A Closer Look at an Advanced Placement Calculus Problem.
ERIC Educational Resources Information Center
Rudd, David
1985-01-01
Answers and justifications for an interesting problem on the Advanced Placement Calculus AB Examination are discussed. The problem provides diverse ways in which students can gain appreciation and understanding for the subject. (MNS)
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…
ERIC Educational Resources Information Center
Subotnik, Rena F.; Strauss, Shiela M.
1995-01-01
Despite scoring lower on the mathematics Scholastic Assessment Test (SAT-M) prior to taking an advanced placement calculus course, female students (n=85) scored as well as males (n=51) on the Advanced Placement BC level calculus test. Predictors of AP scores were: first, scores on the Calculus Readiness Test; second, scores on the SAT-M; and…
ERIC Educational Resources Information Center
de Wolf, Virginia A.
Freshmen placed into the second or third quarter of the first year calculus sequence at the University of Washington were studied. Two major findings were: freshmen eligible for advanced placement earned mean mathematics Grade Point Averages (GPAs) which were quite high; and advanced placement students earned mean mathematics GPAs substantially…
The Impact of the Calculator on the Content Validity of Advanced Placement Calculus Problems.
ERIC Educational Resources Information Center
Gimmestad, Beverly J.
Nineteen Calculus II students were randomly sampled and divided into calculator (n=9) and noncalculator (n=10) groups. These students were asked to "think aloud" while solving 24 Advanced Placement calculus problems. Each student interview was videotaped, coded and analyzed for reasoning process as well as outcome. The results indicated that the…
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…
ERIC Educational Resources Information Center
Lazzaro, Christopher; Jones, Lee; Webb, David C.; Grover, Ryan; Di Giacomo, F. Tony; Marino, Katherine Adele
2016-01-01
This report will determine to what degree the AP Physics 1 and 2 and AP Calculus AB and BC frameworks are aligned with the Trends in International Mathematics and Science Study (TIMSS) Advanced Physics and Mathematics frameworks. This will enable an exploration of any differences in content coverage and levels of complexity, and will set the stage…
ERIC Educational Resources Information Center
Ohio Council on Advanced Placement, Columbus.
THE DOCUMENT PRESENTS A DESCRIPTION OF THE ADVANCED PLACEMENT PROGRAM IN OHIO. ANSWERS ARE GIVEN TO KEY QUESTIONS ON THE FUNCTION OF ADVANCED PLACEMENT, ACADEMIC AREAS COVERED, PROGRAM ADMINISTRATION, COSTS, BENEFITS, VARIOUS ORGANIZATIONAL PATTERNS, STUDENT PARTICIPANTS, COLLEGES AND UNIVERSITIES IN OHIO AND REPRESENTATIVE NATIONAL INSTITUTIONS…
ERIC Educational Resources Information Center
Fry, Dale Eugene
College students' performance in their first two calculus-level mathematics courses was studied by comparing students skipping, on any basis, one or more courses in the regular calculus sequence and students reaching these same courses through the regular sequence. Those skipping via CEEB AP and those skipping for any other reason were also…
Raise Test Scores: Integrate Biology and Calculus.
ERIC Educational Resources Information Center
Lukens, Jeffrey D.; Feinstein, Sheryl
This paper presents the results of research that compared the academic achievement of high school students enrolled in an integrated Advanced Placement Biology/Advanced Placement Calculus course with students enrolled in traditional Advanced Placement Biology and Advanced Placement Calculus courses. Study subjects included high school students…
Factors Associated with Success in College Calculus II
ERIC Educational Resources Information Center
Rosasco, Margaret E.
2013-01-01
Students are entering college having earned credit for college Calculus 1 based on their scores on the College Board's Advanced Placement (AP) Calculus AB exam. Despite being granted credit for college Calculus 1, it is unclear whether these students are adequately prepared for college Calculus 2. College calculus classes are often taught…
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 mastery for…
Advanced Placement Courses and American Indian Performance
ERIC Educational Resources Information Center
Moore, George; Slate, John R.
2010-01-01
Enrollment in Advanced Placement (AP) courses and performance on Advanced Placement examinations for American Indians in the U.S. for 2007 was analyzed. Scores on AP examinations, overall and then for five AP courses, were compared to the AP examination scores of White students. In every case, American Indians had AP examination scores that were…
Advances in Pediatric Gastrostomy Placement.
McSweeney, Maireade E; Smithers, C Jason
2016-01-01
Placement of gastrostomy tubes in infants and children has become increasingly commonplace. A historical emphasis on use of open gastrostomy has been replaced by less invasive methods of placement, including percutaneous endoscopic gastrostomy and laparoscopically assisted gastrostomy procedures. Various complications, ranging from minor to the more severe, have been reported with all methods of placement. Many pediatric patients who undergo gastrostomy tube placement will require long-term enteral therapy. Given the prolonged time pediatric patients may remain enterally dependent, further quality improvement and education initiatives are needed to improve long-term care and outcomes of these patients.
ERIC Educational Resources Information Center
Gregory, Sally W.
2009-01-01
This research study focused on the relationship between student outcomes (indicated by Advanced Placement enrollment, Advanced Placement course grades, Advanced Placement exam scores, Advanced Placement exam passing rate) and student demographic factors as well as student support programs (such as AVID, an AP Incentive Program, and a summer AP…
ERIC Educational Resources Information Center
Gibson, Megan
2013-01-01
Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the…
Exposing Calculus Students to Advanced Mathematics
ERIC Educational Resources Information Center
Griffiths, Barry J.; Haciomeroglu, Erhan Selcuk
2014-01-01
To ensure the competitiveness of the USA in the global economy, and its role as a leader in science and engineering, it is important to cultivate the next generation of home grown mathematicians. However, while universities across the USA offer calculus classes to thousands of undergraduate students each year, very few of them go on to major in…
Advanced fiber placement of composite fuselage structures
NASA Technical Reports Server (NTRS)
Anderson, Robert L.; Grant, Carroll G.
1991-01-01
The Hercules/NASA Advanced Composite Technology (ACT) program will demonstrate the low cost potential of the automated fiber placement process. The Hercules fiber placement machine was developed for cost effective production of composite aircraft structures. The process uses a low cost prepreg tow material form and achieves equivalent laminate properties to structures fabricated with prepreg tape layup. Fiber placement demonstrations planned for the Hercules/NASA program include fabrication of stiffened test panels which represent crown, keel, and window belt segments of a typical transport aircraft fuselage.
Exposing calculus students to advanced mathematics
NASA Astrophysics Data System (ADS)
Griffiths, Barry J.; Selcuk Haciomeroglu, Erhan
2014-07-01
To ensure the competitiveness of the USA in the global economy, and its role as a leader in science and engineering, it is important to cultivate the next generation of home grown mathematicians. However, while universities across the USA offer calculus classes to thousands of undergraduate students each year, very few of them go on to major in mathematics. This paper posits that one of the main reasons is that the mathematical community does not expose calculus students to the beauty and complexity of upper-level mathematics, and that by doing so before they fully commit to their programme of study, the number of students with a qualification in mathematics can be increased. The results show a significant increase in the number of students planning to add a minor in mathematics, and an increased likelihood among freshmen and sophomores to change their major.
Where Should We Go With Advanced Placement?
NASA Astrophysics Data System (ADS)
Lichten, William
2001-04-01
This is a review of the Advanced Placement (AP)Program. In disagreement with claims of the College Board, there is firm evidence that the average test performance level has dropped. The College Board's scale and claims for AP qualification disagree seriously with college standards. A majority of tests taken do not qualify. It appears that "advanced placement" is coming closer to "placement." This paper recommends that the College Board's policy, which previously has concentrated on the numbers of participants, should include an emphasis on student performance and program quality. AP could accomplish its goal of reaching a wider range of students by changing along the lines followed in college introductory physics courses: multiple tracks.
Advanced Placement: Do Minorities Have Equal Opportunity?
ERIC Educational Resources Information Center
Klopfenstein, Kristin
2004-01-01
Black and Hispanic high school students enroll in Advanced Placement (AP) courses at approximately half the rate of white students. This paper develops a microeconomic model of the AP participation decision and finds that low income is the single most important factor behind the minority AP participation gap. In addition, minority students enroll…
Advanced Placement Economics. Teacher Resource Manual.
