectrometry in terms of 26 metals and metalloids, including toxic heavy metals. Toxic heavy metals, arsenic (p < 0.05), cadmium (p < 0.05), lead (p < 0.01), manganese (p < 0.01) and vanadium (p < 0.01) levels were significantly higher in smokers than non-smokers. The levels of other examined elements were similar in both groups (p > 0.05). Within the limitations of this study, it can be concluded that the elementary composition of dental calculus may be affected by environmental factors such as tobacco smoke. Therefore, dental calculus may be utilized as a non-invasive diagnostic biological material for monitoring chronic oral heavy metal exposition. However, further studies are required to evaluate its diagnostic potential. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Correlation between calcium and phosphate levels to calculus accumulation on coronary heart disease patients

NASA Astrophysics Data System (ADS)

Cahaya, Cindy; Masulili, Sri Lelyati C.; Lessang, Robert; Radi, Basuni

2017-02-01

Coronary Artery Disease (CAD) or Coronary Heart Disease (CHD) is a disease that happened because of blood flow being blocked by atherosclerosis. Atherosclerosis is a process of hardening of the arteries which characterized by thickening and loss of elasticity of the intimal layer of vascular wall, by lipid deposit. Periodontitis is a chronic multifactorial inflammatory disease caused by microorganism and characterized by progressive destruction of the tooth supporting apparatus leading to tooth loss. Many studies use saliva as a valuable source for clinically information, as an asset for early diagnosis, prognostic and reviewer for pascatherapy status. Dental calculus had happened as a consequence of saliva supersaturation by calcium and phosphate. Salivary flow rate and its composition influence the formation of calculus. Increasing salivary calcium levels is characteristic of periodontitis patients. An important hipotesis in Cardiology is chronic infections contribute in atherosclerosis. Objective: To analyse the correlation between calcium and phosphate levels in saliva to calculus accumulation on CHD patients. Result: Correlation analysis between salivary calcium levels with calculus accumulation in patients with CHD and non-CHD showed no significant p value, p=0.59 and p=0.518. Correlation analysis between salivary phosphate levels and calculus accumulation showed no significant p value, p=0.836 for CHD patients and p=0.484 for non-CHD patients. Conclusion: There are no correlation between calcium levels and phosphate levels with calculus accumulation in CHD patients. Further research need to be done.

Analysis of Errors and Misconceptions in the Learning of Calculus by Undergraduate Students

ERIC Educational Resources Information Center

Muzangwa, Jonatan; Chifamba, Peter

2012-01-01

This paper is going to analyse errors and misconceptions in an undergraduate course in Calculus. The study will be based on a group of 10 BEd. Mathematics students at Great Zimbabwe University. Data is gathered through use of two exercises on Calculus 1&2.The analysis of the results from the tests showed that a majority of the errors were due…

Assessment of Peer-Led Team Learning in Calculus I: A Five-Year Study

ERIC Educational Resources Information Center

Merkel, John Conrad; Brania, Abdelkrim

2015-01-01

This five-year study of the peer-led team learning (PLTL) paradigm examined its implementation in a Calculus I course at an all-male HBCU institution. For this study we set up a strong control group and measured the effect of PLTL in the teaching and learning of Calculus I through two points of measure: retention and success rates and learning…

Security Modeling and Correctness Proof Using Specware and Isabelle

DTIC Science & Technology

2008-12-01

proving requires substantial knowledge and experience in logical calculus . 15. NUMBER OF PAGES 146 14. SUBJECT TERMS Formal Method, Theorem...although the actual proving requires substantial knowledge and experience in logical calculus . vi THIS PAGE INTENTIONALLY LEFT BLANK vii TABLE OF...formal language and provides tools for proving those formulas in a logical calculus ” [5]. We are demonstrating in this thesis that a specification in

Study Modules for Calculus-Based General Physics. [Includes Modules 24-26: Electric Potential; Ohm's Law; and Capacitors].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Using an Advanced Graphing Calculator in the Teaching and Learning of Calculus

ERIC Educational Resources Information Center

Leng, Ng Wee

2011-01-01

The purpose of this study was to investigate how the use of TI-Nspire[TM] could enhance the teaching and learning of calculus. A conceptual framework for the use of TI-Nspire[TM] for learning calculus in a mathematics classroom is proposed that describes the interactions among the students, TI-Nspire[TM], and the learning tasks, and how they lead…

What Is Old Is New Again: A Systemic Approach to the Challenges of Calculus Instruction

ERIC Educational Resources Information Center

Carreon, Fernando; DeBacker, Stephen; Kessenich, Paul; Kubena, Angela; LaRose, P. Gavin

2018-01-01

In the abstract for "Calculus for a New Century: A Pump, Not a Filter," Lynn Steen wrote: "The authors agree on the forces that are reshaping calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory, yet disagree about new content emphases. They agree that the neglect of…

Collaborate and Innovate: One Department's Perspective on Factors Supporting and Sustaining Pedagogical Change in Calculus I

ERIC Educational Resources Information Center

Schroeder, Larissa Bucchi; McGivney-Burelle, Jean; Haruta, Mako E.; Xue, Fei

2018-01-01

At the University of Hartford we transformed our approach to Calculus I--moving it away from a lecture-dominant format to one that focuses squarely on students solving problems and discussing and presenting their mathematical ideas for the majority of class time. In this article, we discuss our Flipping Calculus project and how a departmental…

Unusual Giant Prostatic Urethral Calculus

PubMed Central

Bello, A.; Maitama, H. Y.; Mbibu, N. H.; Kalayi, G. D.; Ahmed, A.

2010-01-01

Giant vesico-prostatic urethral calculus is uncommon. Urethral stones rarely form primarily in the urethra, and they are usually associated with urethral strictures, posterior urethral valve or diverticula. We report a case of a 32-year-old man with giant vesico-prostatic (collar-stud) urethral stone presenting with sepsis and bladder outlet obstruction. The clinical presentation, management, and outcome of the giant prostatic urethral calculus are reviewed. PMID:22091328

A phenomenological calculus of Wiener description space.

PubMed

Richardson, I W; Louie, A H

2007-10-01

The phenomenological calculus is a categorical example of Robert Rosen's modeling relation. This paper is an alligation of the phenomenological calculus and generalized harmonic analysis, another categorical example. Our epistemological exploration continues into the realm of Wiener description space, in which constitutive parameters are extended from vectors to vector-valued functions of a real variable. Inherent in the phenomenology are fundamental representations of time and nearness to equilibrium.

Using `min' and `max' functions in calculus teaching

NASA Astrophysics Data System (ADS)

Satianov, Pavel; Dagan, Miriam; Amram, Meirav

2015-08-01

In this paper, we discuss the use of the min and max functions in teaching calculus to engineering students. Our experience illustrates that such functions have great possibilities in the development of a student's analytical thinking. The types of problems we present here are not common in most instructional texts, which lead us to suggest that the paper will be interesting and useful to calculus lecturers.

Diagnosis and treatment of melamine-associated urinary calculus complicated with acute renal failure in infants and young children.

PubMed

Sun, Ning; Shen, Ying; Sun, Qiang; Li, Xu-ran; Jia, Li-qun; Zhang, Gui-ju; Zhang, Wei-ping; Chen, Zhi; Fan, Jian-feng; Jiang, Ye-ping; Feng, Dong-chuan; Zhang, Rui-feng; Zhu, Xiao-yu; Xiao, Hong-zhan

2009-02-05

Infants in some areas of China developed urinary lithiasis after being fed with powdered milk that was tainted with melamine in 2008 and very small proportion of the infants developed acute renal failure caused by urinary tract calculus obstruction. The aim of this article was to summarize clinical characteristics, diagnosis and treatment of infants with urinary calculus and acute renal failure developed after being fed with melamine tainted formula milk. Data of infant patients with urinary calculus and acute renal failure due to melamine tainted formula milk admitted to the Beijing Children's Hospital Affiliated to the Capital Medical University and the Xuzhou Children's Hospital in 2008 were used to analyze the epidemiological characteristics, clinical manifestations, imaging features as well as effects of 4 types of therapies. All the 34 infants with urinary calculus were complicated with acute renal failure, their blood urea nitrogen (BUN) was (24.1+/-8.2) mmol/L and creatinine (Cr) was (384.2+/-201.2) micromol/L. The chemical analysis on the urinary calculus sampled from 15 of the infants showed that the calculus contained melamine and acidum uricum. The time needed for the four types of therapies for returning Cr to normal was (3.5+/-1.9) days for cystoscopy group, (2.7+/-1.1) days for lithotomy group, (3.8+/-2.3) days for dialysis group, and (2.7+/-1.6) days for medical treatment group, which had no statistically significant difference (P=0.508). Renal failure of all the 34 infants was relieved within 1 to 7 days, averaging (3.00+/-1.78) days. Melamine tainted formula milk may cause urinary calculus and obstructive acute renal failure. It is suggested that firstly the patients with urinary calculus complicated with acute renal failure should be treated with dialysis or medication to correct electrolyte disturbance, in particular hyperkalemia, and then relieve the obstruction with available medical and surgical methods as soon as possible. It was observed that the short-term prognosis was satisfactory.

Identification of Actinobacillus actinomycetemcomitans, Treponema denticola and Porphyromonas gingivalis within human dental calculus: a pilot investigation.

PubMed

Calabrese, Nicolino; Galgut, Peter; Mordan, Nicola

2007-10-01

Dental calculus is considered to be simply a "plaque-retentive factor", and therefore only a secondary aetiological factor in the pathogenesis of periodontitis. Recent studies have suggested a more active role for calculus. Our objective was to demonstrate the presence of periodontal pathogens in the non-mineralised areas of supra- and subgingival dental calculus. Subjects for the study were derived from patients with substantial amounts of supragingival calculus in the lower anterior region who had moderate periodontal disease, having been referred to the periodontal department at the Eastman Dental Hospital for periodontal care. Calculus was removed in as large pieces as possible by the use of a sickle or a push scaler placed underneath the apical or facial border of the calculus and fracturing it from the tooth surface in a single stroke. The orientation and absence of dental plaque was confirmed using light microscopy for each sample prior to inclusion in this study. Samples were prepared for transmission electron microscopic (TEM) observation after immunogold staining with polyclonal antibodies for the presence of Actinobacillus actinomycetemcomitans (A. a.), Porphyromonas gingivalis (P. g.) and Treponema denticola (T. d.). Most of the samples contained at least one of the bacterial species examined, either in the lacunae or in the covering dental plaque. T. d. was the most frequently identified species and was found in nearly all of the subgingival samples, whilstA. a. was rarely observed. In this limited study, supra- and subgingival dental calculus appears to be capable of maintaining periodontal pathogens within the deep recesses of its structural lacunae and channels. Therefore, calculus could possibly play a relevant role in the aetiology and pathogenesis of periodontitis. The presence of T. d. in the majority of specimens requires further investigation as its pathogenic potential may be underestimated in current published microbiological research, and further work is required to determine its role in the pathogenesis of periodontal diseases. However, further work by way of a large-scale definitive study is necessary to confirm the results of this investigation.

Primary vaginal calculus in a middle-aged woman with mental and physical disabilities.

PubMed

Ikeda, Yuji; Oda, Katsutoshi; Matsuzawa, Naoki; Shimizu, Ken

2013-07-01

Vaginal calculi are rarely encountered and are often misdiagnosed as bladder calculi because of the difficulty in achieving an appropriate diagnosis. Most vaginal calculi result from the presence of a urethrovaginal fistula; those occurring in the absence of such fistulas are extremely rare. We present a case of a 42-year-old bedridden woman with mental and physical disabilities who had been misdiagnosed for a decade as having a bladder calculus. We removed the calculus nonsurgically and the analyzed the components. Results demonstrated the presence of a primary vaginal calculus. Vaginal calculi may occasionally occur in disabled women, but further investigation of the etiology of such calculi is required.

Large bladder calculus masking a stone in single-system ureterocele.

PubMed

Bhaskar, Ved; Sinha, Rahul Janak; Purkait, Bimalesh; Singh, Vishwajeet

2017-06-14

Ureterocele in an elderly is a rare entity. The presence of stone within ureterocele along with a large bladder calculus is an even rarer presentation. This phenomenon has not been reported so far to the best of our knowledge. We present an unusual case of a large bladder calculus with a concomitant stone in the associated ureterocele. The diagnosis was missed in the first instance due to the masking effect by the larger bladder calculus. Herein, we discuss this case and its management. © BMJ Publishing Group Ltd (unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

A cross-national study of calculus

NASA Astrophysics Data System (ADS)

Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen

2015-05-01

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan students showed a larger gain and normalized gain, and hence narrowed the gap. ECNU's superior performance was especially striking on the subset of problems requiring only a pre-calculus background. On those, Michigan's post-test scores were below ECNU's pre-test scores and, indeed, ECNU's higher performance on both the overall pre-test and overall post-test is attributable to its success on these problems.

The feasibility of using microwave-induced thermoacoustic tomography for detection and evaluation of renal calculi.

PubMed

Cao, Caijun; Nie, Liming; Lou, Cunguang; Xing, Da

2010-09-07

Imaging of renal calculi is important for patients who suffered a urinary calculus prior to treatment. The available imaging techniques include plain x-ray, ultrasound scan, intravenous urogram, computed tomography, etc. However, the visualization of a uric acid calculus (radiolucent calculi) is difficult and often impossible by the above imaging methods. In this paper, a new detection method based on microwave-induced thermoacoustic tomography was developed to detect the renal calculi. Thermoacoustic images of calcium oxalate and uric acid calculus were compared with their x-ray images. The microwave absorption differences among the calcium oxalate calculus, uric acid calculus and normal kidney tissue could be evaluated by the amplitude of the thermoacoustic signals. The calculi hidden in the swine kidney were clearly imaged with excellent contrast and resolution in the three orthogonal thermoacoustic images. The results indicate that thermoacoustic imaging may be developed as a complementary method for detecting renal calculi, and its low cost and effective feature shows high potential for clinical applications.

Conformally Invariant Powers of the Laplacian, Q-Curvature, and Tractor Calculus

NASA Astrophysics Data System (ADS)

Gover, A. Rod; Peterson, Lawrence J.

We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian. Conformal tractor calculus is the natural induced bundle calculus associated to the conformal Cartan connection. Applications discussed include standard formulae for these operators in terms of the Levi-Civita connection and its curvature and a direct definition and formula for T. Branson's so-called Q-curvature (which integrates to a global conformal invariant) as well as generalisations of the operators and the Q-curvature. Among examples, the operators of order 4, 6 and 8 and the related Q-curvatures are treated explicitly. The algorithm exploits the ambient metric construction of Fefferman and Graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions. This is partly based on [12], where the relationship of the normal standard tractor bundle to the ambient construction is described.

The calculus of differences: Effects of a psychosocial, cultural, and pedagogical intervention in an all women's university calculus class

NASA Astrophysics Data System (ADS)

Steele, Diana F.; Levin, Amy K.; Blecksmith, Richard; Shahverdian, Jill

2005-10-01

The purpose of this study was to investigate the ways in which a multi-layered women's calculus course influenced the participants' learning of mathematics. This study, conducted in a state university in the Midwestern region of the United States, revealed not only that women in this particular section of calculus were likely to select careers that involved mathematics, but that the focus on peer support, psychosocial issues such as self-confidence, and pedagogy helped the young women overcome gender barriers, as well as barriers of class, poverty, and race. In this article we provide some of the relevant quantitative statistics and relate the stories of two particular women through excerpts from interviews, student artefacts, and participant observation data. We selected these young women because they faced multiple barriers to success in Calculus I and might not have completed the course or taken additional mathematics courses without the support structures that were fundamental to the course.

Profile of Metacognition of Mathematics Pre-Service Teachers in Understanding the Concept of Integral Calculus with Regard Gender Differences

NASA Astrophysics Data System (ADS)

Misu, L.; Budayasa, I. K.; Lukito, A.

2018-01-01

This research is to describe metacognition profile of female and male mathematics’ pre-service teachers in understanding the concept of integral calculus. The subjects of this study are one female and 1 male mathematics’ pre-service teachers who have studied integral calculus. This research type is an explorative study with the qualitative approach. The main data collection of this research was obtained by using Interview technique. In addition, there are supporting data which is the result of the written work of research subjects (SP) in understanding the question of integral calculus. The results of this study are as follows: There is a difference in metacognition profiles between male and female mathematics’ pre-service teachers in the understanding concept of integral calculus in the interpreting category, especially the definite integral concept. While in the category of exemplifying, there is no difference in metacognition profile between male and female mathematics’ pre-service teachers either the definite integral concept and the indefinite integral concept.

Study Modules for Calculus-Based General Physics. [Includes Modules 11-14: Collisions; Equilibrium of Rigid Bodies; Rotational Dynamics; and Fluid Mechanics].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Vaginal Calculus in a Woman With Mixed Urinary Incontinence and Vaginal Mesh Exposure.

PubMed

Winkelman, William D; Rabban, Joseph T; Korn, Abner P

2016-01-01

Vaginal calculi are extremely rare and are most commonly encountered in the setting of an urethrovaginal or vesicovaginal fistula. We present a case of a 72-year-old woman with mixed urinary incontinence and vaginal mesh exposure incidentally found to have a large vaginal calculus. We removed the calculus surgically and analyzed the components. Results demonstrated the presence of ammonium-magnesium phosphate hexahydrate and carbonate apatite.

Study Modules for Calculus-Based General Physics. [Includes Modules 8-10: Conservation of Energy; Impulse and Momentum; and Rotational Motion].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Deriving the Work Done by an Inverse Square Force in Non-Calculus-Based Introductory Physics Courses

ERIC Educational Resources Information Center

Hu, Ben Yu-Kuang

2012-01-01

I describe a method of evaluating the integral of 1/r[superscript 2] with respect to r that uses only algebra and the concept of area underneath a curve, and which does not formally employ any calculus. This is useful for algebra-based introductory physics classes (where the use of calculus is forbidden) to derive the work done by the force of one…

Future Directions in Fractional Calculus Research and Applications

DTIC Science & Technology

2017-10-31

Report: Future Directions in Fractional Calculus Research and Applications The views, opinions and/or findings contained in this report are those of the...SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 REPORT...Future Directions in Fractional Calculus Research and Applications Report Term: 0-Other Email: mcubed@msu.edu Distribution Statement: 1-Approved for

Study Modules for Calculus-Based General Physics. [Includes Modules 3-5: Planar Motion; Newton's Laws; and Vector Multiplication].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Study Modules for Calculus-Based General Physics. [Includes Modules 27-30: Direct-Current Circuits; Magnetic Forces; Ampere's Law; and Faraday's Law].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules indlude study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Functional Itô versus Banach space stochastic calculus and strict solutions of semilinear path-dependent equations

NASA Astrophysics Data System (ADS)

Cosso, Andrea; Russo, Francesco

2016-11-01

Functional Itô calculus was introduced in order to expand a functional F(t,Xṡ+t,Xt) depending on time t, past and present values of the process X. Another possibility to expand F(t,Xṡ+t,Xt) consists in considering the path Xṡ+t = {Xx+t,x ∈ [-T, 0]} as an element of the Banach space of continuous functions on C([-T, 0]) and to use Banach space stochastic calculus. The aim of this paper is threefold. (1) To reformulate functional Itô calculus, separating time and past, making use of the regularization procedures which match more naturally the notion of horizontal derivative which is one of the tools of that calculus. (2) To exploit this reformulation in order to discuss the (not obvious) relation between the functional and the Banach space approaches. (3) To study existence and uniqueness of smooth solutions to path-dependent partial differential equations which naturally arise in the study of functional Itô calculus. More precisely, we study a path-dependent equation of Kolmogorov type which is related to the window process of the solution to an Itô stochastic differential equation with path-dependent coefficients. We also study a semilinear version of that equation.