ERIC Educational Resources Information Center
Morton, John S.
This book, in conjunction with the student activities books for macroeconomics and microeconomics, is designed for teaching the Advanced Placement Economics course. The book contains five units for the microeconomic portion and six units for the macroeconomic portion of the text. Along with the many activities are sample multiple-choice questions,…
Population in Advanced Placement Human Geography.
ERIC Educational Resources Information Center
Sharma, Martha B.
2000-01-01
Addresses the population section of the Advanced Placement course outline for human geography, focusing on four themes: (1) geographical analysis of population; (2) population distribution and composition; (3) population growth and decline over time and space; and (4) population movement. Identifies strategies for instructional activities.…
Advanced Placement European History: A New Approach.
ERIC Educational Resources Information Center
Beaber, Lawrence
A new approach to the teaching of European history is being implemented in Advanced Placement secondary classes. In the latter 1950's a Committee of Examiners composed of European history professors and secondary teachers formulated a course description comprised of a brief outline of an introductory survey in European history. It was organized…
Advanced Placement Economics. Microeconomics: Student Activities.
ERIC Educational Resources Information Center
Morton, John S.
This book is designed to help advanced placement students better understand microeconomic concepts through various activities. The book contains 5 units with 73 activities, sample multiple-choice questions, sample short essay questions, and sample long essay questions. The units are entitled: (1) "The Basic Economic Problem"; (2) "The Nature and…
Advanced Placement Economics. Macroeconomics: Student Activities.
ERIC Educational Resources Information Center
Morton, John S.
This book is designed to help advanced placement students better understand macroeconomic concepts through various activities. The book contains 6 units with 64 activities, sample multiple-choice questions, sample short essay questions, and sample long essay questions. The units are entitled: (1) "Basic Economic Concepts"; (2) "Measuring Economic…
Photoelectron Spectroscopy in Advanced Placement Chemistry
ERIC Educational Resources Information Center
Benigna, James
2014-01-01
Photoelectron spectroscopy (PES) is a new addition to the Advanced Placement (AP) Chemistry curriculum. This article explains the rationale for its inclusion, an overview of how the PES instrument records data, how the data can be analyzed, and how to include PES data in the course. Sample assessment items and analysis are included, as well as…
Advanced Placement: Model Policy Components. Policy Analysis
ERIC Educational Resources Information Center
Zinth, Jennifer
2016-01-01
Advanced Placement (AP), launched in 1955 by the College Board as a program to offer gifted high school students the opportunity to complete entry-level college coursework, has since expanded to encourage a broader array of students to tackle challenging content. This Education Commission of the State's Policy Analysis identifies key components of…
ERIC Educational Resources Information Center
Cirillo, Mary Grupe
2010-01-01
The purpose of this study was to determine the impact of Virginia school divisions' policy of paying the fee for students to take Advanced Placement exams on Advanced Placement course enrollment, the number of Advanced Placement exams taken by students, the average scores earned and the percent of students earning qualifying scores of 3, 4, or 5…
Advanced Jones calculus for the classification of periodic metamaterials
NASA Astrophysics Data System (ADS)
Menzel, Christoph; Rockstuhl, Carsten; Lederer, Falk
2010-11-01
By relying on an advanced Jones calculus, we analyze the polarization properties of light upon propagation through metamaterial slabs in a comprehensive manner. Based on symmetry considerations, we show that all periodic metamaterials may be divided into five different classes only. It is shown that each class differently affects the polarization of the transmitted light and sustains different eigenmodes. We show how to deduce these five classes from symmetry considerations and provide a simple algorithm that can be applied to decide to which class a given metamaterial belongs by measuring only the transmitted intensities.
Advanced Jones calculus for the classification of periodic metamaterials
Menzel, Christoph; Rockstuhl, Carsten; Lederer, Falk
2010-11-15
By relying on an advanced Jones calculus, we analyze the polarization properties of light upon propagation through metamaterial slabs in a comprehensive manner. Based on symmetry considerations, we show that all periodic metamaterials may be divided into five different classes only. It is shown that each class differently affects the polarization of the transmitted light and sustains different eigenmodes. We show how to deduce these five classes from symmetry considerations and provide a simple algorithm that can be applied to decide to which class a given metamaterial belongs by measuring only the transmitted intensities.
ERIC Educational Resources Information Center
Steckroth, Jeffrey J.
2010-01-01
For nearly three decades, during which the author taught everything from basic algebra to advanced placement calculus, the author thought of himself as a secondary school mathematics teacher. The notion of teaching elementary school math never appealed to him because of its simplicity. The author stresses that anyone could teach children to count,…
A TENTATIVE GUIDE, DIFFERENTIAL AND INTEGRAL CALCULUS.
ERIC Educational Resources Information Center
BRANT, VINCENT; GERARDI, WILLIAM
THE COURSE IS INTENDED TO GO BEYOND THE REQUIREMENTS OF THE ADVANCED PLACEMENT PROGRAM IN MATHEMATICS AS DESIGNED BY THE COLLEGE ENTRANCE EXAMINATION BOARD. THE ADVANCED PLACEMENT PROGRAM CONSISTS OF A 1-YEAR COURSE COMBINING ANALYTIC GEOMETRY AND CALCULUS. PRESUPPOSED HERE ARE--A SEMESTER COURSE IN ANALYTIC GEOMETRY AND A THOROUGH KNOWLEDGE OF…
Privilege, Equity, and the Advanced Placement Program: Tug of War
ERIC Educational Resources Information Center
Schneider, Jack
2009-01-01
The Advanced Placement Program is growing at a striking rate in US high schools and at the same time being abandoned by high-status schools. This paper explores the history of the Advanced Placement Program, from its roots in the 1950s as a programme for challenging high-achieving students at high-status schools, through its equity-motivated…
Advance Placement Policies of Nursing Education in North Carolina.
ERIC Educational Resources Information Center
North Carolina State Board of Education, Raleigh.
Advance placement policies are identified in this booklet designed to aid persons who are potentially qualified by prior training or experience for advance placement in programs leading to graduation in nursing or practical nursing. The information was gathered from all 82 programs approved by the state board for 1975. The trend toward improving…
ERIC Educational Resources Information Center
Mercurio, Joseph; And Others
1984-01-01
Compared performance of Syracuse University Project Advance (PA) chemistry students (N=35) with advanced placement (AP) candidates on the AP chemistry examination. PA students scored slightly above the national average on the examination, and students who performed well (B or better) in AP chemistry also did well on the examination. (JN)
Technological advances for PICC placement and management.
Pettit, Janet
2007-06-01
Placement of a peripherally inserted central catheter (PICC) is often complicated by the infant's small size and previous use of the peripheral veins, making the traditional means of insertion inadequate. New techniques and technologies, previously reserved for pediatric and adult patients, are now available for use in neonates and can enhance the practice of neonatal PICC teams. The modified Seldinger technique allows insertion of the PICC via smaller peripheral veins while decreasing venous trauma and enhancing the rate of successful placement. A second useful technique, the catheter exchange procedure, allows insertion of a new catheter within the same vein when complications such as occlusion, breakage, or inappropriate position occur and require removal of the currently dwelling PICC. Clinicians caring for neonates and infants must continually update their knowledge and skill by incorporating new techniques into their practice.
Advanced Placement Economics Improves Both Merit and Equity
ERIC Educational Resources Information Center
Meek, Sally; Morton, John
2009-01-01
In 1989, microeconomics and macroeconomics examinations debuted on the Advanced Placement (AP) scene. At that time, many professors of economics were skeptical that college freshmen had the skills and maturity to understand the concepts in principles of economics courses. They thought teaching these concepts to high school students was even more…
Teaching Melodic Dictation in Advanced Placement Music Theory
ERIC Educational Resources Information Center
Paney, Andrew S.; Buonviri, Nathan O.