Cadmium Profiles in Dental Calculus: a Cross-Sectional Population-Based Study in Hunan Province of China.

PubMed

Zhang, Bo; Tan, Xiaodan; Zhang, Kunlun

2018-01-24

We aimed to investigate whether the cadmium concentrations differ in human dental calculus obtained from the residents with no smoking living in the contaminated area and those with no smoking living in noncontaminated area. In total, there were 260 samples of dental calculus from the adults (n = 50) with no smoking living in contaminated area, the adults (n = 60) with no smoking living in mountainous area, and the adults (n = 150) with no smoking living in low altitude area in Hunan province of China. All samples were analyzed by inductively coupled plasma mass spectrometry (ICP-MS) for cadmium levels. The cadmium levels in dental calculus were significantly higher in the adults with no smoking living in contaminated area than those living in mountainous area and in low altitude area (p < 0.01). The cadmium levels in dental calculus were also higher in the adults with no smoking living in low altitude area than those living in mountainous region (p < 0.01). The results suggested that measuring cadmium levels in dental calculus may be a useful noninvasive method for analysis of environmental exposure to cadmium in the human oral cavity. The low altitude region may have an area contaminated with cadmium in Hunan province of China.

Effect of occlusal calculus utilized as a potential "biological sealant" in special needs patients with gastric feeding tubes: a qualitative in vitro contrast to pit and fissure sealant restorations.

PubMed

Owens, Barry M; Sharp, Harry K; Fourmy, Emily E; Phebus, Jeffrey G

2016-01-01

The aim of this case report and in vitro investigation was to evaluate the marginal microleakage of intact occlusal calculus of primary molars extracted from a special needs patient who received nutrition via a gastric feeding tube. An adolescent with a history of developmental disturbance presented for routine dental care in a hospital facility. Prophylaxis was performed, and 2 mandibular permanent molars were restored. Five primary molars were extracted due to mobility and delayed retention. Heavy deposits of intact calculus were present on the occlusal surfaces of the primary teeth. The extracted teeth were immersed in methylene blue dye solution, invested in acrylic resin, sectioned into blocks, and photographed at 20× and 40× magnification. Previously photographed calculus-free molars with pit and fissure sealants were reviewed and served as contrasting "restorations." The occlusal calculus on the primary teeth extracted from the patient absorbed the dye, while the comparison teeth containing pit and fissure sealants exhibited varying degrees of marginal dye penetration (microleakage). No marginal microleakage was noted in the calculus specimens, indicating that this substrate may serve as a "natural" occlusal surface sealant and that its removal from occlusal surfaces during routine oral prophylaxis may be unnecessary.

Beyond food: The multiple pathways for inclusion of materials into ancient dental calculus.

PubMed

Radini, Anita; Nikita, Efthymia; Buckley, Stephen; Copeland, Les; Hardy, Karen

2017-01-01

Dental calculus (mineralized dental plaque) was first recognised as a potentially useful archaeological deposit in the 1970s, though interest in human dental calculus as a resource material has increased sharply in the past few years. The majority of recent research has focused on the retrieval of plant microfossils embedded in its matrix and interpretation of these finds as largely the result of deliberate consumption of plant-derived food. However, while most of the material described in published works does represent food, dental calculus is in fact a "depositional environment" as material can enter the mouth from a range of sources. In this respect, it therefore represents an archaeological deposit that can also contain extensive non-dietary debris. This can comprise a wide variety of cultural and environmental material which reaches the mouth and can become embedded in dental calculus through alternative pathways. Here, we explore the human behaviors and activities besides eating that can generate a flux of particles into the human mouth, the broad range of additional cultural and environmental information that can be obtained through the analysis and contextualisation of this material, and the implications of the additional pathways by which material can become embedded in dental calculus. © 2017 American Association of Physical Anthropologists.

Ancient DNA analysis of dental calculus.

PubMed

Weyrich, Laura S; Dobney, Keith; Cooper, Alan

2015-02-01

Dental calculus (calcified tartar or plaque) is today widespread on modern human teeth around the world. A combination of soft starchy foods, changing acidity of the oral environment, genetic pre-disposition, and the absence of dental hygiene all lead to the build-up of microorganisms and food debris on the tooth crown, which eventually calcifies through a complex process of mineralisation. Millions of oral microbes are trapped and preserved within this mineralised matrix, including pathogens associated with the oral cavity and airways, masticated food debris, and other types of extraneous particles that enter the mouth. As a result, archaeologists and anthropologists are increasingly using ancient human dental calculus to explore broad aspects of past human diet and health. Most recently, high-throughput DNA sequencing of ancient dental calculus has provided valuable insights into the evolution of the oral microbiome and shed new light on the impacts of some of the major biocultural transitions on human health throughout history and prehistory. Here, we provide a brief historical overview of archaeological dental calculus research, and discuss the current approaches to ancient DNA sampling and sequencing. Novel applications of ancient DNA from dental calculus are discussed, highlighting the considerable scope of this new research field for evolutionary biology and modern medicine. Copyright © 2014 Elsevier Ltd. All rights reserved.

Analysis of root surface properties by fluorescence/Raman intensity ratio.

PubMed

Nakamura, Shino; Ando, Masahiro; Hamaguchi, Hiro-O; Yamamoto, Matsuo

2017-11-01

The aim of this study is to evaluate the existence of residual calculus on root surfaces by determining the fluorescence/Raman intensity ratio. Thirty-two extracted human teeth, partially covered with calculus on the root surface, were evaluated by using a portable Raman spectrophotometer, and a 785-nm, 100-mW laser was applied for fluorescence/Raman excitation. The collected spectra were normalized to the hydroxyapatite Raman band intensity at 960 cm -1 . Raman spectra were recorded from the same point after changing the focal distance of the laser and the target radiating angle. In seven teeth, the condition of calculus, cementum, and dentin were evaluated. In 25 teeth, we determined the fluorescence/Raman intensity ratio following three strokes of debridement. Raman spectra collected from the dentin, cementum, and calculus were different. After normalization, spectra values were constant. The fluorescence/Raman intensity ratio of calculus region showed significant differences compared to the cementum and dentin (p < 0.05). The fluorescence/Raman intensity ratio decreased with calculus debridement. For this analysis, the delta value was defined as the difference between the values before and after three strokes, with the final 2 delta values close to zero, indicating a gradual asymptotic curve and the change in intensity ratio approximating that of individual constants. Fluorescence/Raman intensity ratio was effectively used to cancel the angle- and distance-dependent fluctuations of fluorescence collection efficiency during measurement. Changes in the fluorescence/Raman intensity ratio near zero suggested that cementum or dentin was exposed, and calculus removed.

The dental calculus metabolome in modern and historic samples.

PubMed

Velsko, Irina M; Overmyer, Katherine A; Speller, Camilla; Klaus, Lauren; Collins, Matthew J; Loe, Louise; Frantz, Laurent A F; Sankaranarayanan, Krithivasan; Lewis, Cecil M; Martinez, Juan Bautista Rodriguez; Chaves, Eros; Coon, Joshua J; Larson, Greger; Warinner, Christina

2017-01-01

Dental calculus is a mineralized microbial dental plaque biofilm that forms throughout life by precipitation of salivary calcium salts. Successive cycles of dental plaque growth and calcification make it an unusually well-preserved, long-term record of host-microbial interaction in the archaeological record. Recent studies have confirmed the survival of authentic ancient DNA and proteins within historic and prehistoric dental calculus, making it a promising substrate for investigating oral microbiome evolution via direct measurement and comparison of modern and ancient specimens. We present the first comprehensive characterization of the human dental calculus metabolome using a multi-platform approach. Ultra performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) quantified 285 metabolites in modern and historic (200 years old) dental calculus, including metabolites of drug and dietary origin. A subset of historic samples was additionally analyzed by high-resolution gas chromatography-MS (GC-MS) and UPLC-MS/MS for further characterization of metabolites and lipids. Metabolite profiles of modern and historic calculus were compared to identify patterns of persistence and loss. Dipeptides, free amino acids, free nucleotides, and carbohydrates substantially decrease in abundance and ubiquity in archaeological samples, with some exceptions. Lipids generally persist, and saturated and mono-unsaturated medium and long chain fatty acids appear to be well-preserved, while metabolic derivatives related to oxidation and chemical degradation are found at higher levels in archaeological dental calculus than fresh samples. The results of this study indicate that certain metabolite classes have higher potential for recovery over long time scales and may serve as appropriate targets for oral microbiome evolutionary studies.

Anti-calculus activity of a toothpaste with microgranules.

PubMed

Chesters, R K; O'Mullane, D M; Finnerty, A; Huntington, E; Jones, P R

1998-09-01

The objective of the trial was to determine the efficacy of the proven anticalculus active system (zinc citrate trihydrate [ZCT] and triclosan), when the ZCT is delivered from microgranules incorporated in a silica-based toothpaste containing 1450 ppm F as sodium fluoride. A monadic, single-blind, two phase design clinical trial was used to compare the effect of the test and a negative control fluoridated toothpaste on the formation of supragingival calculus. Male and female calculus-forming volunteers, aged 18 or over, were recruited for the study following a 2-week screening phase. All subjects were given a scale and polish of their eight lower anterior teeth at the start of both the pre-test and test phases. Subjects were supplied with a silica-based 1450 F ppm fluoridated toothpaste with no anti-calculus active for use during an 8-week pre-test phase. Calculus was assessed at the end of the pre-test and test phases using the Volpe-Manhold index (VMI). Subjects were stratified according to their pre-test VMI score (8-10, 10.5-12, > 12) and gender and then allocated at random to test or negative control toothpaste groups. Subjects with < 8 mm of calculus were excluded from further participation. The outcome variable was the mean VMI score for the test and negative control groups. The test toothpaste caused a statistically significant 30% reduction in calculus compared with the control paste after a 13-week use. No adverse events were reported during the study. The incorporation of the ZCT in microgranules did not adversely affect the anticalculus activity of the new formulation.

An Introduction to Lagrangian Differential Calculus.

ERIC Educational Resources Information Center

Schremmer, Francesca; Schremmer, Alain

1990-01-01

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Study Modules for Calculus-Based General Physics. [Includes Modules 18-20: Sound; Temperature, Heat, and Thermodynamics: First Law; and Kinetic Theory of Gases].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Study Modules for Calculus-Based General Physics. [Includes Modules 31-34: Inductance; Wave Properties of Light; Interference; and Introduction to Quantum Physics].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is Part of a series of 41 Calculus Based Physics (CBP) modules totaling about 1,000 Pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized courses in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Dental Calculus and the Evolution of the Human Oral Microbiome.

PubMed

Warinner, Christina

2016-07-01

Characterizing the evolution of the oral microbiome is a challenging, but increasingly feasible, task. Recently, dental calculus has been shown to preserve ancient biomolecules from the oral microbiota, host tissues and diet for tens of thousands of years. As such, it provides a unique window into the ancestral oral microbiome. This article reviews recent advancements in ancient dental calculus research and emerging insights into the evolution and ecology of the human oral microbiome.

Fisher information, Borges operators, and q-calculus

NASA Astrophysics Data System (ADS)

Pennini, F.; Plastino, A.; Ferri, G. L.

2008-10-01

We discuss applying the increasingly popular q-calculus, or deformed calculus, so as to suitably generalize Fisher’s information measure and the Cramer-Rao inequality. A q-deformation can be attained in multiple ways, and we show that most of them do not constitute legitimate procedures. Within such a context, the only completely acceptable q-deformation is that ensuing from using the so-called Borges derivative [E.P. Borges, Physica A 340 (2004) 95].

Ureterolithotripsy for a Ureteral Calculus at the Ureteroureterostomy of a Renal-transplant Recipient.

PubMed

Mitsui, Yosuke; Wada, Koichiro; Araki, Motoo; Yoshioka, Takashi; Ariyoshi, Yuichi; Nishimura, Shingo; Kobayashi, Yasuyuki; Sasaki, Katsumi; Watanabe, Toyohiko; Nasu, Yasutomo

2017-10-01

We describe a 40-year-old living-donor renal-transplant recipient who underwent successful ureterolithotripsy. He had been on hemodialysis for >15 years pre-transplant and underwent ureteroureterostomy along with the surgery. One year post-transplant, ultrasound examination demonstrated hydronephrosis, and CT showed a 6-mm ureteral calculus at the ureteroureterostomy site. No pain and no elevated serum creatinine were present. As the ureter was easily accessed, we performed a ureterolithotripsy, which would confirm whether a suture caused the calculus. Despite ureteral tortuosity, laser stone fragmentation succeeded. The calculus was completely removed with an antegrade guidewire. Mild postoperative ureteral stenosis resolved with a temporary ureteral stent without balloon dilation. Ureterolithotripsy is effective even in renal transplant recipients with ureteroureterostomy.

Laser ablation of dental calculus at 400 nm using a Ti:sapphire laser

NASA Astrophysics Data System (ADS)

Schoenly, Joshua E.; Seka, Wolf; Rechmann, Peter

2009-02-01

A Nd:YAG laser-pumped, frequency-doubled Ti:sapphire laser is used for selective ablation of calculus. The laser provides <=25 mJ at 400 nm (60-ns pulse width, 10-Hz repetition rate). The laser is coupled into an optical multimode fiber coiled around a 4-in.-diam drum to generate a top-hat output intensity profile. With coaxial water cooling, this is ideal for efficient, selective calculus removal. This is in stark contrast with tightly focused Gaussian beams that are energetically inefficient and lead to irreproducible results. Calculus is well ablated at high fluences >=2J/cm2 stalling occurs below this fluence because of photobleaching. Healthy hard tissue is not removed at fluences <=3 J/cm2.

Projectile motion without calculus

NASA Astrophysics Data System (ADS)

Rizcallah, Joseph A.

2018-07-01

Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are kept at a fairly elementary level, some, such as determining the safe domain, involve not so elementary techniques, which can hardly be assumed of the targeted audience. In the literature, several attempts have been undertaken to avoid calculus altogether and keep the exposition entirely within the realm of algebra and/or geometry. In this paper, we propose yet another non-calculus approach which uses the projectile’s travel times to shed new light on these problems and provide instructors with an alternate method to address them with their students.

Pre- and Post-Conditions Expressed in Variants of the Modal µ-Calculus

NASA Astrophysics Data System (ADS)

Tanabe, Yoshinori; Sekizawa, Toshifusa; Yuasa, Yoshifumi; Takahashi, Koichi

Properties of Kripke structures can be expressed by formulas of the modal µ-calculus. Despite its strong expressive power, the validity problem of the modal µ-calculus is decidable, and so are some of its variants enriched by inverse programs, graded modalities, and nominals. In this study, we show that the pre- and post-conditions of transformations of Kripke structures, such as addition/deletion of states and edges, can be expressed using variants of the modal µ-calculus. Combined with decision procedures we have developed for those variants, the properties of sequences of transformations on Kripke structures can be deduced. We show that these techniques can be used to verify the properties of pointer-manipulating programs.

The giant calculus within the prostatic urethra.

PubMed

Demir, Omer; Kefi, Aykut; Cahangirov, Asif; Cihan, Ahmet; Obuz, Funda; Esen, Adil Ahmet; Celebi, Ilhan

2011-08-01

The giant calculus within the prostatic urethra is a rare clinical entity in the young population. Most of the calculi within the urethra migrate from the urinary bladder and obliterate the urethra. These stones are often composed of calcium phosphate or calcium oxalate. The decision of treatment strategy is affected by the size, shape and position of the calculus and by the status of the urethra. If the stone is large and immovable, it may be extracted via the perineal or the suprapubic approach. In most cases, the giant calculi were extracted via the transvesical approach and external urethrotomy. Our case is the biggest prostatic calculus, known in the literature so far, which was treated endoscopically by the combination of laser and the pneumatic lithotriptor.

Prevalence of gingivitis and calculus in 12-year-old Puerto Ricans: a cross-sectional study.

PubMed

Elias-Boneta, Augusto R; Ramirez, Karol; Rivas-Tumanyan, Sona; Murillo, Margarita; Toro, Milagros J

2018-01-19

Gingivitis is a common oral health problem. Untreated gingivitis may progress to periodontitis, a common cause of tooth loss. The prevalence of gingivitis and calculus among Puerto Rican children is unknown. Understanding this prevalence can support early public health preventative strategies. This study aims to estimate the prevalence of gingivitis and calculus among 12-year-old Puerto Ricans by health region and to explore differences in distribution by school type (proxy for socio-economic status) and gender. A probability-based sample of 113 schools was selected proportional to enrollment size and stratified by health region, school type, and gender. Two trained examiners evaluated the presence of gingivitis and both supragingival and subgingival dental calculus. Gingivitis was defined as the presence of gingival bleeding upon gentle probing (BOP) in at least one site, and the extent of the problem was classified according to the percentage of teeth whose gingiva presented BOP (limited: 25-49% of the teeth tested; extensive: >50% of teeth tested). Logistic and linear regression models, adjusted for health regions, were used to compare gingivitis and calculus prevalence and extent between genders and school types. Gingivitis was found in 80.41% of the 1586 children evaluated. Urban-public schoolchildren had a slightly higher prevalence (83.24%) compared to private (79.15%, p = 0.16); those in rural-public (77.59%) and private schools had similar prevalence (p = 0.15). Extensive gingivitis was present in 60.81% of all children. The mean percentage of sites presenting BOP (BOP%) was 17.79%. Rural and urban public schoolchildren presented significantly higher BOP% compared to children from private schools (p = 0.0005, p = 0.002, respectively). Dental calculus was detected in 61.59% of the sample, boys presenting significantly higher (p = 0.005) total and supragingival calculus. Rural-public schoolchildren had a significantly higher prevalence of subgingival calculus compared to private schoolchildren (p = 0.02). Gingivitis prevalence is higher among 12-year-old Puerto Ricans compared to data reported for U.S. adolescents. Public schoolchildren presented significantly higher BOP% sites compared to private schoolchildren. Boys presented a significantly higher total and supragingival calculus prevalence than girls. Oral health disparities related to gender and school type were identified by this study. Studies exploring the reasons for these disparities are recommended.

Women 1.5 Times More Likely to Leave STEM Pipeline after Calculus Compared to Men: Lack of Mathematical Confidence a Potential Culprit.

PubMed

Ellis, Jessica; Fosdick, Bailey K; Rasmussen, Chris

2016-01-01

The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this pathway and has been shown to often dissuade people from pursuing STEM fields. We examine the characteristics of students who begin college interested in STEM and either persist or switch out of the calculus sequence after taking Calculus I, and hence either continue to pursue a STEM major or are dissuaded from STEM disciplines. The data come from a unique, national survey focused on mainstream college calculus. Our analyses show that, while controlling for academic preparedness, career intentions, and instruction, the odds of a woman being dissuaded from continuing in calculus is 1.5 times greater than that for a man. Furthermore, women report they do not understand the course material well enough to continue significantly more often than men. When comparing women and men with above-average mathematical abilities and preparedness, we find women start and end the term with significantly lower mathematical confidence than men. This suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that if women persisted in STEM at the same rate as men starting in Calculus I, the number of women entering the STEM workforce would increase by 75%.