2014-01-01
In this study approaches to teaching melodic dictation skills used by Advanced Placement (AP) Music Theory teachers were examined. Twelve high school teachers from four states were interviewed. Four themes emerged from the interview transcripts: cognitive frameworks, processing strategies, rhythm, and course design. Participants generally…
Cities and Urban Land Use in Advanced Placement Human Geography.
ERIC Educational Resources Information Center
Ford, Larry R.
2000-01-01
Discusses the cities and urban land use section of the Advanced Placement (AP) human geography course, focusing on the: (1) definitions of urbanism; (2) origin and evolution of cities; (3) functional character of contemporary cities; (4) built environment and social space; and (5) responses to urban growth. (CMK)
Beginning an Advanced Placement Music Course. Edition Y.
ERIC Educational Resources Information Center
Thomson, William; And Others
The College Entrance Examination Board has prepared this publication to help secondary school teachers develop Advanced Placement (AP) courses in music. The discussion of strategy recommendations, reading materials, and record collections should be adapted to suit local preferences and individual skills. An opening section of general remarks…
75 FR 75666 - Advanced Placement (AP) Test Fee Program
Federal Register 2010, 2011, 2012, 2013, 2014
2010-12-06
...: On September 1, 2010, we published in the Federal Register (75 FR 53681) a notice inviting... in the September 1, 2010 notice (75 FR 53682-53683). We encourage eligible applicants to submit their... Advanced Placement (AP) Test Fee Program AGENCY: Office of Elementary and Secondary Education...
Gifted Spanish Speaking English Learners' Participation in Advanced Placement Programs
ERIC Educational Resources Information Center
Torres, Luz Adriana
2010-01-01
This qualitative study sought to uncover the contextual factors of the schooling process that affect the enrollment of gifted Spanish speaking English Learners (ELs) in Advanced Placement (AP) courses. In addition, this study investigated the perceptions of gifted Spanish speaking ELs toward AP courses and how these perceptions might affect their…
Surviving a Midlife Crisis: Advanced Placement Turns Fifty
ERIC Educational Resources Information Center
Mollison, Andrew
2006-01-01
In 1956, 1,220 college-bound juniors and seniors in 104 American high schools took the first Advanced Placement (AP) exams conducted by the Educational Testing Service for the College Board. The AP program was unabashedly elitist and designed to fortify the education of the nation's future leaders in anticipation of Cold War national security…
Advanced Placement Computer Science with Pascal. Volume 2. Experimental Edition.
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY.
This curriculum guide presents 100 lessons for an advanced placement course on programming in Pascal. Some of the topics covered include arrays, sorting, strings, sets, records, computers in society, files, stacks, queues, linked lists, binary trees, searching, hashing, and chaining. Performance objectives, vocabulary, motivation, aim,…
AP: A Critical Examination of the Advanced Placement Program
ERIC Educational Resources Information Center
Sadler, Philip M., Ed.; Sonnert, Gerhard, Ed.; Tai, Robert H., Ed.; Klopfenstein, Kristin, Ed.
2010-01-01
With an annual yearly growth rate of 9.3 percent over the last two decades, Advanced Placement courses have become a juggernaut in American high school education. AP courses are routinely perceived as an indicator of educational rigor, and many schools push to enroll low-income or minority students in these courses in the hope of preparing them…
Industrialization and Economic Development in Advanced Placement Human Geography.
ERIC Educational Resources Information Center
Bailey, Adrian J.
2000-01-01
Focuses on the industrialization and economic development section of the Advanced Placement (AP) human geography course, addressing four specific aspects: (1) the character of industrialization; (2) spatial aspects of the rise of industrial economies; (3) contemporary global patterns of industrialization and resource extraction; and (4) impacts of…
The Preparation and Experience of Advanced Placement in Economics Instructors
ERIC Educational Resources Information Center
Scahill, Edward M.; Melican, Claire
2005-01-01
The authors summarize the results of a survey of 1,365 instructors of advanced placement (AP) economics courses; responses were received from 296 instructors (21.7 percent). The authors discuss the respondents' textbook preferences, graduate and undergraduate backgrounds, teaching experiences, and evaluations of nontextbook teaching materials.
Amityville Memorial High School History Journal Advance Placement History.
ERIC Educational Resources Information Center
Howlett, Charles F., Ed.
The history of Amityville, New York, compiled by 11th and 12th grade advance placement history students, is presented in journal form. Six papers focus on: (1) South Oaks: The Long Island Home; (2) A History of Bethel African Methodist Episcopal Church, Amityville; (3) Amityville: A Vacationland; (4) Amityville School System from 1904 to Present;…
Conceptualizing a Framework for Advanced Placement Statistics Teaching Knowledge
ERIC Educational Resources Information Center
Haines, Brenna
2015-01-01
The purpose of this article is to sketch a conceptualization of a framework for Advanced Placement (AP) Statistics Teaching Knowledge. Recent research continues to problematize the lack of knowledge and preparation among secondary level statistics teachers. The College Board's AP Statistics course continues to grow and gain popularity, but is a…
Federal Register 2010, 2011, 2012, 2013, 2014
2011-03-16
... Advanced Placement Incentive Program; Office of Elementary and Secondary Education; Overview Information...: Promoting Science, Technology, Engineering, and Mathematics (STEM) Education and the competitive preference... Advanced Placement Programs is from section 1705(c) of the Elementary and Secondary Education Act of...
Materials and Area of Study for Advanced Placement Program in American History.
ERIC Educational Resources Information Center
Santos, Peter A.
This paper describes and evaluates benefits of advanced placement programs and identifies materials which can help high school history classroom teachers develop effective advanced placement programs. An advanced placement program is defined as a program which requires a student to do extensive research and writing throughout the school year.…
Again, Maryland Ranks #1 in Advanced Placement (AP) Exam Performance
ERIC Educational Resources Information Center
Maryland State Department of Education, 2010
2010-01-01
For a second year in a row, Maryland ranked first nationwide in the percentage of public school students scoring 3 or higher on at least one AP (Advanced Placement) exam. A score of 3 or higher on the 5-point scale is considered mastery of college-level work. Maryland also continues to show strong gains in the number of students taking an AP exam,…
Gender Differences in STEM Related Advanced Placement Exams
ERIC Educational Resources Information Center
Morris, Jill B.
2013-01-01
Purpose: The purpose of this study was to examine differences between boys and girls in their performance on STEM related AP exams. Specifically, gender differences were examined for the following STEM related AP exams: Calculus AB, Calculus BC, Physics B, Physics C: Electricity and Magnetism, Physics C: Mechanics, Chemistry, and Computer Science…
NASA Astrophysics Data System (ADS)
Urbina, Josue N.
There is a national need to increase the STEM-related workforce. Among factors leading towards STEM careers include the number of advanced high school mathematics and science courses students complete. Florida's enrollment patterns in STEM-related Advanced Placement (AP) courses, however, reveal that only a small percentage of students enroll into these classes. Therefore, screening tools are needed to find more students for these courses, who are academically ready, yet have not been identified. The purpose of this study was to investigate the extent to which scores from a national standardized test, Preliminary Scholastic Assessment Test/ National Merit Qualifying Test (PSAT/NMSQT), in conjunction with and compared to a state-mandated standardized test, Florida Comprehensive Assessment Test (FCAT), are related to selected AP exam performance in Seminole County Public Schools. An ex post facto correlational study was conducted using 6,189 student records from the 2010 - 2012 academic years. Multiple regression analyses using simultaneous Full Model testing showed differential moderate to strong relationships between scores in eight of the nine AP courses (i.e., Biology, Environmental Science, Chemistry, Physics B, Physics C Electrical, Physics C Mechanical, Statistics, Calculus AB and BC) examined. For example, the significant unique contribution to overall variance in AP scores was a linear combination of PSAT Math (M), Critical Reading (CR) and FCAT Reading (R) for Biology and Environmental Science. Moderate relationships for Chemistry included a linear combination of PSAT M, W (Writing) and FCAT M; a combination of FCAT M and PSAT M was most significantly associated with Calculus AB performance. These findings have implications for both research and practice. FCAT scores, in conjunction with PSAT scores, can potentially be used for specific STEM-related AP courses, as part of a systematic approach towards AP course identification and placement. For courses with
Visual thinking and gender differences in high school calculus
NASA Astrophysics Data System (ADS)
Selcuk Haciomeroglu, Erhan; Chicken, Eric
2012-04-01
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 collected from 183 Advanced Placement calculus students in five high schools. Students' visual preferences were not influenced by gender. Statistically significant differences in visual preference scores were found among high- and low-performing students. Thus, the results suggest that stronger preference for visual thinking was associated with higher mathematical performances.
Block Scheduling and Advanced Placement Mathematics: When Tradition and Reform Collide.
ERIC Educational Resources Information Center
Howard, Elizabeth
1997-01-01
This case study reflects block scheduling's effects on advanced-placement mathematics courses of one veteran teacher tracking personal progress since 1989. Block scheduling began in 1994, creating problems for the teacher, whose resistance to the reform was based on declining advanced-placement scores. Teacher attitude and insufficient…
Advanced Placement Academy: Case Study of a Program within a School
ERIC Educational Resources Information Center
Swanson, Julie Dingle; Nagy, Steven
2014-01-01
The focus of this study was the first year of implementation of the Advanced Placement Academy (APA), a program within a high school providing honors and Advanced Placement coursework for high-ability African American students with previously limited access to rigorous courses. The qualitative investigation explores practical solutions from…
77 FR 8848 - Application for New Awards; Advanced Placement (AP) Test Fee Program
Federal Register 2010, 2011, 2012, 2013, 2014
2012-02-15
... Application for New Awards; Advanced Placement (AP) Test Fee Program AGENCY: Office of Elementary and Secondary Education, Department of Education. ACTION: Notice. Overview Information: Advanced Placement Test.... Full Text of Announcement I. Funding Opportunity Description Purpose of Program: The AP Test...
78 FR 19691 - Applications for New Awards; Advanced Placement (AP) Test Fee Program
Federal Register 2010, 2011, 2012, 2013, 2014
2013-04-02
... Applications for New Awards; Advanced Placement (AP) Test Fee Program AGENCY: Office of Elementary and Secondary Education, Department of Education. ACTION: Notice. Overview Information Advanced Placement Test... Announcement I. Funding Opportunity Description Purpose of Program: The AP Test Fee program awards grants...
ERIC Educational Resources Information Center
Jimenez-Castellanos, Oscar
2008-01-01
The Advanced Placement (AP) program was initiated during the early 1950's in response to growing concerns regarding the educational needs of high ability secondary school students. The Advanced Placement "Status Quo" (AP Status Quo) framework suggests that there has been an emphasis on preparing a few students while excluding the majority of…
Hispanic Student Performance on Advanced Placement Exams: A Multiyear, National Investigation
ERIC Educational Resources Information Center
Jara, Teresa Dianne
2013-01-01
Purpose: The purpose of this study was to analyze the Advanced Placement exams that Hispanic students complete and to compare their overall performance with the performance of White students from 2000 to 2012. A second purpose was to determine which Advanced Placement exams were the most difficult exams for Hispanic students and which Advanced…
A Critical Investigation of Advanced Placement U.S. History Textbooks
ERIC Educational Resources Information Center
Cramer, Gregory J.
2012-01-01
This dissertation critically investigates how Advanced Placement (AP) U.S. History textbooks portray key events in Latino/a history. The investigation is made in light of claims made by the College Board, the ACLU, scholars, and federal and state governments that the Advanced Placement program is the path to educational equity for Latino/a…
ERIC Educational Resources Information Center
Holifield-Scott, April
2011-01-01
A study was conducted to determine the extent to which high school and college/university Advanced Placement English Language and Composition readers value and implement the curricular requirements of Advanced Placement English Language and Composition. The participants were 158 readers of the 2010 Advanced Placement English Language and…
Advancing Prediction of Foster Placement Disruption Using Brief Behavioral Screening
ERIC Educational Resources Information Center
Hurlburt, Michael S.; Chamberlain, Patricia; DeGarmo, David; Zhang, Jinjin; Price, Joe M.
2010-01-01
Objective: Behavioral difficulties increase the risk that children will experience negative placement disruptions while in foster care. Chamberlain et al. (2006) found that the Parent Daily Report (PDR), a brief measure of parent-reported child behaviors, was a strong predictor of negative placement changes over 1 year among children receiving…
NASA Astrophysics Data System (ADS)
Ramsey, Susan Brady
The purpose of this study is to examine the effectiveness of the National Math and Science Initiative's Advanced Placement Training and Incentive Program (APTIP) on the number of students taking AP science courses and their performance. The study evaluated 39 schools over a six-year period in six states that participate in the APTIP. The National Math and Science Initiative provided data for cohort I. A general linear model for repeated measures was used to evaluate the data. Data was evaluated three years prior to the intervention and three years during the intervention, which will actually continue for two more years (2012 and 2013) since cohort I schools were awarded five years of support. Students in APTIP schools enrolled in more AP science exams (AP Biology, AP Chemistry, AP Environmental Science, and AP Physics-B) over the course of the intervention. The quantity of students earning qualifying scores increased during the intervention years. APTIP is a multi-tiered program that includes seven days of teacher training, three six-hour student prep sessions, school equipment, reduced exam fees, and monetary incentives for students and teachers. This program positively impacted the quantity of enrollment and qualifying scores during the three years evaluated in this study. Increases in the number of female and African American students' test takers their and qualifying scores were seen in all three years of the APTIP intervention. This study supports the premise that the first step to increasing the Science, technology, engineering, and math (STEM) pipeline is giving access to advanced courses to more students in high schools.
Advanced in In Situ Inspection of Automated Fiber Placement Systems
NASA Technical Reports Server (NTRS)
Juarez, Peter D.; Cramer, K. Elliott; Seebo, Jeffrey P.
2016-01-01
Automated Fiber Placement (AFP) systems have been developed to help take advantage of the tailorability of composite structures in aerospace applications. AFP systems allow the repeatable placement of uncured, spool fed, preimpregnated carbon fiber tape (tows) onto substrates in desired thicknesses and orientations. This automated process can incur defects, such as overlapping tow lines, which can severely undermine the structural integrity of the part. Current defect detection and abatement methods are very labor intensive, and still mostly rely on human manual inspection. Proposed is a thermographic in situ inspection technique which monitors tow placement with an on board thermal camera using the preheated substrate as a through transmission heat source. An investigation of the concept is conducted, and preliminary laboratory results are presented. Also included will be a brief overview of other emerging technologies that tackle the same issue. Keywords: Automated Fiber Placement, Manufacturing defects, Thermography
Using Data Mining to Explore Which Students Use Advanced Placement to Reduce Time to Degree
ERIC Educational Resources Information Center
Eykamp, Paul W.
2006-01-01
This chapter explores how multiple approaches including data mining can help examine how the lengths of student enrollment are associated with varying numbers of advanced placement units. (Contains 3 tables and 5 figures.)
What Do You Mean You Don't Do Advanced Placement?: Confessions of an Educational Heretic.
ERIC Educational Resources Information Center
Briley, Ron
2000-01-01
Explains why Advanced Placement courses are not offered at Sandia Preparatory School, a college preparatory school located in Albuquerque, New Mexico. Focuses on the school mission, overall philosophy, and how this relates to the history classroom in particular. (CMK)
Advances in in situ inspection of automated fiber placement systems
NASA Astrophysics Data System (ADS)
Juarez, Peter D.; Cramer, K. Elliott; Seebo, Jeffrey P.
2016-05-01
Automated Fiber Placement (AFP) systems have been developed to help take advantage of the tailorability of composite structures in aerospace applications. AFP systems allow the repeatable placement of uncured, spool fed, preimpregnated carbon fiber tape (tows) onto substrates in desired thicknesses and orientations. This automated process can incur defects, such as overlapping tow lines, which can severely undermine the structural integrity of the part. Current defect detection and abatement methods are very labor intensive, and still mostly rely on human manual inspection. Proposed is a thermographic in situ inspection technique which monitors tow placement with an on board thermal camera using the preheated substrate as a through transmission heat source. An investigation of the concept is conducted, and preliminary laboratory results are presented. Also included will be a brief overview of other emerging technologies that tackle the same issue.