Women 1.5 Times More Likely to Leave STEM Pipeline after Calculus Compared to Men: Lack of Mathematical Confidence a Potential Culprit

PubMed Central

Ellis, Jessica; Fosdick, Bailey K.; Rasmussen, Chris

2016-01-01

The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this pathway and has been shown to often dissuade people from pursuing STEM fields. We examine the characteristics of students who begin college interested in STEM and either persist or switch out of the calculus sequence after taking Calculus I, and hence either continue to pursue a STEM major or are dissuaded from STEM disciplines. The data come from a unique, national survey focused on mainstream college calculus. Our analyses show that, while controlling for academic preparedness, career intentions, and instruction, the odds of a woman being dissuaded from continuing in calculus is 1.5 times greater than that for a man. Furthermore, women report they do not understand the course material well enough to continue significantly more often than men. When comparing women and men with above-average mathematical abilities and preparedness, we find women start and end the term with significantly lower mathematical confidence than men. This suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that if women persisted in STEM at the same rate as men starting in Calculus I, the number of women entering the STEM workforce would increase by 75%. PMID:27410262

A double blind randomised controlled clinical trial comparing a novel anti-stain and calculus reducing dentifrice with a standard fluoride dentifrice.

PubMed

Jowett, Adrian K; Marlow, Ian; Rawlinson, Andrew

2013-04-01

This clinical trial tested the anti-stain efficacy at 3 and 6 months of a novel, sodium polyaspartate-containing, anti-stain dentifrice. In addition, the efficacy of the new dentifrice in controlling gingival inflammation and inhibition of calculus deposition was tested. Participants were recruited to this double blind randomised control clinical trial, and allocated to either test or control groups. The presence of stain and calculus were entry criteria. Measurements of stain, calculus and gingival inflammation were recorded using the Shaw and Murray Stain score, Volpe-Manhold Calculus score and the Modified Gingival Index respectively. Measurements were made at baseline, prior to the removal of stain and calculus, and after 3 and 6 months. Missing data were imputed by and the outcomes were analysed using univariate analysis. At three months, toothpaste containing sodium polyaspartate was better (difference of mean 1.13 with SEM 0.57) than control for the control of dental stain (p<0.05). Stain scores also showed a trend in favour of the test product (difference of mean 1.03 with SEM 0.78) at six months (p>0.05). There was no difference between toothpastes with respect to calculus deposition or gingival inflammation. Toothpaste containing sodium polyaspartate was more effective than a control toothpaste at preventing deposition of dental stain for 3 months after professional tooth cleaning but showed no significant effect at 6 months. Sodium polyaspartate toothpaste was more effective than a control toothpaste at preventing dental stain formation and maybe helpful in controlling staining between episodes of scaling and polishing. Copyright © 2012 Elsevier Ltd. All rights reserved.

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

NASA Astrophysics Data System (ADS)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

On the geometry of inhomogeneous quantum groups

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aschieri, Paolo

1998-01-01

The author gives a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case. He further analyzes the relation between differential calculus and quantum Lie algebra of left (right) invariant vectorfields. Equivalent definitions of bicovariant differential calculus are studied and their geometrical interpretation is explained. From these data he constructs and analyzes the space of vectorfields, and naturally introduces a contraction operator and a Lie derivative. Their properties are discussed.

A Default Temporal Logic for Regulatory Conformance Checking

DTIC Science & Technology

2008-04-01

proofs. In Section 4.3, we provide an axiomatization using Fitting’s sequent calculus [25]. Completeness is proved in Section 4.4. We conclude, in...axiomatize RefL. 4.3 Sequent Calculus We use Fitting’s sequent calculus [25]. A sequent is a statement of the form Γ → ∆, where Γ and ∆ are finite sets of...T.D., Vail, M.W., Anton , A.I.: Towards regulatory compliance: Extracting rights and obligations to align requirements with regulations. In

Generalized Cartan Calculus in general dimension

DOE PAGES

Wang, Yi -Nan

2015-07-22

We develop the generalized Cartan Calculus for the groups G = SL(2,R) × R +, SL(5,R) and SO(5,5). They are the underlying algebraic structures of d=9,7,6 exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincar\\'e lemmas in this new differential geometry is also discussed. Lastly, we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.

Some problems in fractal differential equations

NASA Astrophysics Data System (ADS)

Su, Weiyi

2016-06-01

Based upon the fractal calculus on local fields, or p-type calculus, or Gibbs-Butzer calculus ([1],[2]), we suggest a constructive idea for "fractal differential equations", beginning from some special examples to a general theory. However, this is just an original idea, it needs lots of later work to support. In [3], we show example "two dimension wave equations with fractal boundaries", and in this note, other examples, as well as an idea to construct fractal differential equations are shown.

Study Modules for Calculus-Based General Physics. [Includes Modules 21-23: Second Law and Entropy; Coulomb's Law and the Electric Field; and Flux and Gauss' Law].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Hermeneutics of differential calculus in eighteenth-century northern Germany.

PubMed

Blanco, Mónica

2008-01-01

This paper applies comparative textbook analysis to studying the mathematical development of differential calculus in northern German states during the eighteenth century. It begins with describing how the four textbooks analyzed presented the foundations of calculus and continues with assessing the influence each of these foundational approaches exerted on the resolution of problems, such as the determination of tangents and extreme values, and even on the choice of coordinates for both algebraic and transcendental curves.

Discrete Calculus as a Bridge between Scales

NASA Astrophysics Data System (ADS)

Degiuli, Eric; McElwaine, Jim

2012-02-01

Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310

The Profit Motive: The Bane of Mathematics Education.

ERIC Educational Resources Information Center

Koblitz, Neal

1992-01-01

Discusses the lack of calculus textbook improvements even though there have been complaints about them from students and professors. Argues against using commercial textbooks in calculus instruction. (ASK)

Laser Ablation of Dental Calculus Around 400 nm Using a Ti:Sapphire Laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schoenly, J.; Seka, W.; Rechmann, P.

2009-10-19

A Nd:YAG laser-pumped, frequency-doubled Ti:sapphire laser is used for selective ablation of calculus. The laser provides ≤25 mJ at 400 nm (60-ns pulse width, 10-Hz repetition rate). The laser is coupled into an optical multimode fiber coiled around a 4-in.-diam drum to generate a top-hat output intensity profile. With coaxial water cooling, this is ideal for efficient, selective calculus removal. This is in stark contrast with tightly focused Gaussian beams that are energetically inefficient and lead to irreproducible results. Calculus is well ablated at high fluences ≥2 J/cm^2; stalling occurs below this fluence because of photobleaching. Healthy hard tissue ismore » not removed at fluences ≤3 J/cm^2.« less

A Tutorial Review on Fractal Spacetime and Fractional Calculus

NASA Astrophysics Data System (ADS)

He, Ji-Huan

2014-11-01

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

Critical Analysis of the Mathematical Formalism of Theoretical Physics. II. Foundations of Vector Calculus

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2014-03-01

A critical analysis of the foundations of standard vector calculus is proposed. The methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is proved that the vector calculus is incorrect theory because: (a) it is not based on a correct methodological basis - the unity of formal logic and of rational dialectics; (b) it does not contain the correct definitions of ``movement,'' ``direction'' and ``vector'' (c) it does not take into consideration the dimensions of physical quantities (i.e., number names, denominate numbers, concrete numbers), characterizing the concept of ''physical vector,'' and, therefore, it has no natural-scientific meaning; (d) operations on ``physical vectors'' and the vector calculus propositions relating to the ''physical vectors'' are contrary to formal logic.

Means and Variances without Calculus

ERIC Educational Resources Information Center

Kinney, John J.

2005-01-01

This article gives a method of finding discrete approximations to continuous probability density functions and shows examples of its use, allowing students without calculus access to the calculation of means and variances.

Stochastic Calculus and Differential Equations for Physics and Finance

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2013-02-01

1. Random variables and probability distributions; 2. Martingales, Markov, and nonstationarity; 3. Stochastic calculus; 4. Ito processes and Fokker-Planck equations; 5. Selfsimilar Ito processes; 6. Fractional Brownian motion; 7. Kolmogorov's PDEs and Chapman-Kolmogorov; 8. Non Markov Ito processes; 9. Black-Scholes, martingales, and Feynman-Katz; 10. Stochastic calculus with martingales; 11. Statistical physics and finance, a brief history of both; 12. Introduction to new financial economics; 13. Statistical ensembles and time series analysis; 14. Econometrics; 15. Semimartingales; References; Index.

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Geometric constrained variational calculus. II: The second variation (Part I)

NASA Astrophysics Data System (ADS)

Massa, Enrico; Bruno, Danilo; Luria, Gianvittorio; Pagani, Enrico

2016-10-01

Within the geometrical framework developed in [Geometric constrained variational calculus. I: Piecewise smooth extremals, Int. J. Geom. Methods Mod. Phys. 12 (2015) 1550061], the problem of minimality for constrained calculus of variations is analyzed among the class of differentiable curves. A fully covariant representation of the second variation of the action functional, based on a suitable gauge transformation of the Lagrangian, is explicitly worked out. Both necessary and sufficient conditions for minimality are proved, and reinterpreted in terms of Jacobi fields.

One Answer to "What Is Calculus?"

ERIC Educational Resources Information Center

Shilgalis, Thomas W.

1979-01-01

A number of questions are posed that can be answered with the aid of calculus. These include best value problems, best shape problems, problems involving integration, and growth and decay problems. (MP)

Catwalk: First-Semester Calculus.

ERIC Educational Resources Information Center

Speiser, Bob; Walter, Chuck

1994-01-01

Describes the use of time-lapse photographs of a running cat as a model to investigate the concepts of function and derivative in a college calculus course. Discusses student difficulties and implications for teachers. (MKR)

Limit Interchange and L'Hopital's Rule

ERIC Educational Resources Information Center

Ecker, Michael W.

2011-01-01

Conventional application of these two calculus staples is stretched here, somewhat recreationally, but also to raise solid questions about the role of limit interchange in analysis--without, however, delving any deeper than first-year Calculus.

A Discrete Approach to Computer-Oriented Calculus.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

1979-01-01

Some of the implications and advantages of an instructional approach using results from the calculus of finite differences and finite sums, both for motivation and as tools leading to applications, are discussed. (MP)

Case Study: Students’ Symbolic Manipulation in Calculus Among UTHM Students

NASA Astrophysics Data System (ADS)

Ali, Maselan; Sufahani, Suliadi; Ahmad, Wan N. A. W.; Ghazali Kamardan, M.; Saifullah Rusiman, Mohd; Che-Him, Norziha

2018-04-01

Words are symbols representing certain aspects of mathematics. The main purpose of this study is to gain insight into students’ symbolic manipulation in calculus among UTHM students. This study make use the various methods in collecting data which are documentation, pilot study, written test and follow up individual interviews. Hence, the results analyzed and interpreted based on action-process-object-schema framework which is based on Piaget’s ideas of reflective abstraction, the concept of relational and instrumental understanding and the zone of proximal development idea. The students’ reply in the interview session is analyzed and then the overall performance is discussed briefly to relate with the students flexibility in symbolic manipulation in linking to the graphical idea, the students interpretation towards different symbolic structure in calculus and the problem that related to overgeneralization in their calculus problems solving.

Vector calculus in non-integer dimensional space and its applications to fractal media

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-02-01

We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

Surface area and volume determination of subgingival calculus using laser fluorescence.

PubMed

Shakibaie, Fardad; Walsh, Laurence J

2014-03-01

Visible red (655 nm) laser fluorescence (LF) devices are currently used for identifying deposits of subgingival calculus on the root surfaces of teeth during dental examination and treatment; however, it is not known how the fluorescence readings produced by commercially available LF systems correlate to the nature of the deposits. This laboratory study explored the correlation between LF digital readings and the surface area and volume of subgingival calculus deposits on teeth. A collection of 30 extracted human posterior teeth with various levels of subgingival deposits of calculus across 240 sites were used in a clinical simulation, with silicone impression material used to replicate periodontal soft tissues. The teeth were scored by two examiners by using three commercial LF systems (DIAGNOdent, DIAGNOdent Pen and KEY3). The silicone was removed, and the teeth were removed for photography at × 20 magnification under white or ultraviolet light. The surface area, thickness, and volume were calculated, and both linear least squares regression and nonlinear (Spearman's rank method) correlation coefficients were determined. Visible red LF digital readings showed better correlation to calculus volume than to surface area. Overall, the best performance was found for the KEY3 system (Spearman coefficient 0.59), compared to the Classic DIAGNOdent (0.56) and the DIAGNOdent Pen (0.49). These results indicate that while visible red LF systems vary somewhat in performance, their LF readings provide a useful estimation of the volume of subgingival calculus deposits present on teeth.

A clinical investigation of the efficacy of two dentifrices for the reduction of supragingival calculus formation.

PubMed

Schiff, Thomas; Delgado, Evaristo; DeVizio, William; Proskin, Howard M

2008-01-01

The objective of this double-blind clinical study, conducted in harmony with Volpe-Manhold design for studies of dental calculus, was to compare the efficacy of a dentifrice containing 0.3% triclosan/2.0% polyvinylmethyl ether/maleic acid (PVM/MA) copolymer/0.243% sodium fluoride in a 17% dual silica base (Colgate Total Advanced Toothpaste) to that of a commercially available dentifrice containing 0.243% sodium fluoride in a silica base (Crest Cavity Protection Toothpaste) with respect to the reduction of supragingival calculus formation. Adult male and female subjects from the San Francisco area were entered into the eight-week pre-test phase of the study. Subjects received an evaluation of oral soft and hard tissues and were given a complete oral prophylaxis. They were provided with a non-tartar control placebo dentifrice and a soft-bristled adult toothbrush, and were instructed to brush their teeth twice daily (morning and evening) for one minute. After eight weeks of using the placebo dentifrice, subjects were examined for baseline supragingival calculus formation using the Volpe-Manhold Calculus Index. Qualifying subjects were randomized into two treatment groups which were balanced for gender and baseline calculus scores. All subjects entered into the twelve-week test phase were given a complete oral prophylaxis, and were provided with their assigned dentifrice and a soft-bristled adult toothbrush for home use. Subjects were instructed to brush their teeth for one minute twice daily (in the morning and evening). Prior to each study visit, subjects refrained from brushing their teeth and eating and drinking for four hours. Seventy-seven (77) subjects complied with the protocol and completed the study. At the twelve-week examination, the Test Dentifrice group presented a mean Volpe-Manhold Calculus Index score of 13.22 and the Control Dentifrice group presented a score of 20.29. After twelve weeks of product use, the Test Dentifrice group exhibited 34.8% less supragingival calculus formation than the Control Dentifrice group (statistically significant at p < 0.05). The overall results of this double-blind clinical study support the conclusion that after twelve weeks' use of a dentifrice containing 0.3% triclosan/2.0% PVM/MA copolymer/0.243% sodium fluoride in a 17% dual silica base provides significantly greater control of supragingival calculus formation relative to that of a commercially available dentifrice containing 0.243% sodium fluoride in a silica base.

Enabling quaternion derivatives: the generalized HR calculus

PubMed Central

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C.; Mandic, Danilo P.

2015-01-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis. PMID:26361555

Enabling quaternion derivatives: the generalized HR calculus.

PubMed

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C; Mandic, Danilo P

2015-08-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis.

Fluorescence properties of human teeth and dental calculus for clinical applications

NASA Astrophysics Data System (ADS)

Lee, Yong-Keun

2015-04-01

Fluorescent emission of human teeth and dental calculus is important for the esthetic rehabilitation of teeth, diagnosis of dental caries, and detection of dental calculus. The purposes of this review were to summarize the fluorescence and phosphorescence of human teeth by ambient ultraviolet (UV) light, to investigate the clinically relevant fluorescence measurement methods in dentistry, and to review the fluorescence of teeth and dental calculus by specific wavelength light. Dentine was three times more phosphorescent than enamel. When exposed to light sources containing UV components, the fluorescence of human teeth gives them the quality of vitality, and fluorescent emission with a peak of 440 nm is observed. Esthetic restorative materials should have fluorescence properties similar to those of natural teeth. Based on the fluorescence of teeth and restorative materials as determined with a spectrophotometer, a fluorescence parameter was defined. As to the fluorescence spectra by a specific wavelength, varied wavelengths were investigated for clinical applications, and several methods for the diagnosis of dental caries and the detection of dental calculus were developed. Since fluorescent properties of dental hard tissues have been used and would be expanded in diverse fields of clinical practice, these properties should be investigated further, embracing newly developed optical techniques.

Dental calculus is associated with death from heart infarction.

PubMed

Söder, Birgitta; Meurman, Jukka H; Söder, Per-Östen

2014-01-01

We studied whether the amount of dental calculus is associated with death from heart infarction in the dental infection-atherosclerosis paradigm. Participants were 1676 healthy young Swedes followed up from 1985 to 2011. At the beginning of the study all subjects underwent oral clinical examination including dental calculus registration scored with calculus index (CI). Outcome measure was cause of death classified according to WHO International Classification of Diseases. Unpaired t-test, Chi-square tests, and multiple logistic regressions were used. Of the 1676 participants, 2.8% had died during follow-up. Women died at a mean age of 61.5 years and men at 61.7 years. The difference in the CI index score between the survivors versus deceased patients was significant by the year 2009 (P < 0.01). In multiple regression analysis of the relationship between death from heart infarction as a dependent variable and CI as independent variable with controlling for age, gender, dental visits, dental plaque, periodontal pockets, education, income, socioeconomic status, and pack-years of smoking, CI score appeared to be associated with 2.3 times the odds ratio for cardiac death. The results confirmed our study hypothesis by showing that dental calculus indeed associated statistically with cardiac death due to infarction.

Fluorescence properties of human teeth and dental calculus for clinical applications.

PubMed

Lee, Yong-Keun

2015-04-01

Fluorescent emission of human teeth and dental calculus is important for the esthetic rehabilitation of teeth, diagnosis of dental caries, and detection of dental calculus. The purposes of this review were to summarize the fluorescence and phosphorescence of human teeth by ambient ultraviolet (UV) light, to investigate the clinically relevant fluorescence measurement methods in dentistry, and to review the fluorescence of teeth and dental calculus by specific wavelength light. Dentine was three times more phosphorescent than enamel. When exposed to light sources containing UV components, the fluorescence of human teeth gives them the quality of vitality, and fluorescent emission with a peak of 440 nm is observed. Esthetic restorative materials should have fluorescence properties similar to those of natural teeth. Based on the fluorescence of teeth and restorative materials as determined with a spectrophotometer, a fluorescence parameter was defined. As to the fluorescence spectra by a specific wavelength, varied wavelengths were investigated for clinical applications, and several methods for the diagnosis of dental caries and the detection of dental calculus were developed. Since fluorescent properties of dental hard tissues have been used and would be expanded in diverse fields of clinical practice, these properties should be investigated further, embracing newly developed optical techniques.

Selective near-UV ablation of subgingival dental calculus: measurement of removal rates

NASA Astrophysics Data System (ADS)

Schoenly, J. E.; Seka, W.; Rechmann, P.

2010-02-01

A noncontact profilometer (laser triangulation) was used to measure the removal rates of subgingival dental calculus irradiated with a frequency-doubled Ti:sapphire laser (60-ns pulse duration, 400-nm wavelength, 10-Hz repetition rate, 7-mJ pulse energy). Profilometer traces before and after irradiation were used to create a removal map with 4-μm axial and 15-μm transverse resolution. Twenty-three teeth (15 with calculus and 8 pristine) were irradiated at 90° and 45° under a cooling water spray with a super-Gaussian beam (~300-μm diameter). Subgingival calculus was selectively removed at 5.6 and 4.0 J/cm2 for 90° and 45°, respecetively, within a range of rates, between 2 to 9 μm/pulse. These ablation rates were constant during these exposures. For comparison, pristine cementum irradiated for 10 min at the same peak fluence and pulse repetition rate showed only craters, 15 to 50 μm deep, corresponding to an equivalent removal rate three orders of magnitude smaller than that obtained for calculus. Pristine enamel was not removed under the same irradiation conditions.

Electron microscopy of octacalcium phosphate in the dental calculus.

PubMed

Kakei, Mitsuo; Sakae, Toshiro; Yoshikawa, Masayoshi

2009-12-01

The purpose of this study was to morphologically demonstrate the presence of octacalcium phosphate in the dental calculus by judging from the crystal lattice image and its rapid transformation into apatite crystal, as part of our serial studies on biomineral products. We also aimed to confirm whether the physical properties of octacalcium phosphate are identical with those of the central dark lines observed in crystals of ordinary calcifying hard tissues. Electron micrographs showed that crystals of various sizes form in the dental calculus. The formation of each crystal seemed to be closely associated with the organic substance, possibly originating from degenerated microorganisms at the calcification front. Many crystals had an 8.2-A lattice interval, similar to that of an apatite crystal. Furthermore, some crystals clearly revealed an 18.7-A lattice interval and were vulnerable to electron bombardment. After electron beam exposure, this lattice interval was quickly altered to about half (i.e. 8.2 A), indicating structural conversion. Consequently, a number of apatite crystals in the dental calculus are possibly created by a conversion mechanism involving an octacalcium phosphate intermediate. However, we also concluded that the calcification process in the dental calculus is not similar to that of ordinary calcifying hard tissues.

Selective Near-UV Ablation of Subgingival Dental Calculus: Measurement of Removal Rates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schoenly, J.E.; Seka, W.; Rechmann, P.

A noncontact profilometer (laser triangulation) was used to measure the removal rates of subgingival dental calculus irradiated with a frequency-doubled Ti:sapphire laser (60-ns pulse duration, 400-nm wavelength, 10-Hz repetition rate, 7-mJ pulse energy). Profilometer traces before and after irradiation were used to create a removal map with 4-μm axial and 15-μm transverse resolution. Twenty-three teeth (15 with calculus and 8 pristine) were irradiated at 90° and 45° under a cooling water spray with a super-Gaussian beam (~300-μm diameter). Subgingival calculus was selectively removed at 5.6 and 4.0 J/cm2 for 90° and 45°, respecetively, within a range of rates, between 2more » to 9 μm/pulse. These ablation rates were constant during these exposures. For comparison, pristine cementum irradiated for 10 min at the same peak fluence and pulse repetition rate showed only craters, 15 to 50 μm deep, corresponding to an equivalent removal rate three orders of magnitude smaller than that obtained for calculus. Pristine enamel was not removed under the same irradiation conditions.« less

Effect of a pre-brush mounthrinse containing triclosan and a copolymer on calculus formation: a three-month clinical study in Thailand.

PubMed

Triratana, T; Kraivaphan, P; Tandhachoon, K; Rustogi, K; Volpe, A R; Petrone, M

1995-01-01

A three-month, double-blind, parallel clinical study was conducted on a population of Thai adults to evaluate the effect of the twice daily use of a commercially available pre-brush mouthrinse on supragingival calculus formation. The mouthrinse test product contained 0.03% triclosan and 0.13% PVM/MA copolymer with the absence of fluoride. The subjects were initially examined for calculus using the Volpe-Manhold procedure. All subjects received an oral prophylaxis and were assigned to the use of either 1) a triclosan-copolymer mouthrinse, or 2) a matching flavored/colored water placebo mouthrinse. Subjects were instructed to rinse twice daily with 10 cc of the assigned mouthrinse for 1 minute, followed by brushing with the provided toothpaste containing fluoride for 45 seconds. After three months of using the assigned mouthrinse, the subjects were reexamined for calculus formation. The results indicated that the subjects using triclosan/copolymer mouthrinse had 23.17% less supragingival calculus than the placebo mouthrinse subjects. This reduction was statistically significant at the 99% or greater (F = 24.35, p<0.001) level of confidence.

Making an Interactive Calculus Textbook.

ERIC Educational Resources Information Center

Larson, Timothy R.

1995-01-01

Presents a case study of the design and production of "Interactive Calculus," an interactive multimedia textbook. Discusses reasons for using multimedia textbooks; what an interactive textbook is; content, organization, graphic design, authoring and composition; and work flow. (AEF)

Cartooning in Algebra and Calculus

ERIC Educational Resources Information Center

Moseley, L. Jeneva

2014-01-01

This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

A Giant Urethral Calculus.

PubMed

Sigdel, G; Agarwal, A; Keshaw, B W

2014-01-01

Urethral calculi are rare forms of urolithiasis. Majority of the calculi are migratory from urinary bladder or upper urinary tract. Primary urethral calculi usually occur in presence of urethral stricture or diverticulum. In this article we report a case of a giant posterior urethral calculus measuring 7x3x2 cm in a 47 years old male. Patient presented with acute retention of urine which was preceded by burning micturition and dribbling of urine for one week. The calculus was pushed in to the bladder through the cystoscope and was removed by suprapubic cystolithotomy.

An intrahepatic calculus superimposed over the right renal shadow: a case of mistaken identity.

PubMed

Learney, Robert M; Shrotri, Nitin

2010-08-01

A 36-year-old Caucasian British woman presented with a classic case of right renal colic. Initial plain abdominal radiography and intravenous urography identified an 8 x 5 mm calculus apparently lying within a right lower pole calyx. Following failed extracorporeal lithotripsy and flexible ureterorenoscopy, cross-sectional imaging revealed a misdiagnosis by superposition of an intrahepatic calculus over the right renal shadow. This case serves to support cross-sectional imaging in the diagnosis of renal calculi. Copyright 2010 Elsevier Inc. All rights reserved.

Mathematics preparation for medical school: do all premedical students need calculus?

PubMed

Nusbaum, Neil J

2006-01-01

The premedical student confronts a disparate set of required and recommended courses from the various medical schools to which the student might apply. Students may feel compelled to take courses such as calculus even though most medical schools do not require it and even though it may not be related to either undergraduate academic plans or the core academic needs of the typical future physician. Basic mathematical knowledge--a knowledge of algebra, statistics, and overall numeracy--are each more important for most future physicians than is the traditional calculus course.

Extreme value problems without calculus: a good link with geometry and elementary maths

NASA Astrophysics Data System (ADS)

Ganci, Salvatore

2016-11-01

Some classical examples of problem solving, where an extreme value condition is required, are here considered and/or revisited. The search for non-calculus solutions appears pedagogically useful and intriguing as shown through a rich literature. A teacher, who teaches both maths and physics, (as happens in Italian High schools) can find in these kinds of problems a mind stimulating exercise compared with the standard solution obtained by the differential calculus. A good link between the geometric and analytical explanations is so established.

ECG artifact cancellation in surface EMG signals by fractional order calculus application.

PubMed

Miljković, Nadica; Popović, Nenad; Djordjević, Olivera; Konstantinović, Ljubica; Šekara, Tomislav B

2017-03-01

New aspects for automatic electrocardiography artifact removal from surface electromyography signals by application of fractional order calculus in combination with linear and nonlinear moving window filters are explored. Surface electromyography recordings of skeletal trunk muscles are commonly contaminated with spike shaped artifacts. This artifact originates from electrical heart activity, recorded by electrocardiography, commonly present in the surface electromyography signals recorded in heart proximity. For appropriate assessment of neuromuscular changes by means of surface electromyography, application of a proper filtering technique of electrocardiography artifact is crucial. A novel method for automatic artifact cancellation in surface electromyography signals by applying fractional order calculus and nonlinear median filter is introduced. The proposed method is compared with the linear moving average filter, with and without prior application of fractional order calculus. 3D graphs for assessment of window lengths of the filters, crest factors, root mean square differences, and fractional calculus orders (called WFC and WRC graphs) have been introduced. For an appropriate quantitative filtering evaluation, the synthetic electrocardiography signal and analogous semi-synthetic dataset have been generated. The examples of noise removal in 10 able-bodied subjects and in one patient with muscle dystrophy are presented for qualitative analysis. The crest factors, correlation coefficients, and root mean square differences of the recorded and semi-synthetic electromyography datasets showed that the most successful method was the median filter in combination with fractional order calculus of the order 0.9. Statistically more significant (p < 0.001) ECG peak reduction was obtained by the median filter application compared to the moving average filter in the cases of low level amplitude of muscle contraction compared to ECG spikes. The presented results suggest that the novel method combining a median filter and fractional order calculus can be used for automatic filtering of electrocardiography artifacts in the surface electromyography signal envelopes recorded in trunk muscles. Copyright © 2017 Elsevier Ireland Ltd. All rights reserved.

Preparing Future College Instructors: The Role of Graduate Student Teaching Assistants (GTAs) in Successful College Calculus Programs

NASA Astrophysics Data System (ADS)

Ellis, Jessica Fabricant

Graduate student Teaching Assistants (GTAs) contribute to calculus instruction in two ways: as the primary teacher and as recitation leaders. GTAs can also be viewed as the next generation of mathematics instructors. Thus, in addition to their immediate contribution to the landscape of Calculus 1 instruction, GTAs will contribute significantly to the long-term state of calculus in their future occupations. However, their preparation for these roles varies widely and is often minimal. In this study, I first compare the mathematical beliefs, instructional practices, and student success of GTAs to other Calculus 1 instructors. I then provide rich descriptions for three GTA professional development (PD) programs that prepare graduate students as course instructors, as recitation leaders, and as future faculty. I then investigate the instructional practices and mathematical beliefs of graduate students coming from these three PD programs. I conclude this work with a description of a framework for GTA-PD programs. To accomplish this work, I conducted a mixed-method analysis on national survey data and case study data from four doctoral granting institutions. These four institutions were chosen because of their higher-than-expected student success in Calculus 1. The results of these analyses indicate that graduate students teach in more innovative ways than other instructors, though their students were less successful. Among the four case study institutions, I identified three models of GTA-PD, each of which appeared successful in accomplishing their goals. These goals included transitioning graduate students into the role of instructor, preparing graduate students to implement an innovative approach to Calculus 1, and supporting graduate students as recitation leaders. These analyses also led to the development of a framework to be used to characterize, evaluate, and consider the implementation of graduate student professional development programs. This GTA-PD framework is thus one of the major contributions put forth by this dissertation.

LOOP CALCULUS AND BELIEF PROPAGATION FOR Q-ARY ALPHABET: LOOP TOWER

DOE Office of Scientific and Technical Information (OSTI.GOV)

CHERTKOV, MICHAEL; CHERNYAK, VLADIMIR

Loop calculus introduced in [1], [2] constitutes a new theoretical tool that explicitly expresses symbol Maximum-A-Posteriori (MAP) solution of a general statistical inference problem via a solution of the Belief Propagation (BP) equations. This finding brought a new significance to the BP concept, which in the past was thought of as just a loop-free approximation. In this paper they continue a discussion of the Loop Calculus, partitioning the results into three Sections. In Section 1 they introduce a new formulation of the Loop Calculus in terms of a set of transformations (gauges) that keeping the partition function of the problemmore » invariant. The full expression contains two terms referred to as the 'ground state' and 'excited states' contributions. The BP equations are interpreted as a special (BP) gauge fixing condition that emerges as a special orthogonality constraint between the ground state and excited states, which also selects loop contributions as the only surviving ones among the excited states. In Section 2 they demonstrate how the invariant interpretation of the Loop Calculus, introduced in Section 1, allows a natural extension to the case of a general q-ary alphabet, this is achieved via a loop tower sequential construction. The ground level in the tower is exactly equivalent to assigning one color (out of q available) to the 'ground state' and considering all 'excited' states colored in the remaining (q-1) colors, according to the loop calculus rule. Sequentially, the second level in the tower corresponds to selecting a loop from the previous step, colored in (q-1) colors, and repeating the same ground vs excited states splitting procedure into one and (q-2) colors respectively. The construction proceeds till the full (q-1)-levels deep loop tower (and the corresponding contributions to the partition function) are established. In Section 3 they discuss an ultimate relation between the loop calculus and the Bethe-Free energy variational approach of [3].« less

Effectiveness of a mouthrinse containing active ingredients in addition to chlorhexidine and triclosan compared with chlorhexidine and triclosan rinses on plaque, gingivitis, supragingival calculus and extrinsic staining.

PubMed

Kumar, S; Patel, S; Tadakamadla, J; Tibdewal, H; Duraiswamy, P; Kulkarni, S

2013-02-01

To assess the effectiveness of three different mouthrinses--chlorhexidine, triclosan + sodium fluoride and chlorhexidine + triclosan + sodium fluoride + zinc chloride--on plaque, calculus, gingivitis and stains and to evaluate the occurrence of adverse effects with these three treatments. Forty-eight healthy subjects participated in a double-blind, randomized, parallel experiment and were randomly allocated to any one of the three experimental mouthrinses: group A (0.2% chlorhexidine (CHX) gluconate), group B (0.03% triclosan + 0.025% sodium fluoride (NaF) + 12% ethyl alcohol) or group C (0.2% CHX + 0.3% triclosan + 0.3% NaF + 0.09% Zn chloride (ZnCl(2)). All the subjects were assessed for gingivitis, plaque, supragingival calculus and extrinsic stains at baseline and at the end of the 21-day experimental period. There was a significant difference (P = 0.046) in the effectiveness for the prevention of gingivitis and plaque, with subjects of group A and group C presenting least and highest gingival and plaque scores, respectively. Significant differences (P = 0.03) were observed for the accumulation of supragingival calculus where the deposition of calculus in group A was nearly double that of the group B, and group B was most effective in the prevention of supragingival calculus. Highest deposition of extrinsic stains was in the group A followed by group C and group B. There was no significant difference between the three treatments for adverse events' occurrence. CHX mouthrinse was most effective in controlling plaque and gingivitis but caused greatest deposition of extrinsic stains. Supragingival calculus deposition was least in triclosan + NaF group followed by CHX + triclosan + NaF + ZnCl(2) and CHX. More than half of the subjects reported adverse events during the experimental phase. © 2012 John Wiley & Sons A/S.

Using Student-Made Games to Learn Mathematics

ERIC Educational Resources Information Center

Gallegos, Irene; Flores, Alfinio

2010-01-01

First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

Forest Carbon Uptake and the Fundamental Theorem of Calculus

ERIC Educational Resources Information Center

Zobitz, John

2013-01-01

Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.

Calculus Student Descending a Staircase.

ERIC Educational Resources Information Center

Mueller, William

1999-01-01

Common student attitudes toward reform methods are conveyed through the thoughts of a student leaving a multivariable calculus exam and musings range over textbooks, homework, workload, group work, writing, noncomputational problems, instructional problems, instructional styles, and classroom activities. (Author/ASK)

Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces

NASA Astrophysics Data System (ADS)

Meljanac, Stjepan; Krešić–Jurić, Saša; Martinić, Tea

2017-07-01

This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra g0, we construct a Lie superalgebra g =g0⊕g1 containing noncommutative coordinates and one-forms. We show that g can be extended by a set of generators TAB whose action on the enveloping algebra U (g ) gives the commutation relations between monomials in U (g0 ) and one-forms. Realizations of noncommutative coordinates, one-forms, and the generators TAB as formal power series in a semicompleted Weyl superalgebra are found. In the special case dim(g0 ) =dim(g1 ) , we also find a realization of the exterior derivative on U (g0 ) . The realizations of these geometric objects yield a bicovariant differential calculus on U (g0 ) as a deformation of the standard calculus on the Euclidean space.

Bacteria and archaea paleomicrobiology of the dental calculus: a review.

PubMed

Huynh, H T T; Verneau, J; Levasseur, A; Drancourt, M; Aboudharam, G

2016-06-01

Dental calculus, a material observed in the majority of adults worldwide, emerged as a source for correlating paleomicrobiology with human health and diet. This mini review of 48 articles on the paleomicrobiology of dental calculus over 7550 years discloses a secular core microbiota comprising nine bacterial phyla - Firmicutes, Actinobacteria, Proteobacteria, Bacteroidetes, TM7, Synergistetes, Chloroflexi, Fusobacteria, Spirochetes - and one archaeal phylum Euryarchaeota; and some accessory microbiota that appear and disappear according to time frame. The diet residues and oral microbes, including bacteria, archaea, viruses and fungi, consisting of harmless organisms and pathogens associated with local and systemic infections have been found trapped in ancient dental calculus by morphological approaches, immunolabeling techniques, isotope analyses, fluorescent in situ hybridization, DNA-based approaches, and protein-based approaches. These observations led to correlation of paleomicrobiology, particularly Streptococcus mutans and archaea, with past human health and diet. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

A probable prehistoric case of meningococcal disease from San Francisco Bay: Next generation sequencing of Neisseria meningitidis from dental calculus and osteological evidence.

PubMed

Eerkens, Jelmer W; Nichols, Ruth V; Murray, Gemma G R; Perez, Katherine; Murga, Engel; Kaijankoski, Phil; Rosenthal, Jeffrey S; Engbring, Laurel; Shapiro, Beth

2018-05-25

Next Generation Sequencing (NGS) of ancient dental calculus samples from a prehistoric site in San Francisco Bay, CA-SCL-919, reveals a wide range of potentially pathogenic bacteria. One older adult woman, in particular, had high levels of Neisseria meningitidis and low levels of Haemophilus influenzae, species that were not observed in the calculus from three other individuals. Combined with the presence of incipient endocranial lesions and pronounced meningeal grooves, we interpret this as an ancient case of meningococcal disease. This disease afflicts millions around the globe today, but little is known about its (pre)history. With additional sampling, we suggest NGS of calculus offers an exciting new window into the evolutionary history of these bacterial species and their interactions with humans. Copyright © 2018 Elsevier Inc. All rights reserved.

Dental wax decreases calculus accumulation in small dogs.