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…
Predicting Advanced Placement Examination Success from FCAT Scores. Research Brief. Volume 0709
ERIC Educational Resources Information Center
Froman, Terry; Brown, Shelly; Tirado, Arleti
2008-01-01
Advanced Placement courses are offered at M-DCPS for students to acquire college credit or advanced college academic standing. A system has been developed in the past by the College Board to use the PSAT for 10th grade students to estimate their potential for AP Examination success. The same test has recently been applied in this district to 9th…
Advanced Placement and International Baccalaureate: Do They Deserve Gold Star Status?
ERIC Educational Resources Information Center
Byrd, Sheila
2007-01-01
For many people committed to strong academic standards, the "advanced" high school courses offered through the College Board's Advanced Placement program and, increasingly, the Diploma Programme of the International Baccalaureate Organisation (IBO) represent the curricular gold standard for secondary education. Admissions directors and professors…
NASA Astrophysics Data System (ADS)
Hoepner, Cynthia Colon
President Obama has recently raised awareness on the need for our nation to grow a larger pool of students with knowledge in science mathematics, engineering, and technology (STEM). Currently, while the number of women pursuing college degrees continues to rise, there remains an under-representation of women in STEM majors across the country. Although research studies offer several contributing factors that point to a higher attrition rate of women in STEM than their male counterparts, no study has investigated the role that high school advanced placement (AP) math and science courses play in preparing students for the challenges of college STEM courses. The purpose of this study was to discover which AP math and science courses and/or influential factors could encourage more students, particularly females, to consider pursuing STEM fields in college. Further, this study examined which, if any, AP math or science courses positively contribute to a student's overall preparation for college STEM courses. This retrospective study combined quantitative and qualitative research methods. The survey sample consisted of 881 UCLA female and male students pursuing STEM majors. Qualitative data was gathered from four single-gender student focus groups, two female groups (15 females) and two male groups (16 males). This study examined which AP math and science courses students took in high school, who or what influenced them to take those courses, and which particular courses influenced student's choice of STEM major and/or best prepared her/him for the challenges of STEM courses. Findings reveal that while AP math and science course-taking patterns are similar of female and male STEM students, a significant gender-gap remains in five of the eleven AP courses. Students report four main influences on their choice of AP courses; self, desire for math/science major, higher grade point average or class rank, and college admissions. Further, three AP math and science courses were
The Impact of Taking a College Pre-Calculus Course on Students' College Calculus Performance
ERIC Educational Resources Information Center
Sonnert, Gerhard; Sadler, Philip M.
2014-01-01
Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and…
ERIC Educational Resources Information Center
Bremigan, Elizabeth George
2005-01-01
In the study reported here, I examined the diagrams that mathematically capable high school students produced in solving applied calculus problems in which a diagram was provided in the problem statement. Analyses of the diagrams contained in written solutions to selected free-response problems from the 1996 BC level Advanced Placement Calculus…
ERIC Educational Resources Information Center
Teuscher, Dawn; Reys, Robert E.
2012-01-01
This study examined Advanced Placement Calculus students' mathematical understanding of rate of change, after studying four years of college preparatory (integrated or single-subject) mathematics. Students completed the Precalculus Concept Assessment (PCA) and two open-ended tasks with questions about rates of change. After adjusting for prior…
ERIC Educational Resources Information Center
Buford, Brandie J.
2012-01-01
The purpose of this mixed methods study was to describe the perceptions of African American students pertaining to their engagement in Advanced Placement English Literature and Composition course and Advanced Placement English Literature and Composition examination. A purposive sampling design was employed to select 12 participants from one urban…
ERIC Educational Resources Information Center
Wehde-Roddiger, Christina, Trevino, Rolando; Anderson, Pamela; Arrambide, Teresa; O'Conor, Juana; Onwuegbuzie, Anthony J.
2012-01-01
As high schools offer more pre-Advanced Placement (pre-AP) and Advanced Placement (AP) courses to prepare students for college academics, students often are given quality grade point average (GPA) points to help compensate for the rigorous curriculum. In states where class ranking determines automatic university admission, fluctuations of class…
ERIC Educational Resources Information Center
Robinson, Ann; Anthony, Tommie Sue; Liu, Yuxiang; Dickerson, Larry R.; Clowers, Robert L.; Stanley, T. D.
The Arkansas Advanced Placement Incentive Program served as a charter for the establishment, organization, and administration of a program designed to improve the course offerings available to high school students. The act provided three incentives: (1) one-time equipment/materials grants; (2) teacher professional development reimbursements; and…
Characteristics of Grosse Pointe High School Students in Advanced Placement Programs.
ERIC Educational Resources Information Center
Kaloger, James Heracles
The purpose of this study was to attempt to identify those factors that influence a high school student's success on the Advanced Placement (AP) Examinations by examining and comparing the variables contained in the high school records of former AP participants. A total of 248 high school students participated in the research. The criterion for…
TEACHERS' GUIDES. WORLD HISTORY FOR THE ACADEMICALLY TALENTED. ADVANCED PLACEMENT EUROPEAN HISTORY.
ERIC Educational Resources Information Center
AUGSPURGER, EVERETT F.; AND OTHERS
PREPARED BY TEACHERS AND SUPERVISORS WORKING WITH A 2-YEAR DEMONSTRATION PROJECT, THIS DOCUMENT CONTAINS GUIDES FOR A WORLD HISTORY COURSE (PREHISTORY TO EARLY 20TH CENTURY) FOR THE GIFTED AND AN ADVANCED PLACEMENT COURSE IN EUROPEAN HISTORY (ANCIENT CIVILIZATION TO EARLY 20TH CENTURY). STUDENTS ARE EXPECTED TO STUDY HISTORICAL ISSUES AND DEVELOP…
Participation of Minority Students Rises 32 Pct. in Advanced-Placement Tests; Many Score High.
ERIC Educational Resources Information Center
Watkins, Beverly T.
1988-01-01
The Advanced Placement Program has become a "program of academic opportunity" for students in high schools that enroll large numbers of minority groups. These schools are raising the expectations of minority students and helping them achieve higher goals, and they are bringing them into professional and graduate schools. (MLW)
ERIC Educational Resources Information Center
Navarro, Maria V.
2016-01-01
This memorandum describes the Advanced Placement (AP) and International Baccalaureate (IB) exams participation and performance of 2013 to 2015 public school graduates in Montgomery County Public Schools (MCPS) and the state of Maryland. The results are disaggregated by demographics and high schools. Students in the MCPS Class of 2015 continued to…
SREB States Maintain Lead in Advanced Placement and International Baccalaureate Programs
ERIC Educational Resources Information Center
Collins, Crystal
2009-01-01
The Southern Regional Education Board (SREB) states lead the nation in student participation in Advanced Placement (AP) and International Baccalaureate (IB) programs. The region also continued to match the nation in the success rates of high school students on AP exams in 2008. SREB's "Challenge to Lead" Goals for Education recognize the…
Perspectives on the Development and Future of Advanced Placement® Human Geography
ERIC Educational Resources Information Center
Hildebrant, Barbara
2016-01-01
Advanced Placement (AP) Human Geography faced a number of hurdles that nearly derailed the course before it launched in 2000-2001. A dedicated cadre of geography professionals and high school teachers rose to the challenge and the course remains one of the fastest growing AP courses currently offered by College Board. Seventeen readers and leaders…
Placing Advanced Placement® Human Geography: Its Role in U.S. Geography Education
ERIC Educational Resources Information Center
Bednarz, Sarah Witham
2016-01-01
This article examines Advanced Placement Human Geography (AP HG) in the context of its place in efforts to reform geography education. It presents a critical analysis of the AP program and its curriculum, asserting that it represents "powerful knowledge" as conceptualized by Young. It concludes with a call for research in AP HG aligned…
ERIC Educational Resources Information Center
Stein, Roger D.