PubMed

Smith, Mark M; Smithson, Christopher W

2014-01-01

A dental wax was evaluated after unilateral application in 20 client-owned, mixed and purebred small dogs using a clean, split-mouth study model. All dogs had clinical signs of periodontal disease including plaque, calculus, and/or gingivitis. The wax was randomly applied to the teeth of one side of the mouth daily for 30-days while the contralateral side received no treatment. Owner parameters evaluated included compliance and a subjective assessment of ease of wax application. Gingivitis, plaque and calculus accumulation were scored at the end of the study period. Owners considered the wax easy to apply in all dogs. Compliance with no missed application days was achieved in 8 dogs. The number of missed application days had no effect on wax efficacy. There was no significant difference in gingivitis or plaque accumulation scores when comparing treated and untreated sides. Calculus accumulation scores were significantly less (22.1 %) for teeth receiving the dental wax.

Quantum Bundle Description of Quantum Projective Spaces

NASA Astrophysics Data System (ADS)

Ó Buachalla, Réamonn

2012-12-01

We realise Heckenberger and Kolb's canonical calculus on quantum projective ( N - 1)-space C q [ C p N-1] as the restriction of a distinguished quotient of the standard bicovariant calculus for the quantum special unitary group C q [ SU N ]. We introduce a calculus on the quantum sphere C q [ S 2 N-1] in the same way. With respect to these choices of calculi, we present C q [ C p N-1] as the base space of two different quantum principal bundles, one with total space C q [ SU N ], and the other with total space C q [ S 2 N-1]. We go on to give C q [ C p N-1] the structure of a quantum framed manifold. More specifically, we describe the module of one-forms of Heckenberger and Kolb's calculus as an associated vector bundle to the principal bundle with total space C q [ SU N ]. Finally, we construct strong connections for both bundles.

Calculation of spontaneous emission from a V-type three-level atom in photonic crystals using fractional calculus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Chih-Hsien; Hsieh, Wen-Feng; Institute of Electro-Optical Science and Engineering, National Cheng Kung University, 1 Dahsueh Rd., Tainan 701, Taiwan

2011-07-15

Fractional time derivative, an abstract mathematical operator of fractional calculus, is used to describe the real optical system of a V-type three-level atom embedded in a photonic crystal. A fractional kinetic equation governing the dynamics of the spontaneous emission from this optical system is obtained as a fractional Langevin equation. Solving this fractional kinetic equation by fractional calculus leads to the analytical solutions expressed in terms of fractional exponential functions. The accuracy of the obtained solutions is verified through reducing the system into the special cases whose results are consistent with the experimental observation. With accurate physical results and avoidingmore » the complex integration for solving this optical system, we propose fractional calculus with fractional time derivative as a better mathematical method to study spontaneous emission dynamics from the optical system with non-Markovian dynamics.« less

Impacted anterior urethral calculus complicated by a stone-containing diverticulum in an elderly man: outcome of transurethral lithotripsy without resection of the diverticulum.

PubMed

Zhou, Tie; Chen, Guanghua; Zhang, Wei; Peng, Yonghan; Xiao, Liang; Xu, Chuangliang; Sun, Yinghao

2013-01-01

The prevalence of lower urinary tract symptoms (LUTS) is about 20% in men aged 40 or above. Other than benign prostatic hyperplasia (BPH), urethral diverticulum or calculus is not uncommon for LUTS in men. Surgical treatment is often recommended for urethral diverticulum or calculus, but treatment for an impacted urethral calculus complicated by a stone-containing diverticulum is challenging. An 82-year-old man had the persistence of LUTS despite having undergone transurethral resection of prostate for BPH. Regardless of treatment with broad spectrum antibiotics and an α-blocker, LUTS and post-void residual urine volume (100 mL) did not improve although repeated urinalysis showed reduction of WBCs from 100 to 10 per high power field. Further radiology revealed multiple urethral calculi and the stone configuration suggested the existence of a diverticulum. He was successfully treated without resecting the urethral diverticulum; and a new generation of ultrasound lithotripsy (EMS, Nyon, Switzerland) through a 22F offset rigid Storz nephroscope (Karl Storz, Tuttingen, Germany) was used to fragment the stones. The operative time was 30 minutes and the stones were cleanly removed. The patient was discharged after 48 hours with no immediate complications and free of LUTS during a 2 years follow-up. When the diverticulum is the result of a dilatation behind a calculus, removal of the calculus is all that is necessary. Compared with open surgery, ultrasound lithotripsy is less invasive with little harm to urethral mucosa; and more efficient as it absorbs stone fragments while crushing stones.

Measurement of efficiency in calculus removal with a frequency-doubled Alexandrite laser on pigs' jaws

NASA Astrophysics Data System (ADS)

Pilgrim, Christian G.; Rechmann, Peter; Goldin, Dan S.; Hennig, Thomas

2000-03-01

Periodontal therapy aims in a most sufficient cleaning of tooth surfaces from supra- and subgingival calculus. As a standard dental procedure teeth are treated with ultrasonic devices. The competence of the frequency doubled Alexandrite laser for a highly effective and selective removal of calculus has been repeatedly proved. Aim of the study presented here was to determine the efficiency at simulated clinical conditions of the frequency doubled Alexandrite laser (laboratory prototype, q-switched, fiber guided, wavelength 377 nm, pulse duration 1 microsecond, pulse repetition rate 70 Hz, water cooling) by quantifying it's calculus removing efficiency. The evaluated data were compared to those obtained with an ultrasonic calculus remover. In the first part of the study sample material consisted of 23 pigs' jaws. They were divided into two groups. The teeth of one group were cleaned on their buccal surfaces using an ultrasonic device (Sonosoft Lux, KaVo, Biberach, Germany; tip #9). Than hand-guided cleaning was performed until no further improvement in cleanness was visible. Cleaning time was measured. Photographic documentation was taken before and after the treatment. The teeth in the second group were cleaned engaging a frequency doubled Alexandrite laser. Treatment time was measured and photographs were taken in the same way. In the second part of the study 21 surfaces of human teeth set up in an artificial pocket model were treated with both systems again. Measurements followed the same protocol. The results strongly support the use of the frequency doubled Alexandrite laser for calculus removal.

PREVALENCE AND ASSOCIATED FACTORS OF DENTAL CARIES, GINGIVITIS, AND CALCULUS DEPOSITS IN SCHOOL CHILDREN OF SARGODHA DISTRICT, PAKISTAN.

PubMed

Umer, Muhammad Farooq; Farooq, Umer; Shabbir, Arham; Zofeen, Shumaila; Mujtaba, Hasan; Tahir, Muhammad

2016-01-01

According to a pathfinder survey conducted by World Health Organization, dental caries is the single most common chronic childhood disease in Pakistan. The update information regarding dental health of school children of Sargodha district is required to plan community caries prevention programs and for better understanding of existing situation, and may improve longevity, treatment, and care. This cross sectional study was conducted in four randomly selected schools of Sargodha district, stratified by gender selected. Two well-trained dentists examined the oral cavities of children for dental caries, gingivitis, and calculus deposits. The sample consisted of children aged between 3-12 years. The overall prevalence rate of gingivitis, calculus, and dental caries was found as 14.5%, 14.3%, and 45.9% respectively. A significant association was found between DMFT score (p < 0.001), gingivitis (p < 0.01), and calculus (p < 0.05) with the increase in age of children. More children living in urban area were detected with gingivitis (p < 0.01), calculus (p < 0.01), and dental caries than children residing in rural areas. Incidence of gingivitis (p < 0.05), calculus, and dental caries in primary (p < 0.001) and permanent teeth were found higher in those children who were not brushing their teeth. Experience of dental caries in primary teeth was found higher (p < 0.01) in children who brushed occasionally. Study also showed that none of the children ever visited dentist for treatment. The results emphasize the need for initiation of awareness programs to achieve 0 DMFT/df scores.

Detection of calculus by laser-induced breakdown spectroscopy (LIBS) using an ultra-short pulse laser system (USPL)

NASA Astrophysics Data System (ADS)

Schelle, F.; Brede, O.; Krueger, S.; Oehme, B.; Dehn, C.; Frentzen, M.; Braun, A.

2011-03-01

The aim of this study was to assess the detection of calculus by Laser Induced Breakdown Spectroscopy (LIBS). The study was performed with an Nd:YVO4 laser, emitting pulses with a duration of 8 ps at a wavelength of 1064 nm. A repetition rate of 500 kHz at an average power of 5 W was used. Employing a focusing lense, intensities of the order of 1011 W/cm2 were reached on the tooth surface. These high intensities led to the generation of a plasma. The light emitted by the plasma was collimated into a fibre and then analyzed by an echelle spectroscope in the wavelength region from 220 nm - 900 nm. A total number of 15 freshly extracted teeth was used for this study. For each tooth the spectra of calculus and cementum were assessed separately. Comprising all single measurements median values were calculated for the whole spectrum, leading to two specific spectra, one for calculus and one for cementum. For further statistical analysis 28 areas of interest were defined as wavelength regions, in which the signal strength differed regarding the material. In 7 areas the intensity of the calculus spectrum differed statistically significant from the intensity of the cementum spectrum (p < 0.05). Thus it can be concluded that Laser Induced Breakdown Spectroscopy is well suited as method for a reliable diagnostic of calculus. Further studies are necessary to verify that LIBS is a minimally invasive method allowing a safe application in laser-guided dentistry.

A transition calculus for Boolean functions. [logic circuit analysis

NASA Technical Reports Server (NTRS)

Tucker, J. H.; Bennett, A. W.

1974-01-01

A transition calculus is presented for analyzing the effect of input changes on the output of logic circuits. The method is closely related to the Boolean difference, but it is more powerful. Both differentiation and integration are considered.

Bridging the Gulf between Formal Calculus and Physical Reasoning.

ERIC Educational Resources Information Center

Van Der Meer, A.

1980-01-01

Some ways to link calculus instruction with the mathematical models used in physics courses are presented. The activity of modelling is presented as a major tool in synchronizing physics and mathematics instruction in undergraduate engineering programs. (MP)

Representations in Calculus: Two Contrasting Cases.

ERIC Educational Resources Information Center

Aspinwall, Leslie; Shaw, Kenneth L.

2002-01-01

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Collaborative Calculus.

ERIC Educational Resources Information Center

Kast, David

1993-01-01

The crisis confronting calculus and mathematics education generally results from a number of failed assumptions implicit in the dominant lecture-homework-exam methodology used in teaching mathematics. Positive resolution of this crisis can be found in adopting a noncompetitive, collaborative approach to mathematics education. (Author)

PREFACE: Fractional Differentiation and its Applications (FDA08) Fractional Differentiation and its Applications (FDA08)

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Tenreiro Machado, J. A.

2009-10-01

The international workshop, Fractional Differentiation and its Applications (FDA08), held at Cankaya University, Ankara, Turkey on 5-7 November 2008, was the third in an ongoing series of conferences dedicated to exploring applications of fractional calculus in science, engineering, economics and finance. Fractional calculus, which deals with derivatives and integrals of any order, is now recognized as playing an important role in modeling multi-scale problems that span a wide range of time or length scales. Fractional calculus provides a natural link to the intermediate-order dynamics that often reflects the complexity of micro- and nanostructures through fractional-order differential equations. Unlike the more established techniques of mathematical physics, the methods of fractional differentiation are still under development; while it is true that the ideas of fractional calculus are as old as the classical integer-order differential operators, modern work is proceeding by both expanding the capabilities of this mathematical tool and by widening its range of applications. Hence, the interested reader will find papers here that focus on the underlying mathematics of fractional calculus, that extend fractional-order operators into new domains, and that apply well established methods to experimental and theoretical problems. The organizing committee invited presentations from experts representing the international community of scholars in fractional calculus and welcomed contributions from the growing number of researchers who are applying fractional differentiation to complex technical problems. The selection of papers in this topical issue of Physica Scripta reflects the success of the FDA08 workshop, with the emergence of a variety of novel areas of application. With these ideas in mind, the guest editors would like to honor the many distinguished scientists that have promoted the development of fractional calculus and, in particular, Professor George M Zaslavsky who supported this special issue but passed away recently. The organizing committee wishes to thank the sponsors and supporters of FDA08, namely Cankaya University represented by the President of the Board of Trustees Sitki Alp and Rector Professor Ziya B Güvenc, The Scientfic and Technological Research Council of Turkey (TUBITAK) and the IFAC for providing the resources needed to hold the workshop, the invited speakers for sharing their expertise and knowledge of fractional calculus, and the participants for their enthusiastic contributions to the discussions and debates.

Experience, gender, and performance: Connecting high school physics experience and gender differences to introductory college physics performance

NASA Astrophysics Data System (ADS)

Tai, Robert H.

Current science educational practice is coming under heavy criticism based on the dismaying results of the Third International Mathematics and Science Study of 1998, the latest in a series of large scale surveys; and from research showing the appallingly low representation of females in science-related fields. These critical evaluations serve to draw attention to science literacy in general and lack of persistence among females in particular, two issues that relate closely to the "preparation for future study" goal held by many high school science teachers. In other words, these teachers often seek to promote future success and to prevent future failure in their students' academic careers. This thesis studies the connection between the teaching practices recommended by reformers and researchers for high school teachers, and their students' subsequent college physics performance. The teaching practices studied were: laboratory experiences, class discussion experiences, content coverage, and reliance on textbooks. This study analyzed a survey of 1500 students from 16 different lecture-format college physics courses at 14 different universities. Using hierarchical linear modeling, this study accounted for course-level variables (Calculus-based/Non-calculus course type, professor's gender, and university selectivity). This study controlled for the student's parents education, high school science/mathematics achievement, high school calculus background, and racial background. In addition, the interactions between gender and both pedagogical/curricular and course-level variables were analyzed. The results indicated that teaching fewer topics in greater depth in high school physics appeared to be helpful to college physics students. An interaction between college course type and content coverage showed that students in Calculus-based physics reaped even greater benefits from a depth-oriented curriculum. Also students with fewer labs per month in high school physics appeared to perform better in college physics than did students with many more labs per month. The only significant interaction was between gender and Calculus-based/Non-calculus college course type. Females appeared to do better on average than their males counterparts in Non-calculus physics, but this trend is clearly reversed for Calculus-based physics. This is a disturbing result for educators who have worked to promote persistence among women in engineering and science research. Recommendations are included for high school physics teachers, students and their parents, and college physics instructors.

Calculus Students' Understanding of Volume

ERIC Educational Resources Information Center

Dorko, Allison; Speer, Natasha M.

2013-01-01

Researchers have documented difficulties that elementary school students have in understanding volume. Despite its importance in higher mathematics, we know little about college students' understanding of volume. This study investigated calculus students' understanding of volume. Clinical interview transcripts and written responses to volume…

Bladder calculus presenting as excessive masturbation.

PubMed

De Alwis, A C D; Senaratne, A M R D; De Silva, S M P D; Rodrigo, V S D

2006-09-01

Masturbation in childhood is a normal behaviour which most commonly begins at 2 months of age, and peaks at 4 years and in adolescence. However excessive masturbation causes anxiety in parents. We describe a boy with a bladder calculus presenting as excessive masturbation.

An operator calculus for surface and volume modeling

NASA Technical Reports Server (NTRS)

Gordon, W. J.

1984-01-01

The mathematical techniques which form the foundation for most of the surface and volume modeling techniques used in practice are briefly described. An outline of what may be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable is presented. By considering the linear operators associated with bivariate and multivariate interpolation/approximation schemes, it is shown how they can be compounded by operator multiplication and Boolean addition to obtain a distributive lattice of approximation operators. It is then demonstrated via specific examples how this operator calculus leads to practical techniques for sculptured surface and volume modeling.

On Anaphora and the Binding Principles in Categorial Grammar

NASA Astrophysics Data System (ADS)

Morrill, Glyn; Valentín, Oriol

In type logical categorial grammar the analysis of an expression is a resource-conscious proof. Anaphora represents a particular challenge to this approach in that the antecedent resource is multiplied in the semantics. This duplication, which corresponds logically to the structural rule of contraction, may be treated lexically or syntactically. Furthermore, anaphora is subject to constraints, which Chomsky (1981) formulated as Binding Principles A, B, and C. In this paper we consider English anaphora in categorial grammar including reference to the binding principles. We invoke displacement calculus, modal categorial calculus, categorial calculus with limited contraction, and entertain addition of negation as failure.

Umbral Calculus and Holonomic Modules in Positive Characteristic

NASA Astrophysics Data System (ADS)

Kochubei, Anatoly N.

2006-03-01

In the framework of analysis over local fields of positive characteristic, we develop algebraic tools for introducing and investigating various polynomial systems. In this survey paper we describe a function field version of umbral calculus developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. We consider modules over the Weyl-Carlitz ring, a function field counterpart of the Weyl algebra. It is shown that some basic objects of function field arithmetic, like the Carlitz module, Thakur's hypergeometric polynomials, and analogs of binomial coefficients arising in the positive characteristic version of umbral calculus, generate holonomic modules.

Dependence of calculus retropulsion dynamics on fiber size and radiant exposure during Ho:YAG lithotripsy.

PubMed

Lee, Ho; Ryan, Robert T; Kim, Jeehyun; Choi, Bernard; Arakeri, Navanit V; Teichman, Joel M H; Welch, A J

2004-08-01

During pulsed laser lithotripsy, the calculus is subject to a strong recoil momentum which moves the calculus away from laser delivery and prolongs the operation. This study was designed to quantify the recoil momentum during Ho:YAG laser lithotripsy. The correlation among crater shape, debris trajectory, laser-induced bubble and recoil momentum was investigated. Calculus phantoms made from plaster of Paris were ablated with free running Ho:YAG lasers. The dynamics of recoil action of a calculus phantom was monitored by a high-speed video camera and the laser ablation craters were examined with Optical Coherent Tomography (OCT). Higher radiant exposure resulted in larger ablation volume (mass) which increased the recoil momentum. Smaller fibers produced narrow craters with a steep contoured geometry and decreased recoil momentum compared to larger fibers. In the presence of water, recoil motion of the phantom deviated from that of phantom in air. Under certain conditions, we observed the phantom rocking towards the fiber after the laser pulse. The shape of the crater is one of the major contributing factors to the diminished recoil momentum of smaller fibers. The re-entrance flow of water induced by the bubble collapse is considered to be the cause of the rocking of the phantom.

Formalization of the Integral Calculus in the PVS Theorem Prover

NASA Technical Reports Server (NTRS)

Butler, Ricky W.

2004-01-01

The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

Simplicial lattices in classical and quantum gravity: Mathematical structure and application

NASA Astrophysics Data System (ADS)

Lafave, Norman Joseph

1989-03-01

Geometrodynamics can be understood more clearly in the language of geometry than in the language of differential equations. This is the primary motivation for the development of calculational schemes based on Regge Calculus as an alternative to those schemes based on Ricci Calculus. The mathematics of simplicial lattices were developed to the same level of sophistication as the mathematics of pseudo--Riemannian geometry for continuum manifolds. This involves the definition of the simplicial analogues of several concepts from differential topology and differential geometry-the concept of a point, tangent spaces, forms, tensors, parallel transport, covariant derivatives, connections, and curvature. These simplicial analogues are used to define the Einstein tensor and the extrinsic curvature on a simplicial geometry. This mathematical formalism was applied to the solution of several outstanding problems in the development of a Regge Calculus based computational scheme for general geometrodynamic problems. This scheme is based on a 3 + 1 splitting of spacetime within the Regge Calculus prescription known as Null-Strut Calculus (NSC). NSC describes the foliation of spacetime into spacelike hypersurfaces built of tetrahedra. These hypersurfaces are coupled by light rays (null struts) to past and future momentum-like structures, geometrically dual to the tetrahedral lattice of the hypersurface. Avenues of investigation for NSC in quantum gravity are described.

Differential Calculus: Concepts and Notation.

ERIC Educational Resources Information Center

Hobbs, David; Relf, Simon

1997-01-01

Suggests that many students with A-level mathematics, and even with a degree in mathematics or a related subject, do not have an understanding of the basic principles of calculus. Describes the approach used in three textbooks currently in use. Contains 14 references. (Author/ASK)

Integrating Precalculus Review with the First Course in Calculus.

ERIC Educational Resources Information Center

Sevilla, Alicia; Somers, Kay

1993-01-01

Describes a course designed by Moravian College, Pennsylvania, to integrate precalculus topics as needed into a first calculus course. The textbook developed for the course covers the concepts of functions, Cartesian coordinates, limits, continuity, infinity, and the derivative. Examples are discussed. (MDH)

Supercalculators and University Entrance Calculus Examinations.

ERIC Educational Resources Information Center

Hong, Ye Yoon; Thomas, Mike; Kiernan, Christine

2000-01-01

Investigates whether the use of computer algebra systems could provide a significant advantage to students taking standard university entrance calculus examinations. Indicates that supercalculators would probably provide a significant advantage, particularly for lower-achieving students. Demonstrates that it is possible to write questions in which…

The Vector Calculus Gap: Mathematics (Does Not Equal) Physics.

ERIC Educational Resources Information Center

Dray, Tevian; Manogue, Corinne A.

1999-01-01

Discusses some of the differences between the ways mathematicians and physicists view vector calculus and the gap between the way this material is traditionally taught by mathematicians and the way physicists use it. Suggests some ways to narrow the gap. (Author/ASK)

Calculus and Sailing.

ERIC Educational Resources Information Center

Palmaccio, Richard J.

1982-01-01

A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)

[Factors affecting residual stones after percutaneous nephrolithotomy in patients with renal calculus].

PubMed

Qiao, Mingzhou; Zhang, Haifang; Zhou, Chenlong

2015-11-24

To explore the factors affecting the residual stones after percutaneous nephrolithotomy (PCNL) in patients with renal calculus. A retrospective analysis was performed for 1 200 patients who were affected by renal calculus and treated with PCNL between Jan 2008 and May 2014 in People's Hospital of Anyang City. Among those patients, 16 were diagnosed as bilateral renal stone and had two successive operations. The size, location and number of stones, previous history of surgery, the degree of hydronephrosis, urinary infection were included in the univariate analysis. Significant factors in univariate analysis were included in the multivariate analysis to determine factors affecting stone residual. A total of 385 cases developed stone residual after surgery. The overall residual rate was 31.7%. In univariate analysis, renal pelvis combined with caliceal calculus (P=0.006), stone size larger than 4 cm (P=0.005), stone number more than 4 (P=0.002), the amount of bleeding more than 200 ml (P=0.025), operation time longer than 120 minutes (P=0.028) were associated with an increased rate of stone residual. When subjected to the Cox multivariate analysis, the independent risk factors for residual stones were renal pelvis combined with caliceal calculus (P=0.049), stone size larger than 4 cm (P=0.038) and stone number more than 4 (P=0.018). Factors affecting the incidence of residual stones after PCNL are the size, location and number of stones. Larger size stone and the presence of renal pelvis combined with caliceal calculus are significantly associated with residual stones. Nevertheless, stone number less than 4 indicates an increased stone clearance rate.

Clinical Effectiveness of Prospectively Reported Sonographic Twinkling Artifact for the Diagnosis of Renal Calculus in Patients Without Known Urolithiasis.

PubMed

Masch, William R; Cohan, Richard H; Ellis, James H; Dillman, Jonathan R; Rubin, Jonathan M; Davenport, Matthew S

2016-02-01

The purpose of this study was to determine the clinical effectiveness of prospectively reported sonographic twinkling artifact for the diagnosis of renal calculus in patients without known urolithiasis. All ultrasound reports finalized in one health system from June 15, 2011, to June 14, 2014, that contained the words "twinkle" or "twinkling" in reference to suspected renal calculus were identified. Patients with known urolithiasis or lack of a suitable reference standard (unenhanced abdominal CT with ≤ 2.5-mm slice thickness performed ≤ 30 days after ultrasound) were excluded. The sensitivity, specificity, and positive likelihood ratio of sonographic twinkling artifact for the diagnosis of renal calculus were calculated by renal unit and stratified by two additional diagnostic features for calcification (echogenic focus, posterior acoustic shadowing). Eighty-five patients formed the study population. Isolated sonographic twinkling artifact had sensitivity of 0.78 (82/105), specificity of 0.40 (26/65), and a positive likelihood ratio of 1.30 for the diagnosis of renal calculus. Specificity and positive likelihood ratio improved and sensitivity declined when the following additional diagnostic features were present: sonographic twinkling artifact and echogenic focus (sensitivity, 0.61 [64/105]; specificity, 0.65 [42/65]; positive likelihood ratio, 1.72); sonographic twinkling artifact and posterior acoustic shadowing (sensitivity, 0.31 [33/105]; specificity, 0.95 [62/65]; positive likelihood ratio, 6.81); all three features (sensitivity, 0.31 [33/105]; specificity, 0.95 [62/65]; positive likelihood ratio, 6.81). Isolated sonographic twinkling artifact has a high false-positive rate (60%) for the diagnosis of renal calculus in patients without known urolithiasis.

The effectiveness of a magnetized water oral irrigator (Hydro Floss) on plaque, calculus and gingival health.

PubMed

Johnson, K E; Sanders, J J; Gellin, R G; Palesch, Y Y

1998-04-01

The purpose of this study was to evaluate the effects of a magnetized water oral irrigator on plaque, calculus and gingival health. 29 patients completed this double-blind crossover study. Each patient was brought to baseline via an oral prophylaxis with a plaque index < or = 1 and a gingival index < or = 1. Subjects used the irrigator for a period of 3 months with the magnet and 3 months without the magnet. After each 3 month interval, data were collected using the plaque index, gingival index, and accretions index. The repeated measures analysis on plaque, gingival and calculus indices yielded a statistically-significant period effect for PlI (p=0.0343), GI (p=0.0091), and approached significance for calculus (p=0.0593). This meant that the effect of irrigation resulted in a decrease of all indices over time. Therefore, the treatment effect on each index was evaluated using only the measurements obtained at the end of the first period (i.e., assuming a parallel design). Irrigation with magnetized water resulted in 64% less calculus compared to the control group. The reduction was statistically significant (p< or =0.02). The reduction by 27% in gingival index was not statistically significant. The reduction in plaque was minimal (2.2%). A strong positive correlation between the plaque index and the Watt accretion index was observed. The magnetized water oral irrigator could be a useful adjunct in the prevention of calculus accumulation in periodontal patients, but appears to have minimal effect on plaque reduction. The results indicated a clinical improvement in the gingival index, but this was not a statistically significant finding.

Geometric Structure-Preserving Discretization Schemes for Nonlinear Elasticity

DTIC Science & Technology

2015-08-13

conditions. 15.  SUBJECT TERMS geometric theory for nonlinear elasticity, discrete exterior calculus 16.  SECURITY CLASSIFICATION OF: 17.  LIMITATION...associated Laplacian. We use the general theory for approximation of Hilbert complexes and the finite element exterior calculus and introduce some stable mixed

Development of Boolean calculus and its applications. [digital systems design

NASA Technical Reports Server (NTRS)

Tapia, M. A.

1980-01-01

The development of Boolean calculus for its application to developing digital system design methodologies that would reduce system complexity, size, cost, speed, power requirements, etc., is discussed. Synthesis procedures for logic circuits are examined particularly asynchronous circuits using clock triggered flip flops.

Inquiry-Based Learning of Transcendental Functions in Calculus

ERIC Educational Resources Information Center

Ekici, Celil; Gard, Andrew

2017-01-01

In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for…

Building an Understanding of Functions: A Series of Activities for Pre-Calculus

ERIC Educational Resources Information Center

Carducci, Olivia M.

2008-01-01

Building block toys can be used to illustrate various concepts connected with functions including graphs and rates of change of linear and exponential functions, piecewise functions, and composition of functions. Five brief activities suitable for a pre-calculus course are described.

Teaching Calculus Students How to Study.

ERIC Educational Resources Information Center

Boelkins, Matthew R.; Pfaff, Thomas J.

1998-01-01

Addresses the problem of poor study habits in calculus students and presents techniques to teach students how to study consistently and effectively. Concludes that many students greatly appreciate the added structure, work harder than in previous courses, and witness newfound success as a consequence. (Author/ASK)

A Note on Discrete Mathematics and Calculus.

ERIC Educational Resources Information Center

O'Reilly, Thomas J.

1987-01-01

Much of the current literature on the topic of discrete mathematics and calculus during the first two years of an undergraduate mathematics curriculum is cited. A relationship between the recursive integration formulas and recursively defined polynomials is described. A Pascal program is included. (Author/RH)

Portfolio Analysis for Vector Calculus

ERIC Educational Resources Information Center

Kaplan, Samuel R.

2015-01-01

Classic stock portfolio analysis provides an applied context for Lagrange multipliers that undergraduate students appreciate. Although modern methods of portfolio analysis are beyond the scope of vector calculus, classic methods reinforce the utility of this material. This paper discusses how to introduce classic stock portfolio analysis in a…

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

A huge bladder calculus causing acute renal failure.

PubMed

Komeya, Mitsuru; Sahoda, Tamami; Sugiura, Shinpei; Sawada, Takuto; Kitami, Kazuo

2013-02-01

A 81-year-old male was referred to our emergency outpatient unit due to acute renal failure. The level of serum creatinine was 276 μmol/l. A CT scan showed bilateral hydronephroureter, large bladder stone (7 cm × 6 cm × 6 cm) and bladder wall thickness. He was diagnosed as post renal failure due to bilateral hydronephroureter. Large bladder stone is thought to be the cause of bilateral hydronephroureter and renal failure. To improve renal failure, we performed open cystolithotomy and urethral catheterization. Three days after the surgery, the level of serum creatinine decreased to 224 μmol/l. He was discharged from our hospital with uneventful course. Bladder calculus is thought to be a rare cause of renal failure. We summarize the characteristics of bladder calculus causing renal failure. We should keep that long-term pyuria and urinary symptom, and repeated urinary tract infection can cause huge bladder calculus and renal failure in mind.

Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

NASA Astrophysics Data System (ADS)

Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

2015-11-01

We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

Unenhanced low-dose versus standard-dose CT localization in patients with upper urinary calculi for minimally invasive percutaneous nephrolithotomy (MPCNL)

PubMed Central

Licheng, Jiang; Yidong, Fan; Ping, Wang; Keqiang, Yan; Xueting, Wang; Yingchen, Zhang; Lei, Gao; Jiyang, Ding; Zhonghua, Xu

2014-01-01

Background & objectives: With the ethical concern about the dose of CT scan and wide use of CT in protocol of suspected renal colic, more attention has been paid to low dose CT. The aim of the present study was to make a comparison of unenhanced low-dose spiral CT localization with unenhanced standard-dose spiral CT in patients with upper urinary tract calculi for minimally invasive percutaneous nephrolithotomy (MPCNL) treatment. Methods: Twenty eight patients with ureter and renal calculus, preparing to take MPCNL, underwent both abdominal low-dose CT (25 mAs) and standard-dose CT (100 mAs). Low-dose CT and standard-dose CT were independently evaluated for the characterization of renal/ureteral calculi, perirenal adjacent organs, blood vessels, indirect signs of renal or ureteral calculus (renal enlargement, pyeloureteral dilatation), and the indices of localization (percutaneous puncture angulation and depth) used in the MPCNL procedure. Results: In all 28 patients, low-dose CT was 100 per cent coincidence 100 per cent sensitive and 100 per cent specific for depicting the location of the renal and ureteral calculus, renal enlargement, pyeloureteral dilatation, adjacent organs, and the presumptive puncture point and a 96.3 per cent coincidence 96 per cent sensitivity and 93 per cent specificity for blood vessel signs within the renal sinus, and with an obvious lower radiation exposure for patients when compared to standard-dose CT (P<0.05). The indices of puncture depth, puncture angulation, and maximum calculus transverse diameter on the axial surface showed no significant difference between the two doses of CT scans, with a significant variation in calculus visualization slice numbers (P<0.05). Interpretation & conclusions: Our findings show that unenhanced low-dose CT achieves a sensitivity and accuracy similar to that of standard-dose CT in assessing the localization of renal ureteral calculus and adjacent organs conditions and identifying the maximum calculus transverse diameter on the axial surface, percutaneous puncture depth, and angulation in patients, with a significant lower radiation exposure, who are to be treated by MPCNL, and can be used as an alternative localization method. PMID:24820832

Unenhanced low-dose versus standard-dose CT localization in patients with upper urinary calculi for minimally invasive percutaneous nephrolithotomy (MPCNL).

PubMed

Licheng, Jiang; Yidong, Fan; Ping, Wang; Keqiang, Yan; Xueting, Wang; Yingchen, Zhang; Lei, Gao; Jiyang, Ding; Zhonghua, Xu

2014-03-01

With the ethical concern about the dose of CT scan and wide use of CT in protocol of suspected renal colic, more attention has been paid to low dose CT. The aim of the present study was to make a comparison of unenhanced low-dose spiral CT localization with unenhanced standard-dose spiral CT in patients with upper urinary tract calculi for minimally invasive percutaneous nephrolithotomy (MPCNL) treatment. Twenty eight patients with ureter and renal calculus, preparing to take MPCNL, underwent both abdominal low-dose CT (25 mAs) and standard-dose CT (100 mAs). Low-dose CT and standard-dose CT were independently evaluated for the characterization of renal/ureteral calculi, perirenal adjacent organs, blood vessels, indirect signs of renal or ureteral calculus (renal enlargement, pyeloureteral dilatation), and the indices of localization (percutaneous puncture angulation and depth) used in the MPCNL procedure. In all 28 patients, low-dose CT was 100 per cent coincidence 100 per cent sensitive and 100 per cent specific for depicting the location of the renal and ureteral calculus, renal enlargement, pyeloureteral dilatation, adjacent organs, and the presumptive puncture point and a 96.3 per cent coincidence 96 per cent sensitivity and 93 per cent specificity for blood vessel signs within the renal sinus, and with an obvious lower radiation exposure for patients when compared to standard-dose CT (P<0.05). The indices of puncture depth, puncture angulation, and maximum calculus transverse diameter on the axial surface showed no significant difference between the two doses of CT scans, with a significant variation in calculus visualization slice numbers (P<0.05). Our findings show that unenhanced low-dose CT achieves a sensitivity and accuracy similar to that of standard-dose CT in assessing the localization of renal ureteral calculus and adjacent organs conditions and identifying the maximum calculus transverse diameter on the axial surface, percutaneous puncture depth, and angulation in patients, with a significant lower radiation exposure, who are to be treated by MPCNL, and can be used as an alternative localization method.

Improving Student Success in Calculus: A Comparison of Four College Calculus Classes

NASA Astrophysics Data System (ADS)

Bagley, Spencer Franklin

The quality of education in science, technology, engineering, and mathematics (STEM) fields is an issue of particular educational and economic importance, and Calculus I is a linchpin course in STEM major tracks. A national study is currently being conducted examining the characteristics of successful programs in college calculus (CSPCC, 2012). In work related to the CSPCC program, this study examines the effects on student outcomes of four different teaching strategies used at a single institution. The four classes were a traditional lecture, a lecture with discussion, a lecture incorporating both discussion and technology, and an inverted model. This dissertation was guided by three questions: (1) What impact do these four instructional approaches have on students' persistence, beliefs about mathematics, and conceptual and procedural achievement in calculus? (2) How do students at the local institution compare to students in the national database? And (3) How do the similarities and differences in opportunities for learning presented in the four classes contribute to the similarities and differences in student outcomes? Quantitative analysis of surveys and exams revealed few statistically significant differences in outcomes, and students in the inverted classroom often had poorer outcomes than those in other classes. Students in the technology-enhanced class scored higher on conceptual items on the final exam than those in other classes. Comparing to the national database, local students had similar switching rates but less expert-like attitudes and beliefs about mathematics than the national average. Qualitative analysis of focus group interviews, classroom observations, and student course evaluations showed that several implementation issues, some the result of pragmatic constraints, others the result of design choice, weakened affordances provided by innovative features and shrunk the differences between classes. There were substantial differences between the inverted classroom in this study and successful implementations in the literature. I identified a set of departures that forms a list of best practices for inverting classrooms. Students in all classes felt that prior calculus experience was a prerequisite for their current calculus class, and that class sessions felt rushed. These concerns implicate the constraints imposed by the curriculum shared by the four classes.

Cystic Calculus in a Laboratory-housed Green Anole (Anolis carolinensis).

PubMed

Birke, Leslie L; Cespedes, Ann M; Schachner, Emma R; Lailvaux, Simon P

2017-03-01

An adult, male, wild-caught, laboratory-housed green anole (Anolis carolinensis) on a locomotor performance study was presented for anorexia. The anole exhibited a 26% weight loss and a thin body condition but was otherwise alert and active. Despite supportive care, the anole's clinical condition deteriorated, necessitating euthanasia. Postmortem examination revealed a 4.5 mm × 2.5-mm cystic calculus, which consisted entirely of sodium urate. Here we describe the clinical findings and locomotor consequences of this disease in a green anole. Although urolithiasis has been reported clinically in reptiles, this report presents the first case of a cystic calculus in a laboratory-housed green anole.

A useful demonstration of calculus in a physics high school laboratory

NASA Astrophysics Data System (ADS)

Alvarez, Gustavo; Schulte, Jurgen; Stockton, Geoffrey; Wheeler, David

2018-01-01

The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an experiment of a falling magnet in a column of self-induced eddy currents. The presented method combines multiple physics concepts such as 1D kinematics, classical mechanics, electromagnetism and non-trivial mathematics. It offers the opportunity for lateral as well as project-based learning.

Hamilton-Jacobi-Bellman equations and approximate dynamic programming on time scales.

PubMed

Seiffertt, John; Sanyal, Suman; Wunsch, Donald C

2008-08-01

The time scales calculus is a key emerging area of mathematics due to its potential use in a wide variety of multidisciplinary applications. We extend this calculus to approximate dynamic programming (ADP). The core backward induction algorithm of dynamic programming is extended from its traditional discrete case to all isolated time scales. Hamilton-Jacobi-Bellman equations, the solution of which is the fundamental problem in the field of dynamic programming, are motivated and proven on time scales. By drawing together the calculus of time scales and the applied area of stochastic control via ADP, we have connected two major fields of research.

DoD Science and Engineering Apprenticeship Program for High-School Students

DTIC Science & Technology

1995-06-01

Mu Alpha Theta for Computers, Calculus, Integral Calculus, and Precalculus ; 1994 Georgia Tech Distinguished Math Scholar; Captain of First Place...Computers. Calr.uIns. TntPg^i Painii»«. and Precalculus ; 1994 Georgia Tech Distinguished Math Scholar;.Captain of.First.Place Brain Bowl

Using CAS to Solve Classical Mathematics Problems

ERIC Educational Resources Information Center

Burke, Maurice J.; Burroughs, Elizabeth A.