1985-01-01
Describes a reading-skill-building curriculum that prepares students to handle the reading in the Advanced Placement Spanish Literature course, a course that treats the works of Borges, Garcia Lorca, Matute, Neruda, and Unamuno. Suggests techniques and texts that aid in the teaching of these skills. (SED)
The Effect of Advanced Placement and Concurrent Enrollment on Post Secondary Math Achievement
ERIC Educational Resources Information Center
Kremers, Angela L.
2010-01-01
Unprepared postsecondary students and poor high school retention rates emphasize a significant issue with education in the U.S. Although there have been increases in the number of programs to address retention and matriculation to degree attainment, little research has been completed to examine outcomes of these programs. Advanced placement and…
A Critical Race Analysis of Advanced Placement Classes: A Case of Educational Inequality.
ERIC Educational Resources Information Center
Solorzano, Daniel G.; Ornelas, Armida
2002-01-01
A study examined Chicano/Latino access to advanced placement (AP) high school classes. Data from a large California school district indicate that Latinos are underrepresented in AP classes; schools that serve urban, low-income, Latino/a communities have low AP enrollment; and even when they attend high schools with high AP enrollment, Latinos are…
The Advanced Placement English Program in Salt Lake and Granite School Districts.
ERIC Educational Resources Information Center
Stratopoulos, Irene Chachas
The main purposes in examining and evaluating the Advanced Placement English Program in Salt Lake and Granite School Districts were to identify the essential curriculum features of the program, to make suggestions for curriculum improvement, and to determine whether or not the quality of the AP English Program surpassed that of the conventional…
Having the AP Conversation: Why It's Time to Re-Evaluate Advanced Placement Courses
ERIC Educational Resources Information Center
Weaver, Roger
2010-01-01
Since its widespread emergence in the mid-1960s, the Advanced Placement (AP) curriculum has successfully established and maintained an identity as the gold standard of transcript currency for college preparatory schools. It is something that nearly all independent school parents and students believe they understand and clearly expect, and it is…
ACT Test Performance by Advanced Placement Students in Memphis City Schools
ERIC Educational Resources Information Center
Mo, Lun; Yang, Fang; Hu, Xiangen; Calaway, Florance; Nickey, John
2011-01-01
The authors investigated the extent to which taking specific types of Advanced Placement (AP) courses and the number of courses taken predicts the likelihood of passing subject benchmarks and earning a score of 19 on the composite score on the ACT test, and examined the role gender plays in the projection. They found evidence that taking an AP…
ERIC Educational Resources Information Center
Shaw, Emily J.; Marini, Jessica P.; Mattern, Krista D.
2013-01-01
The current study evaluated the relationship between various operationalizations of the Advanced Placement[R] (AP) exam and course information with first-year grade point average (FYGPA) in college to better understand the role of AP in college admission decisions. In particular, the incremental validity of the different AP variables, above…
Advanced Placement and International Baccalaureate Programs: A "Fit" for Gifted Learners?
ERIC Educational Resources Information Center
Hertberg-Davis, Holly; Callahan, Carolyn M.; Kyburg, Robin M.
2006-01-01
Although limited research exists on the appropriateness of Advanced Placement (AP) and International Baccalaureate (IB) Programs for gifted secondary learners, these courses serve as the primary methods of meeting the needs of gifted students in most high schools. This qualitative study employed a grounded theory approach to investigate how…
ERIC Educational Resources Information Center
Milburn, Kristine M.
2011-01-01
Problem: An increasing number of high-achieving American high school students are enrolling in multiple Advanced Placement (AP) courses. As a result, high schools face a growing need to understand the impact of taking multiple AP courses concurrently on the social-emotional lives of high-achieving students. Procedures: This phenomenological…
Melodic Dictation Instruction: A Survey of Advanced Placement Music Theory Teachers
ERIC Educational Resources Information Center
Buonviri, Nathan O.; Paney, Andrew S.
2015-01-01
Based on relevant literature and recent qualitative findings, the purpose of this survey research was to identify pedagogical approaches to melodic dictation employed by Advanced Placement (AP) Music Theory teachers across the United States. The researcher-designed survey questions focused on pitch and rhythm skills, instructional resources,…
The Oral Histories of Six African American Males in Their Ecology of Advanced Placement Biology
ERIC Educational Resources Information Center
Halasa, Katrina Bassam
2012-01-01
The major purpose of this qualitative study was to examine the past in order to understand the complex phenomenon of students engaging in science (Newman, Ridenour, Newman, & DeMarco, 2003) specifically through the oral histories of six self-identified African American males enrolled in a high school Advanced Placement Biology class and the…
Advanced Placement European History: An Anatomy of the Essay Examination, 1956-2000
ERIC Educational Resources Information Center
Blackey, Robert
2002-01-01
The College Board's Advanced Placement European History examination has evolved over the course of its first half-century of existence in virtually all respects: the types and subject matter of questions asked (and not asked); the nature of the history those questions reflect; the number of questions both offered and to be answered, as well as how…
What Does a Student Know Who Earns a Top Score on the Advanced Placement Chemistry Exam?
ERIC Educational Resources Information Center
Claesgens, Jennifer; Daubenmire, Paul L.; Scalise, Kathleen M.; Balicki, Scott; Gochyyev, Perman; Stacy, Angelica M.
2014-01-01
This paper compares the performance of students at a high-performing U.S. public school (n = 64) on the advanced placement (AP) chemistry exam to their performance on the ChemQuery assessment system. The AP chemistry exam was chosen because, as the National Research Council acknowledges, it is the "perceived standard of excellence and school…
ERIC Educational Resources Information Center
Marks, Susan F.
2013-01-01
Students in the Montgomery County (Maryland) Public Schools (MCPS) Class of 2012 continued to outperform Maryland and the nation on Advanced Placement (AP) examinations based on the "AP Report to the Nation" released by the College Board on February 20, 2013. In 2012, 67.3 percent of MCPS graduates took one or more AP exams. A striking…
The Advanced Placement Program: A Case Study of One Urban High School
ERIC Educational Resources Information Center
Manos, Marika Elizabeth
2010-01-01
While Advanced Placement (AP) programs have been traditionally targeted toward academically prepared students, some secondary administrators make AP courses accessible to all students in order to support college readiness. The purpose of the present study is to explore how the AP program is being implemented in an urban school where many students…
The Advanced Placement Opportunity Gap in Arizona: Access, Participation, and Success
ERIC Educational Resources Information Center
Cisneros, Jesus; Holloway-Libell, Jessica; Gomez, Laura M.; Corley, Kathleen M.; Powers, Jeanne M.
2014-01-01
Participation in Advanced Placement (AP) classes and AP test-taking are widely viewed as indicators of students' college readiness. We analyzed enrollment in AP courses and AP test outcomes in Arizona to document disparities in students' access to rigorous curricula in high school and outline some implications of these patterns for…
Growth and Achievement Trends of Advanced Placement (AP) Exams in American High Schools
ERIC Educational Resources Information Center
Judson, Eugene; Hobson, Angela
2015-01-01
This exploratory study examined and compared overall trends in growth and student achievement of the Advanced Placement (AP) program. Using data from the past two decades, analyses indicated there has been steady and extensive growth of AP participation, particularly among underclassmen and some minority groups. However, overall achievement, as…
ERIC Educational Resources Information Center
Warne, Russell T.; Larsen, Ross; Anderson, Braydon; Odasso, Alyce J.
2015-01-01
The Advanced Placement (AP) program is an educational program that permits high school students to take introductory college-level courses and receive college credit by passing a standardized end-of-course exam. Data were obtained from a statewide database of 2 high school graduating cohorts (N = 90,044). We used a series of propensity score…
WCPSS Advanced Placement (AP) Results, 2010-11. D&A Report No. 11.25
ERIC Educational Resources Information Center
Gilleland, Kevin
2012-01-01
One method of delivering college-level coursework to high school students is through the Advanced Placement (AP) program. Many colleges and universities provide credit to students who earn a qualifying score on any of the 34 available AP exams offered by the College Board. All qualified comprehensive high schools in the Wake County Public School…
Examining the Role of Advanced Placement[R] Exam Participation in 4-Year College Enrollment
ERIC Educational Resources Information Center
Chajewski, Michael; Mattern, Krista D.; Shaw, Emily J.
2011-01-01
The purpose of the current study was to examine the relationship between Advanced Placement (AP) exam participation and enrollment in a 4-year postsecondary institution. A positive relationship was expected given that the primary purpose of offering AP courses is to allow students to engage in college-level academic work while in high school, and…
Measuring Success: Examining Achievement and Perceptions of Online Advanced Placement Students
ERIC Educational Resources Information Center
Johnston, Sharon; Barbour, Michael K.
2013-01-01
The purpose of the research was to compare student performance on Advanced Placement (AP) exams from 2009 to 2011 at Florida Virtual School and to explore student perceptions of their online course experience compared with the classroom-based AP experiences. The data indicated that students performed at levels comparable to the national sample but…
ERIC Educational Resources Information Center
Batiwalla, Mary
2014-01-01
In 2013, Tennessee counted nearly 7,000 students in the senior cohort whose academic skills when they entered high school suggested they were on track to earn college credits through Advanced Placement (AP) exams. Yet just over half of these students actually graduated with an AP credit, and less than a third of the economically disadvantaged…
ERIC Educational Resources Information Center
King, Justyna Plichta
2010-01-01
This dissertation examines educators' perceptions regarding open access Advanced Placement (AP) program courses and their impact on non-traditional AP students in one suburban school district. The data were collected during the 2009-2010 school year through a 15-item Likert scale (and one open-ended item) survey which was disseminated during…
ERIC Educational Resources Information Center
Flores, Sergio; Gomez, Martin O.
2011-01-01
Some school leaders have viewed programs such as Advanced Placement (AP) as an attractive option to resolve the ongoing achievement gap problem. However, the ongoing debate in the field about maintaining the ostensible purity of the AP program versus diluting it with program expansion has hindered the full utilization of AP classes to close the…
The Advanced Placement Arms Race and the Reproduction of Educational Inequality
ERIC Educational Resources Information Center
Klugman, Joshua
2013-01-01
Background: Access to Advanced Placement (AP) courses is stratified by class and race. Researchers have identified how schools serving disadvantaged students suffer from various kinds of resource deprivations, concluding that interventions are needed to equalize access to AP courses. On the other hand, the theory of Effectively Maintained…
ERIC Educational Resources Information Center
Sanderson, Geoffrey T.
2015-01-01
Beginning in 2006, Maryland has led the nation as the state with the highest percentage of graduates who earned one or more Advanced Placement (AP) exam scores of 3 or higher. Students in the Montgomery County (Maryland) Public Schools (MCPS) Class of 2014 continued to outperform students in the state of Maryland on AP examinations based on AP…
ERIC Educational Resources Information Center
Sanderson, Geoffrey T.
2014-01-01
Beginning in 2006, Maryland has led the nation as the state with the highest percentage of graduates who earned one or more Advanced Placement (AP) exam scores of 3 or higher. Students in the Montgomery County Public Schools (MCPS) Class of 2013 continued to outperform students in the state of Maryland and the nation on AP examinations, based on…
Maryland Ranks #1 in the Nation on Advanced Placement Exams for Participation and Performance
ERIC Educational Resources Information Center
Maryland State Department of Education, 2009
2009-01-01
Maryland public high school students outperformed all others in the nation on the rigorous Advanced Placement (AP) exams, according to the College Board's fifth annual analysis of the AP program. Maryland ranked first nationwide in the percentage of public school students scoring 3 or higher on at least one AP exam. A score of 3 or higher on the…
Teacher Scaffolding of Academic Language in an Advanced Placement U.S. History Class
ERIC Educational Resources Information Center
Gritter, Kristine; Beers, Scott; Knaus, Robert W.
2013-01-01
This article examines teacher scaffolding of academic language in an Advanced Placement United States History (APUSH) course throughout a school year for one student who received a perfect score on the end of year APUSH exam. Data includes four months of observation of teacher instructional strategies to scaffold student writing and vignettes of…
Advanced Placement English in a Solipsistic Era: How Structuralism Can Renew Meaning
ERIC Educational Resources Information Center
Rauh, John
2014-01-01
Advanced Placement (AP) courses within secondary English education can fail to meet the needs of gifted students in the postmodern era. Because AP courses often are standardized, despite the College Board's efforts to allow freedom in course design, gifted students, as especially attuned to discrepancies between practice and theory, are being…
ERIC Educational Resources Information Center
Kelley-Kemple, Thomas; Proger, Amy; Roderick, Melissa
2011-01-01
The current study provides an in-depth look at Advanced Placement (AP) math and science course-taking in one school district, the Chicago Public Schools (CPS). Using quasi-experimental methods, this study examines the college outcomes of students who take AP math and science courses. Specifically, this study asks whether students who take AP math…
Using an advanced graphing calculator in the teaching and learning of calculus
NASA Astrophysics Data System (ADS)
Leng, Ng Wee
2011-10-01
The purpose of this study was to investigate how the use of TI-Nspire™ could enhance the teaching and learning of calculus. A conceptual framework for the use of TI-Nspire™ for learning calculus in a mathematics classroom is proposed that describes the interactions among the students, TI-Nspire™, and the learning tasks, and how they lead to the learning of calculus. A design experiment was conducted in a class of 35 students from a secondary school in Singapore. Use of TI-Nspire™ was integrated into the teaching and learning of calculus concepts in the classroom with the aid of TI-Nspire™ Navigator, a wireless classroom network system that enables instant and active interaction between students and teachers. It was found that the appropriate use of graphical, numerical and algebraic representations of calculus concepts using TI-Nspire™ enabled students to better visualize the concepts and make generalizations about relevant mathematical properties. In addition, the students were able to link multiple representations, especially algebraic and graphical representations, to improve their conceptual understanding and problem-solving skills. Six roles of TI-Nspire™ in classroom mathematical practice were identified from the findings of the experiment; TI-Nspire™ was used as an exploratory tool, graphing tool, confirmatory tool, problem-solving tool, visualization tool and calculation tool. This suggests that TI-Nspire™ is a multi-dimensional tool that supports mathematics learning. Overall, the findings of the study indicate that TI-Nspire™ is an effective tool to develop mathematical concepts and promote learning and problem solving.
Advanced Placement Results, 2013-14. Measuring Up. D&A Report No.15.01
ERIC Educational Resources Information Center
Gilleland, Kevin; Muli, Juliana
2015-01-01
Advanced Placement (AP) outcomes for Wake County Public School System (WCPSS) students have continued an upward trend for over 18 years, out-performing the state and the nation in all measures. In 2013-14 there were 13,757 exams taken by 6,955 WCPSS test-takers with almost 76% of the exams resulting in scores at or above 3, outperforming Guilford…
Myth 19: Is Advanced Placement an Adequate Program for Gifted Students?
ERIC Educational Resources Information Center
Gallagher, Shelagh A.
2009-01-01
Is it a myth that Advanced Placement (AP) is an adequate program for gifted students? AP is so covered with myths and assumptions that it is hard to get a clear view of the issues. In this article, the author finds the answer about AP by looking at current realties. First, AP is hard for gifted students to avoid. Second, AP never was a program…
Where the girls aren't: High school girls and advanced placement physics enrollment
NASA Astrophysics Data System (ADS)
Barton, Susan O'brien
During the high school years, when many students first have some choice in course selection, research indicates that girls choose to enroll in more math and science courses, take more advanced placement courses, and take more honors courses in English, biology, chemistry, mathematics, and foreign languages than ever before. Yet, not only are boys more likely to take all of the three core science courses (biology, chemistry, and physics), boys enroll in advanced placement physics approximately three times as often as do girls. This study examines the perceptions, attitudes, and aspirations of thirty high school girls enrolled in senior-level science electives in an attempt to understand their high school science course choices, and what factors were influencing them. This is a qualitative investigation employing constructivist grounded theory methods. There are two main contributions of this study. First, it presents a new conceptual and analytical framework to investigate the problem of why some high school girls do not enroll in physics coursework. This framework is grounded in the data and is comprised of three existing feminist perspectives along the liberal/radical continuum of feminist thought. Second, this study illuminates a complex set of reasons why participants avoided high school physics (particularly advanced placement physics) coursework. These reasons emerged as three broad categories related to: (a) a lack of connectedness with physics curriculum and instruction; (b) prior negative experiences with physics and math classroom climates; and (c) future academic goals and career aspirations. Taken together, the findings of this study indicate that the problem of high school girls and physics enrollment---particularly advanced placement physics enrollment---is a problem that cannot be evaluated or considered from one perspective.