2009-01-01

Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…

Flipping Freshman Mathematics

ERIC Educational Resources Information Center

Zack, Laurie; Fuselier, Jenny; Graham-Squire, Adam; Lamb, Ron; O'Hara, Karen

2015-01-01

Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…

Online Calculus: The Course and Survey Results.

ERIC Educational Resources Information Center

Allen, G. Donald

2001-01-01

Describes the development and implementation of a Web-based calculus course at Texas A & M University. Discusses the course design, layout of content and the contrast with textbook structure, results of course surveys that included student reactions, and how students learn form Web-based materials. (Author/LRW)

On Flipping First-Semester Calculus: A Case Study

ERIC Educational Resources Information Center

Petrillo, Joseph

2016-01-01

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are "flipping" (or inverting) their classrooms. By flipping, we…

Boolean integral calculus for digital systems

NASA Technical Reports Server (NTRS)

Tucker, J. H.; Tapia, M. A.; Bennett, A. W.

1985-01-01

The concept of Boolean integration is introduced and developed. When the changes in a desired function are specified in terms of changes in its arguments, then ways of 'integrating' (i.e., realizing) the function, if it exists, are presented. Boolean integral calculus has applications in design of logic circuits.

Individualized Additional Instruction for Calculus

ERIC Educational Resources Information Center

Takata, Ken

2010-01-01

College students enrolling in the calculus sequence have a wide variance in their preparation and abilities, yet they are usually taught from the same lecture. We describe another pedagogical model of Individualized Additional Instruction (IAI) that assesses each student frequently and prescribes further instruction and homework based on the…

Pushing the Limit: A Class Project

ERIC Educational Resources Information Center

Odafe, Victor U.

2012-01-01

Instructors are constantly struggling to help students understand mathematical concepts as well as the relevance of mathematics to the real world. In calculus, students possess misconceptions of the limit concept. "Pushing the Limit" refers to a semester-long calculus class project that required students to read about, interview calculus…

Assessing Online Homework in First-Semester Calculus

ERIC Educational Resources Information Center

Callahan, Jason T.

2016-01-01

This paper describes and assesses the implementation of online homework in a first-semester calculus course. Comparing sections of the course before implementation to those after, we find statistically significant improvements in retention rates, measures of student engagement, and participation on homework. We do not, however, find statistically…

Making Implicit Multivariable Calculus Representations Explicit: A Clinical Study

ERIC Educational Resources Information Center

McGee, Daniel; Moore-Russo, Deborah; Martinez-Planell, Rafael

2015-01-01

Reviewing numerous textbooks, we found that in both differential and integral calculus textbooks the authors commonly assume that: (i) students can generalize associations between representations in two dimensions to associations between representations of the same mathematical concept in three dimensions on their own; and (ii) explicit…

Revitalization of Nonstandard Calculus.

ERIC Educational Resources Information Center

Fetta, Iris B.

This project developed materials for an innovative new approach to calculus for students in business, economics, liberal arts, management, and the social sciences. With the focus on rates and accumulation of change and their interpretations in real life situations, the materials are data driven, technology based, and feature a unique modeling…

A Planar Calculus for Infinite Index Subfactors

NASA Astrophysics Data System (ADS)

Penneys, David

2013-05-01

We develop an analog of Jones' planar calculus for II 1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.

Students' Difficulties with Vector Calculus in Electrodynamics

ERIC Educational Resources Information Center

Bollen, Laurens; van Kampen, Paul; De Cock, Mieke

2015-01-01

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven…

Computerized Business Calculus Using Calculators, Examples from Mathematics to Finance.

ERIC Educational Resources Information Center

Vest, Floyd

1991-01-01

After discussing the role of supercalculators within the business calculus curriculum, several examples are presented which allow the reader to examine the capabilities and codes of calculators specific to different major manufacturers. The topics examined include annuities, Newton's method, fixed point iteration, graphing, solvers, and…

Mathematics for the New Millennium

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2004-01-01

Courses below calculus need to be refocused to emphasise conceptual understanding and realistic applications via mathematical modelling rather than an overarching focus on developing algebraic skills that may be needed for calculus. Without understanding the concepts, students will not be able to transfer the mathematics to new situations or to…

Using Discovery in the Calculus Class

ERIC Educational Resources Information Center

Shilgalis, Thomas W.

1975-01-01

This article shows how two discoverable theorems from elementary calculus can be presented to students in a manner that assists them in making the generalizations themselves. The theorems are the mean value theorems for derivatives and for integrals. A conjecture is suggested by pictures and then refined. (Author/KM)

Exploring Flipped Classroom Instruction in Calculus III

ERIC Educational Resources Information Center

Wasserman, Nicholas H.; Quint, Christa; Norris, Scott A.; Carr, Thomas

2017-01-01

In an undergraduate Calculus III class, we explore the effect of "flipping" the instructional delivery of content on both student performance and student perceptions. Two instructors collaborated to determine daily lecture notes, assigned the same homework problems, and gave identical exams; however, compared to a more traditional…

Suggested Courseware for the Non-Calculus Physics Student: Measurement, Vectors, and One-Dimensional Motion.

ERIC Educational Resources Information Center

Mahoney, Joyce; And Others

1988-01-01

Evaluates 16 commercially available courseware packages covering topics for introductory physics. Discusses the price, sub-topics, program type, interaction, time, calculus required, graphics, and comments of each program. Recommends two packages in measurement and vectors, and one-dimensional motion respectively. (YP)

Fractional calculus in bioengineering, part 3.

PubMed

Magin, Richard L

2004-01-01

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. By expanding the range of mathematical operations to include fractional calculus, we can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner. In Part 2 of this review (Crit Rev Biomed Eng 2004; 32(1):105-193), fractional calculus was applied to problems in nerve stimulation, dielectric relaxation, and viscoelastic materials by extending the governing differential equations to include fractional order terms. In this third and final installment, we consider distributed systems that represent shear stress in fluids, heat transfer in uniform one-dimensional media, and subthreshold nerve depolarization. Classic electrochemical analysis and impedance spectroscopy are also reviewed from the perspective of fractional calculus, and selected examples from recent studies in neuroscience, bioelectricity, and tissue biomechanics are analyzed to illustrate the vitality of the field.

Determination of neuroprotective oxysterols in Calculus bovis, human gallstones, and traditional Chinese medicine preparations by liquid chromatography with mass spectrometry.

PubMed

Wang, Yalong; Jiang, Han; Huang, Huizhi; Xie, Yanqi; Zhao, Yunshi; You, Xiuhua; Tang, Lipeng; Wang, Youqiong; Yin, Wei; Qiu, Pengxin; Yan, Guangmei; Hu, Haiyan

2015-03-01

So far, the components responsible for the neuroprotective effects of Calculus bovis are unclear. Cholesterol, one of the major components in Calculus bovis, is easily oxidized into oxysterols, which possess direct or indirect neuroprotective effects proved by our and others' previous studies. Therefore, a liquid chromatography with mass spectrometry method coupled with ultrasonic extraction and solid-phase extraction was developed for the determination of neuroprotective oxysterols in Calculus bovis, human gallstones, and traditional Chinese medicine preparations. Chromatographic separation was achieved on a C18 column with isocratic elution at a flow rate of 1 mL/min. The established method showed good linearity (R(2) > 0.998), sensitivity with low limits of detection (0.06-0.39 μg/g), acceptable precisions (relative standard deviations ≤ 7.4%), stability (relative standard deviations ≤ 5.9%), and satisfactory accuracy (92.4-102.9%) for all analytes identified by different retention times, which could be applied for the determination of oxysterols. Five kinds of oxysterols proved to function as neuroprotectants were detected at different concentrations. Among them, 7β-hydroxycholesterol and cholestane-3β,5α,6β-triol were rather abundant in the samples. It could be concluded that the potential neuroprotective components in Calculus bovis may be these oxysterols. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Development and validation of a sensitive LC-MS-MS method for the simultaneous determination of multicomponent contents in artificial Calculus Bovis.

PubMed

Peng, Can; Tian, Jixin; Lv, Mengying; Huang, Yin; Tian, Yuan; Zhang, Zunjian

2014-02-01

Artificial Calculus Bovis is a major substitute in clinical treatment for Niuhuang, a widely used, efficacious but rare traditional Chinese medicine. However, its chemical structures and the physicochemical properties of its components are complicated, which causes difficulty in establishing a set of effective and comprehensive methods for its identification and quality control. In this study, a simple, sensitive and reliable liquid chromatography-tandem mass spectrometry method was successfully developed and validated for the simultaneous determination of bilirubin, taurine and major bile acids (including six unconjugated bile acids, two glycine-conjugated bile acids and three taurine-conjugated bile acids) in artificial Calculus Bovis using a Zorbax SB-C18 column with a gradient elution of methanol and 10 mmol/L ammonium acetate in aqueous solution (adjusted to pH 3.0 with formic acid). The mass spectra were obtained in the negative ion mode using dehydrocholic acid as the internal standard. The content of each analyte in artificial Calculus Bovis was determined by monitoring specific ion pairs in the selected reaction monitoring mode. All analytes demonstrated perfect linearity (r(2) > 0.994) in a wide dynamic range, and 10 batches of samples from different sources were further analyzed. This study provided a comprehensive method for the quality control of artificial Calculus Bovis.

The Use of Geogebra Software as a Calculus Teaching and Learning Tool

ERIC Educational Resources Information Center

Nobre, Cristiane Neri; Meireles, Magali Rezende Gouvêa; Vieira, Niltom, Jr.; de Resende, Mônica Neli; da Costa, Lucivânia Ester; da Rocha, Rejane Corrêa

2016-01-01

Information and Communication Technologies (ICT) in education provide a new learning environment where the student builds his own knowledge, allowing his visualization and experimentation. This study evaluated the Geogebra software in the learning process of Calculus. It was observed that the proposed activities helped in the graphical…

The Negative Sign and Exponential Expressions: Unveiling Students' Persistent Errors and Misconceptions

ERIC Educational Resources Information Center

Cangelosi, Richard; Madrid, Silvia; Cooper, Sandra; Olson, Jo; Hartter, Beverly

2013-01-01

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential…

Conceptual Precalculus: Strengthening Students' Quantitative and Covariational Reasoning

ERIC Educational Resources Information Center

Madison, Bernard L.; Carlson, Marilyn; Oehrtman, Michael; Tallman, Michael

2015-01-01

Research over the past few decades points to ways precalculus and calculus courses can be strengthened to improve student learning in these courses. This research has informed the development of the Algebra and Precalculus Concept Readiness (APCR) and the Calculus Concept Readiness (CCR) assessments. In this article, the authors present three…

Geometric Demonstration of the Fundamental Theorems of the Calculus

ERIC Educational Resources Information Center

Sauerheber, Richard D.

2010-01-01

After the monumental discovery of the fundamental theorems of the calculus nearly 350 years ago, it became possible to answer extremely complex questions regarding the natural world. Here, a straightforward yet profound demonstration, employing geometrically symmetric functions, describes the validity of the general power rules for integration and…

Predicting Performance in a First Engineering Calculus Course: Implications for Interventions

ERIC Educational Resources Information Center

Hieb, Jeffrey L.; Lyle, Keith B.; Ralston, Patricia A. S.; Chariker, Julia

2015-01-01

At the University of Louisville, a large, urban institution in the south-east United States, undergraduate engineering students take their mathematics courses from the school of engineering. In the fall of their freshman year, engineering students take "Engineering Analysis I," a calculus-based engineering analysis course. After the…

The Characteristic of the Process of Students' Metacognition in Solving Calculus Problems

ERIC Educational Resources Information Center

Purnomo, Dwi; Nusantara, Toto; Subanji; Rahardjo, Swasono

2017-01-01

This article is the result of research aims to describe the patterns and characteristics of the process of metacognition student of mathematics in solving calculus problems. Description was done by looking at changes in "awareness," "evaluation," and "regulation" as components of metacognition. The changes in…

Calculus Courses' Assessment Data

ERIC Educational Resources Information Center

Pauna, Matti

2017-01-01

In this paper we describe computer-aided assessment methods used in online Calculus courses and the data they produce. The online learning environment collects a lot of time-stamped data about every action a student makes. Assessment data can be harnessed into use as a feedback, predictor, and recommendation facility for students and instructors.…

Peer Conferences in Calculus: The Impact of Systematic Training

ERIC Educational Resources Information Center

Reinholz, Daniel

2017-01-01

This paper describes an intervention for improving the quality of peer assessment conferences in calculus. Although a body of work highlights the learning benefits of peer assessment, few papers have described the nature of student conversations during peer conferences/assessment in detail. This paper provides deeper insight into what those…

On Transitions between Representations: The Role of Contextual Reasoning in Calculus Problem Solving

ERIC Educational Resources Information Center

Zazkis, Dov

2016-01-01

This article argues for a shift in how researchers discuss and examine students' uses and understandings of multiple representations within a calculus context. An extension of Zazkis, Dubinsky, and Dautermann's (1996) visualization/analysis framework to include contextual reasoning is proposed. Several examples that detail transitions between…

Some Problems of Extremes in Geometry and Construction

ERIC Educational Resources Information Center

Yanovsky, Levi

2008-01-01

Two original problems in geometry are presented with solutions utilizing to differential calculus: (a) rectangle inscribed in a sector; (b) point on the ray of the angle. The possibility of applying mathematics in general and differential calculus in particular for solution of practical problems is discussed. (Contains 8 figures.)

Calculus of Elementary Functions, Part IV. Teacher's Commentary. Preliminary Edition.

ERIC Educational Resources Information Center

Herriot, Sarah T.; And Others

This teacher's guide is designed for use with the SMSG textbook "Calculus of Elementary Functions." It contains solutions to exercises found in Chapter 9, Integration Theory and Technique; Chapter 10, Simple Differential Equations; Appendix 5, Area and Integral; Appendix 6; Appendix 7, Continuity Theory; and Appendix 8, More About…

A Graphical Introduction to the Derivative

ERIC Educational Resources Information Center

Samuels, Jason

2017-01-01

Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the…

A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

ERIC Educational Resources Information Center

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

On Online Assignments in a Calculus Class

ERIC Educational Resources Information Center

Jungic, Veselin; Kent, Deborah; Menz, Petra

2012-01-01

In this paper, we describe our experience with the creation and utilization of online assignments for several calculus classes at Simon Fraser University (SFU). We present our findings regarding available software by considering the needs and perspectives of the instructors, students, and administrators. We provide a list of questions that guide…

Simplifying the Mathematical Treatment of Radioactive Decay

ERIC Educational Resources Information Center

Auty, Geoff

2011-01-01

Derivation of the law of radioactive decay is considered without prior knowledge of calculus or the exponential series. Calculus notation and exponential functions are used because ultimately they cannot be avoided, but they are introduced in a simple way and explained as needed. (Contains 10 figures, 1 box, and 1 table.)

Calculus in Elementary School: An Example of ICT-Based Curriculum Transformation

ERIC Educational Resources Information Center

Fluck, Andrew; Ranmuthugala, Dev; Chin, Chris; Penesis, Irene

2012-01-01

Integral calculus is generally regarded as a fundamental but advanced aspect of mathematics, and it is not generally studied until students are aged about fifteen or older. Understanding the transformative potential of information and communication technology, this project undertook an investigation in four Australian schools to train students…

Reading the World with Calculus

ERIC Educational Resources Information Center

Verzosa, Debbie

2015-01-01

It is now increasingly recognized that mathematics is not a neutral value-free subject. Rather, mathematics can challenge students' taken-for-granted realities and promote action. This article describes two issues, namely deforestation and income inequality. These were specifically chosen because they can be related to a range of calculus concepts…

Geometric Error Analysis in Applied Calculus Problem Solving

ERIC Educational Resources Information Center

Usman, Ahmed Ibrahim

2017-01-01

The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…

A Transformative Model for Undergraduate Quantitative Biology Education

ERIC Educational Resources Information Center

Usher, David C.; Driscoll, Tobin A.; Dhurjati, Prasad; Pelesko, John A.; Rossi, Louis F.; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B.

2010-01-01

The "BIO2010" report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3)…

Modeling an Outbreak of Anthrax

ERIC Educational Resources Information Center

Sturdivant, Rod; Watts, Krista

2010-01-01

This article presents material that has been used as a classroom activity in a calculus-based probability and statistics course. The application was used in the first few lessons of this course. Students had three previous semesters of math, including calculus (single and multivariable), differential equations, and a course in mathematical…

A "Model" Multivariable Calculus Course.

ERIC Educational Resources Information Center

Beckmann, Charlene E.; Schlicker, Steven J.

1999-01-01

Describes a rich, investigative approach to multivariable calculus. Introduces a project in which students construct physical models of surfaces that represent real-life applications of their choice. The models, along with student-selected datasets, serve as vehicles to study most of the concepts of the course from both continuous and discrete…

Use of WIRIS Quizzes in an Online Calculus Course

ERIC Educational Resources Information Center

Calm, Remei; Masià, Ramon; Olivé, Carme; Parés, Núria; Pozo, Francesc; Ripoll, Jordi; Sancho-Vinuesa, Teresa

2017-01-01

Calculus courses often present a large number of difficulties to undergraduate students of scientific studies, especially in engineering degrees. These difficulties are sometimes related to teaching and assessment strategies. In this paper, a teaching innovation experience is presented within the framework of the Universitat Oberta de Catalunya.…

Examining Students' Reluctance to Use Graphs

ERIC Educational Resources Information Center

Dyke, Frances Van; White, Alexander

2004-01-01

An evaluation designed to test basic graphical-thinking skills to students entering calculus or applied calculus at American University was given to use the assessment to discover the underlying causes for student's inability to use graphs effectively. The study indicates that graphical representation is not emphasized properly in the curriculum…

Projectile Motion without Calculus

ERIC Educational Resources Information Center

Rizcallah, Joseph A.

2018-01-01

Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are kept at a fairly elementary level, some, such as determining the safe domain, involve not so elementary…

Design Research on Inquiry-Based Multivariable Calculus: Focusing on Students' Argumentation and Instructional Design

ERIC Educational Resources Information Center

Kwon, Oh Nam; Bae, Younggon; Oh, Kuk Hwan

2015-01-01

In this study, researchers design and implement an inquiry based multivariable calculus course in a university which aims at enhancing students' argumentation in rich mathematical discussions. This research aims to understand the characteristics of students' argumentation in activities involving proof constructions through mathematical…

Calculus Students' and Instructors' Conceptualizations of Slope: A Comparison across Academic Levels

ERIC Educational Resources Information Center

Nagle, Courtney; Moore-Russo, Deborah; Viglietti, Janine; Martin, Kristi

2013-01-01

This study considers tertiary calculus students' and instructors' conceptualizations of slope. Qualitative techniques were employed to classify responses to 5 items using conceptualizations of slope identified across various research settings. Students' responses suggest that they rely on procedurally based conceptualizations of…

Calculus Student Understanding of Continuity

ERIC Educational Resources Information Center

Wangle, Jayleen Lillian

2013-01-01

Continuity is a central concept in calculus. Yet very few students seem to understand the nature of continuity. The research described was conducted in two stages. Students were asked questions in multiple choice and true/false format regarding function, limit and continuity. These results were used to identify participants as strong, weak or…

Using Matlab in a Multivariable Calculus Course.

ERIC Educational Resources Information Center

Schlatter, Mark D.

The benefits of high-level mathematics packages such as Matlab include both a computer algebra system and the ability to provide students with concrete visual examples. This paper discusses how both capabilities of Matlab were used in a multivariate calculus class. Graphical user interfaces which display three-dimensional surfaces, contour plots,…

Fractional vector calculus for fractional advection dispersion

NASA Astrophysics Data System (ADS)

Meerschaert, Mark M.; Mortensen, Jeff; Wheatcraft, Stephen W.

2006-07-01

We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection-dispersion equation for flow in heterogeneous porous media.

Self-Paced Calculus: A Case Study.

ERIC Educational Resources Information Center

Johnson, Guy, Jr.; Pascarella, Ernest T.

Increasingly higher education is confronted with the task of educating a population of students whose entry aptitudes and skills have grown more heterogeneous. Perhaps nowhere is this diversity of abilities more apparent, and at the same time more difficult to deal with, than in courses in introductory calculus. This paper outlines an experimental…

A Calculus Activity with Foundations in Geometric Learning

ERIC Educational Resources Information Center

Wagner, Jennifer; Sharp, Janet

2017-01-01

Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the…

Writing-to-Learn Activities to Provoke Deeper Learning in Calculus

ERIC Educational Resources Information Center

Jaafar, Reem

2016-01-01

For students with little experience in mathematical thinking and conceptualization, writing-to-learn activities (WTL) can be particularly effective in promoting discovery and understanding. For community college students embarking on a first calculus course in particular, writing activities can help facilitate the transition from an "apply…

The Pendulum and the Calculus.

ERIC Educational Resources Information Center

Sworder, Steven C.

A pair of experiments, appropriate for the lower division fourth semester calculus or differential equations course, are presented. The second order differential equation representing the equation of motion of a simple pendulum is derived. The period of oscillation for a particular pendulum can be predicted from the solution to this equation. As a…

Four Ways to Skin a Definite Integral

ERIC Educational Resources Information Center

Dence, Thomas; Dence, Joseph

2010-01-01

The integral of 1/(1 + x[superscript 2]) is standard in elementary calculus, but the related integral 1/(1 + x[superscript 4]) rarely appears. In this article we examine the latter integral, computing its value by four different methods; several that involve standard elementary calculus techniques, and several involving complex integration.

An Investigation of Calculus Learning Using Factorial Modeling.

ERIC Educational Resources Information Center

Dick, Thomas P.; Balomenos, Richard H.

Structural covariance models that would explain the correlations observed among mathematics achievement and participation measures and related cognitive and affective variables were developed. A sample of college calculus students (N=268; 124 females and 144 males) was administered a battery of cognitive tests (including measures of spatial-visual…

Encouraging Example Generation: A Teaching Experiment in First-Semester Calculus

ERIC Educational Resources Information Center

Wagner, Elaine Rumsey; Orme, Susan Marla; Turner, Heidi Jean; Yopp, David

2017-01-01

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article…

Individual Differences Related to College Students' Course Performance in Calculus II

ERIC Educational Resources Information Center

Hart, Sara A.; Daucourt, Mia; Ganley, Colleen M.

2017-01-01

In this study, we explore student achievement in a semester-long flipped Calculus II course, combining various predictor measures related to student attitudes (math anxiety, math confidence, math interest, math importance) and cognitive skills (spatial skills, approximate number system), as well as student engagement with the online system…

Are Homeschoolers Prepared for College Calculus?

ERIC Educational Resources Information Center

Wilkens, Christian P.; Wade, Carol H.; Sonnert, Gerhard; Sadler, Philip M.

2015-01-01

Homeschooling in the United States has grown considerably over the past several decades. This article presents findings from the Factors Influencing College Success in Mathematics (FICSMath) survey, a national study of 10,492 students enrolled in tertiary calculus, including 190 students who reported homeschooling for a majority of their high…

Understanding the Integral: Students' Symbolic Forms

ERIC Educational Resources Information Center

Jones, Steven R.

2013-01-01

Researchers are currently investigating how calculus students understand the basic concepts of first-year calculus, including the integral. However, much is still unknown regarding the "cognitive resources" (i.e., stable cognitive units that can be accessed by an individual) that students hold and draw on when thinking about the integral. This…

Flipping the Calculus Classroom: A Cost-Effective Approach

ERIC Educational Resources Information Center

Young, Andrea

2015-01-01

This article discusses a cost-effective approach to flipping the calculus classroom. In particular, the emphasis is on low-cost choices, both monetarily and with regards to faculty time, that make the daunting task of flipping a course manageable for a single instructor. Student feedback and overall impressions are also presented.

Students' Exploratory Thinking about a Nonroutine Calculus Task

ERIC Educational Resources Information Center

Nabb, Keith

2013-01-01

In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect.…

Mathematics Placement at Cottey College.

ERIC Educational Resources Information Center

Callahan, Susan

In response to the large numbers of students who were failing or dropping out of basic algebra and calculus classes, Cottey College, in Missouri, developed a math placement program in 1982 using Basic Algebra (BA) and Calculus Readiness (CR) tests from the Mathematical Association of America's Placement Testing Program. Cut off scores for the…

Giant primary vaginal calculus secondary to vesicovaginal fistula with partial vaginal outlet obstruction in a 12-year-old girl.

PubMed

Chen, Shushang; Ge, Rong; Zhu, Lingfeng; Yang, Shunliang; Wu, Weizhen; Yang, Yin; Tan, Jianming

2011-10-01

A vesicovaginal fistula with vagina obstruction associated with vaginal calculi is an extremely rare medical condition. We report a giant primary vaginal calculus resulting from vesicovaginal fistula with partial vaginal outlet obstruction secondary to perineum trauma and surgery in a 12-year-old girl. Episiotomy was performed and the adhesive labia minora was split. After the removal of a giant calculus in the vagina, approximately 8 cm in diameter, the fistula tract was completely excised, followed by the repair of the vesicovagina fistula and the vagina. The patient was symptom-free at 6-month follow-up examination. Copyright © 2011 Elsevier Inc. All rights reserved.

Solving multi-customer FPR model with quality assurance and discontinuous deliveries using a two-phase algebraic approach.

PubMed

Chiu, Yuan-Shyi Peter; Chou, Chung-Li; Chang, Huei-Hsin; Chiu, Singa Wang

2016-01-01

A multi-customer finite production rate (FPR) model with quality assurance and discontinuous delivery policy was investigated in a recent paper (Chiu et al. in J Appl Res Technol 12(1):5-13, 2014) using differential calculus approach. This study employs mathematical modeling along with a two-phase algebraic method to resolve such a specific multi-customer FPR model. As a result, the optimal replenishment lot size and number of shipments can be derived without using the differential calculus. Such a straightforward method may assist practitioners who with insufficient knowledge of calculus in learning and managing the real multi-customer FPR systems more effectively.

Students' difficulties with vector calculus in electrodynamics

NASA Astrophysics Data System (ADS)

Bollen, Laurens; van Kampen, Paul; De Cock, Mieke

2015-12-01

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven encounter with the divergence and curl of a vector field in mathematical and physical contexts. We have found that they are quite skilled at doing calculations, but struggle with interpreting graphical representations of vector fields and applying vector calculus to physical situations. We have found strong indications that traditional instruction is not sufficient for our students to fully understand the meaning and power of Maxwell's equations in electrodynamics.

Vector 33: A reduce program for vector algebra and calculus in orthogonal curvilinear coordinates

NASA Astrophysics Data System (ADS)

Harper, David

1989-06-01

This paper describes a package with enables REDUCE 3.3 to perform algebra and calculus operations upon vectors. Basic algebraic operations between vectors and between scalars and vectors are provided, including scalar (dot) product and vector (cross) product. The vector differential operators curl, divergence, gradient and Laplacian are also defined, and are valid in any orthogonal curvilinear coordinate system. The package is written in RLISP to allow algebra and calculus to be performed using notation identical to that for operations. Scalars and vectors can be mixed quite freely in the same expression. The package will be of interest to mathematicians, engineers and scientists who need to perform vector calculations in orthogonal curvilinear coordinates.

A calculus based on a q-deformed Heisenberg algebra

DOE PAGES

Cerchiai, B. L.; Hinterding, R.; Madore, J.; ...

1999-04-27

We show how one can construct a differential calculus over an algebra where position variables $x$ and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra has a subalgebra generated by cursive Greek chi and its inverse which we call the coordinate algebra. A physical field is considered to be an element of the completion of this algebra. We can construct a derivative which leaves invariant the coordinate algebra and so takes physical fields into physical fields. A generalized Leibniz rule for this algebra can be found. Based on thismore » derivative differential forms and an exterior differential calculus can be constructed.« less

Productive and ineffective efforts: how student effort in high school mathematics relates to college calculus success

NASA Astrophysics Data System (ADS)

Barnett, M. D.; Sonnert, G.; Sadler, P. M.

2014-10-01

Relativizing the popular belief that student effort is the key to success, this article finds that effort in the most advanced mathematics course in US high schools is not consistently associated with college calculus performance. We distinguish two types of student effort: productive and ineffective efforts. Whereas the former carries the commonly expected benefits, the latter is associated with negative consequences. Time spent reading the course text in US high schools was negatively related to college calculus performance. Daily study time, however, was found to be either a productive or an ineffective effort, depending on the level of high school mathematics course and the student's performance in it.

Mathematical Features of the Calculus

ERIC Educational Resources Information Center

Sauerheber, Richard D.

2010-01-01

The fundamental theorems of the calculus describe the relationships between derivatives and integrals of functions. The value of any function at a particular location is the definite derivative of its integral and the definite integral of its derivative. Thus, any value is the magnitude of the slope of the tangent of its integral at that position,…

Will Discrete Mathematics Surpass Calculus in Importance? and Responses .

ERIC Educational Resources Information Center

Ralston, Anthony; And Others

1984-01-01

Ralston proposes that the decrease in the importance of calculus in the world of mathematics is accelerating and the world of applied mathematics is changing rapidly. He briefly presents arguments for discrete mathematics. Then follow reactions from McLane, Wagner, Hilton, Woodriff, Kleitman, and Lax, and a response by Ralston. (MNS)

Complex Mapping of Aerofoils--A Different Perspective

ERIC Educational Resources Information Center

Matthews, Miccal T.

2012-01-01

In this article an application of conformal mapping to aerofoil theory is studied from a geometric and calculus point of view. The problem is suitable for undergraduate teaching in terms of a project or extended piece of work, and brings together the concepts of geometric mapping, parametric equations, complex numbers and calculus. The Joukowski…

A Comparison of Mathematics Teachers' and Professors' Views on Secondary Preparation for Tertiary Calculus

ERIC Educational Resources Information Center

Wade, Carol; Sonnert, Gerhard; Sadler, Philip M.; Hazari, Zahra; Watson, Charity

2016-01-01

This article compares the views of teachers and professors about the transition from secondary mathematics to tertiary calculus. Quantitative analysis revealed five categories where teachers and professors differed significantly in the relative frequency of addressing them. Using the rite of passage theory, the separation and incorporation phases…

Teaching Calculus with Wolfram|Alpha

ERIC Educational Resources Information Center

Dimiceli, Vincent E.; Lang, Andrew S. I. D.; Locke, LeighAnne

2010-01-01

This article describes the benefits and drawbacks of using Wolfram|Alpha as the platform for teaching calculus concepts in the lab setting. It is a result of our experiences designing and creating an entirely new set of labs using Wolfram|Alpha. We present the reasoning behind our transition from using a standard computer algebra system (CAS) to…

Some Factors Effected Student's Calculus Learning Outcome

ERIC Educational Resources Information Center

Rajagukguk, Wamington

2016-01-01

The purpose of this study is to determine the factors effected calculus learning outcome of the student. This study was conducted with 176 respondents, which were selected randomly. The data were obtained by questionnaire, and then analyzed by using multiple regressions, and correlation, at level of a = 0.05. The findings showed there is the…

POGIL in the Calculus Classroom

ERIC Educational Resources Information Center

Bénéteau, Catherine; Guadarrama, Zdenka; Guerra, Jill E.; Lenz, Laurie; Lewis, Jennifer E.; Straumanis, Andrei

2017-01-01

In this paper, we will describe the experience of the authors in using process-oriented guided inquiry learning (POGIL) in calculus at four institutions across the USA. We will briefly examine how POGIL compares to and fits in with other kinds of inquiry-based learning approaches. In particular, we will first discuss the unique structure of a…

Non-Mathematics Students' Reasoning in Calculus Tasks

ERIC Educational Resources Information Center

Jukic Matic, Ljerka

2015-01-01

This paper investigates the reasoning of first year non-mathematics students in non-routine calculus tasks. The students in this study were accustomed to imitative reasoning from their primary and secondary education. In order to move from imitative reasoning toward more creative reasoning, non-routine tasks were implemented as an explicit part of…

Constructivized Calculus in College Mathematics

ERIC Educational Resources Information Center

Lawrence, Barbara Ann

2012-01-01

The purpose of this study is to present some of the classical concepts, definitions, and theorems of calculus from the constructivists' point of view in the spirit of the philosophies of L.E.J. Brouwer and Errett Bishop. This presentation will compare the classical statements to the constructivized statements. The method focuses on giving…

A Comparative Study of Definitions on Limit and Continuity of Functions

ERIC Educational Resources Information Center

Shipman, Barbara A.

2012-01-01

Differences in definitions of limit and continuity of functions as treated in courses on calculus and in rigorous undergraduate analysis yield contradictory outcomes and unexpected language. There are results about limits in calculus that are false by the definitions of analysis, functions not continuous by one definition and continuous by…

Motivation, Volition and Belief Change Strategies to Improve Mathematics Learning

ERIC Educational Resources Information Center

Kim, C.; Keller, J. M.

2010-01-01

The purpose of this study was to investigate the effects of motivation, volition and belief change strategies, implemented with personal and group email messages, on students' attitudes, study habits and achievement in a calculus course for non-mathematics majors. Eighty four undergraduates enrolled in a calculus course received emails over a…

Maple Graphing Tools for Calculus III

ERIC Educational Resources Information Center

Cook, Darwyn

2006-01-01

For those instructors lacking artistic skills, teaching 3-dimensional calculus can be a challenge. Although some instructors spend a great deal of time working on their illustrations, trying to get them just right, students nevertheless often have a difficult time understanding some of them. To address this problem, the author has written a series…

Using Peer Instruction and I-Clickers to Enhance Student Participation in Calculus

ERIC Educational Resources Information Center

Lucas, Adam

2009-01-01

In my Calculus classes I encourage my students to actively reflect on course material, to work collaboratively, and to generate diverse solutions to questions. To facilitate this I use peer instruction (PI), a structured questioning process, and i-clickers, a radio frequency classroom response system enabling students to vote anonymously. This…

Calculus Limits Involving Infinity: The Role of Students' Informal Dynamic Reasoning

ERIC Educational Resources Information Center

Jones, Steven R.

2015-01-01

Few studies on calculus limits have centred their focus on student understanding of limits at infinity or infinite limits that involve continuous functions (as opposed to discrete sequences). This study examines student understanding of these types of limits using both pure mathematics and applied-science functions and formulas. Seven calculus…

Calculus, Radio Dials and the Straight-Line Frequency Variable Capacitor

ERIC Educational Resources Information Center

Boyadzhiev, Khristo N.

2010-01-01

Most often radio dials of analogue radios are not uniformly graded; the frequencies are cramped on the left side or on the right side. This makes tuning more difficult. Why are dials made this way? We shall see here that simple calculus can help understand this problem and solve it. (Contains 7 figures.)

Engineering Students' Experiences of Interactive Teaching in Calculus

ERIC Educational Resources Information Center

Weurlander, Maria; Cronhjort, Mikael; Filipsson, Lars

2017-01-01

This study reports on an educational development initiative where peer instruction was used instead of traditional lectures in a calculus course for first-year engineering students. The aim of the study was to explore students' experiences of this method. Data were collected by means of an open-ended questionnaire on two occasions: early and late…

Understanding Introductory Students' Application of Integrals in Physics from Multiple Perspectives

ERIC Educational Resources Information Center

Hu, Dehui

2013-01-01

Calculus is used across many physics topics from introductory to upper-division level college courses. The concepts of differentiation and integration are important tools for solving real world problems. Using calculus or any mathematical tool in physics is much more complex than the straightforward application of the equations and algorithms that…

An Experiment in "Flipped" Teaching in Freshman Calculus

ERIC Educational Resources Information Center

Anderson, Laura; Brennan, Joseph Phillip

2015-01-01

At Binghamton, Calculus 1 is taught to over 1000 students each fall in sections of about 30-40 students, with graduate student instructors teaching most sections. Despite having small classrooms instead of lecture halls, the satisfaction and performance of students has historically been poor. We had hoped to improve student success by changing how…

The Impact of Instructor Pedagogy on College Calculus Students' Attitude toward Mathematics

ERIC Educational Resources Information Center

Sonnert, Gerhard; Sadler, Philip M.; Sadler, Samuel M.; Bressoud, David M.

2015-01-01

College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students' attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students'…

Modeling the Sliding/Falling Ladder Paradox

ERIC Educational Resources Information Center

Fox, William P.; Fox, James B.

2003-01-01

Recently we were presented with an interesting twist to the sliding ladder problem viewed in the related rates section of most calculus textbooks. Our problem concerning a sliding ladder that eventually hits the ground. At first, those attempting this problem fell into the calculus trap using only related rates. Previous work for this problem…

Assessing the Impact of Computer Programming in Understanding Limits and Derivatives in a Secondary Mathematics Classroom

ERIC Educational Resources Information Center

de Castro, Christopher H.

2011-01-01

This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…

It's about Time: The Relationships between Coverage and Instructional Practices in College Calculus

ERIC Educational Resources Information Center

Johnson, Estrella; Ellis, Jessica; Rasmussen, Chris

2016-01-01

This paper is based on a large-scale empirical study designed to investigate Calculus I programmes across the United States to better understand the relationship between instructors' concerns about coverage, instructional practices, and the nature of the material covered. We found that there was no association between instructors feeling pressured…

Optimization in First Semester Calculus: A Look at a Classic Problem

ERIC Educational Resources Information Center

LaRue, Renee; Infante, Nicole Engelke

2015-01-01

Optimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students' activity through the lens of Tall and Vinner's concept image and Carlson and Bloom's multidimensional…

Reference Framework for Describing and Assessing Students' Understanding in First Year Calculus

ERIC Educational Resources Information Center

Kannemeyer, Larry

2005-01-01

This paper presents aspects of a study that investigates the development of an instrument, a reference framework, to analyse students' written responses to non-routine problems in a first year calculus course in order to describe the complexities of their understanding and to assess their understanding of particular mathematical concepts.…

Integrating Supplementary Application-Based Tutorials in the Multivariable Calculus Course

ERIC Educational Resources Information Center

Verner, I. M.; Aroshas, S.; Berman, A.

2008-01-01

This article presents a study in which applications were integrated in the Multivariable Calculus course at the Technion in the framework of supplementary tutorials. The purpose of the study was to test the opportunity of extending the conventional curriculum by optional applied problem-solving activities and get initial evidence on the possible…