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…
Gilbert, Christopher R; Toth, Jennifer W; Osman, Umar; Reed, Michael F
2015-03-01
The development of a persistent air leak after pneumothorax can be encountered in patients with underlying structural lung disease. In those with advanced malignancy or other comorbidities, the ability to tolerate general anesthesia and thoracoscopic procedures may limit definitive management. We describe the case of a 68-y-old male with refractory acute myelogenous leukemia presenting with recurrent secondary spontaneous pneumothorax and persistent air leak related to an underlying fungal pneumonia. Endobronchial valve placement allowed for timely chest tube removal and discharge from the hospital, as well as avoidance of a thoracoscopic procedure and pleurodesis.
Polynomial calculus: rethinking the role of calculus in high schools
NASA Astrophysics Data System (ADS)
Grant, Melva R.; Crombie, William; Enderson, Mary; Cobb, Nell
2016-08-01
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 their definition and exposition. We develop the beginning concepts of differential and integral calculus using only concepts and skills found in secondary algebra and geometry. It is our underlining objective to strengthen students' knowledge of these topics in an effort to prepare them for advanced mathematics study. The purpose of this reconstruction is not to alter the teaching of limit-based calculus but rather to affect students' learning and understanding of mathematics in general by introducing key concepts during secondary mathematics courses. This approach holds the promise of strengthening more students' understanding of limit-based calculus and enhancing their potential for success in post-secondary mathematics.
ERIC Educational Resources Information Center
Howard, Lori A.; Potts, Elizabeth A.; Linz, Ed
2013-01-01
As the federal government encourages all students to attempt advanced math and science courses, more students with disabilities are enrolling in Advanced Placement (AP) science classes. AP science teachers can better serve these students by understanding the various types of disabilities (whether physical, learning, emotional, or behavioral),…
ERIC Educational Resources Information Center
Thieken, John
2012-01-01
A sample of 127 high school Advanced Placement (AP) Calculus students from two schools was utilized to study the effects of an engineering design-based problem solving strategy on student performance with AP style Related Rate questions and changes in conceptions, beliefs, and influences. The research design followed a treatment-control multiple…
ERIC Educational Resources Information Center
Maina, Nyambura Susan
2015-01-01
At the request of the Office of Curriculum and Instructional Programs, the Office of Shared Accountability examined the impact of offering Advanced Grade 8 U.S. History on enrollment and performance in Advanced Placement (AP) social studies courses in Grade 9. The study compared Grade 9 enrollment and performance in AP U.S. History or AP U.S.…
ERIC Educational Resources Information Center
Mercurio, Joseph A.; And Others
1983-01-01
Syracuse University's Project Advance (one of the first high school college cooperative programs in the United States through which college courses, taught in high schools by high school faculty, are taken for college credit) is described. (MLW)
ERIC Educational Resources Information Center
Davis, Pamela; Davis, Michael P.; Mobley, Jerry A.
2014-01-01
This study describes the collaboration among a school counselor, a school counselor intern, an Advanced Placement Psychology teacher, and a counselor educator to improve African-American access to Advanced Placement (AP) coursework and increase success on the AP Psychology national examination. The team initiated a process that recruited African…
ERIC Educational Resources Information Center
Nabb, Keith A.
2013-01-01
The research literature has made calls for greater coherence and consistency with regard to the meaning and use of the term advanced mathematical thinking (AMT) in mathematics education (Artigue, Batanero, & Kent, 2007; Selden & Selden, 2005). Educators and researchers agree that students should be engaged in AMT but it is unclear…
ERIC Educational Resources Information Center
McCarthy, Christopher J.; Lambert, Richard G.; Crowe, Elizabeth W.; McCarthy, Colleen J.
2010-01-01
This study examined the relationship of teachers' perceptions of coping resources and demands to job satisfaction factors. Participants were 158 Advanced Placement Statistics high school teachers who completed measures of personal resources for stress prevention, classroom demands and resources, job satisfaction, and intention to leave the field…
ERIC Educational Resources Information Center
Lewis, Traschell S.
2012-01-01
The purpose of this study was to examine the effectiveness of selected Advanced Placement (AP) programs on the academic performance and college readiness of high school students. Specifically, the researcher was concerned with ascertaining the effectiveness of social science, math, science, English, music/art and language AP programs on the…
ERIC Educational Resources Information Center
Perrett, Jamis J.
2012-01-01
This article demonstrates how textbooks differ in their description of the term "experimental unit". Advanced Placement Statistics teachers and students are often limited in their statistical knowledge by the information presented in their classroom textbook. Definitions and descriptions differ among textbooks as well as among different editions…
ERIC Educational Resources Information Center
Cooney, Siobhan M.; McKillip, Mary E. M.; Smith, Kara
2013-01-01
The present study investigates how current college students perceive their experiences in high school Advanced Placement Program (AP) courses. The goal of this research was twofold: We wanted to not only add to the existing literature on outcomes for AP students but also investigate possible benefits for students without success (i.e., a score of…
A Portrait of Advanced Placement Teachers' Practices. Research Report No. 2005-7. ETS RR-05-09
ERIC Educational Resources Information Center
Paek, Pamela L.; Ponte, Eva; Sigel, Irv; Braun, Henry; Powers, Don
2005-01-01
The Advanced Placement Program® (AP®) is dedicated to providing high school students opportunities to enroll in college-level courses while in high school. The advantages of such accelerated opportunities are both financial and educational. The AP Program is available internationally. As a result of its widespread availability, considerable effort…
ERIC Educational Resources Information Center
Foust, Regan Clark; Hertberg-Davis, Holly; Callahan, Carolyn M.
2008-01-01
The gifted can suffer from too many demands on their time and attention. This qualitative study tested the theory that advanced placement (AP) and international baccalaureate (IB) participants may feel forced to choose between academic success and social acceptance. The results, however, did not support the theory. Not only did gifted students not…
ERIC Educational Resources Information Center
Alper, Seth M.
2013-01-01
This mixed-methods study investigated the relationship between Advanced Placement (AP) social studies teachers' utilization of academic course blogs and student achievement. Simultaneously, the study examined the participating teachers' perceptions on the use of course blogs and other social media as supplemental learning resources. The…
ERIC Educational Resources Information Center
Williams, Jermaine F.
2010-01-01
This quantitative study examined the impact of Advanced Placement (AP) and Dual Enrollment (DE) on early college academic performance by analyzing and comparing first year and sophomore year persistence rates and grade point averages (GPAs) of four student cohorts who began their education at a large urban research I university in fall 2007. These…
ERIC Educational Resources Information Center
Scott, Timothy P.; Tolson, Homer; Lee, Yi-Hsuan
2010-01-01
The College Board Advanced Placement Program allows high school students to take college-level courses and if an appropriate score on an exam is received, college credit is earned. While the program has had its detractors (access in rural and inner-city schools, lack of diversity, pre-selection of talented students, poor articulation with actual…
Federal Register 2010, 2011, 2012, 2013, 2014
2012-04-24
.... ACTION: Notice reopening the AP Test Fee fiscal year 2012 competition. Catalog of Federal Domestic Assistance (CFDA) Number: 84.330B. SUMMARY: On February 15, 2012, we published in the Federal Register (77 FR... Application for New Awards; Advanced Placement (AP) Test Fee Program--Reopening the AP Test Fee Fiscal...
ERIC Educational Resources Information Center
Bridgeman, Brent; Lewis, Charles
Essay and multiple-choice scores from Advanced Placement (AP) examinations in American History, European History, English Language and Composition, and Biology were matched with freshman grades in a sample of 32 colleges. Multiple-choice scores from the American History and Biology examinations were superior to essays for predicting overall grade…
ERIC Educational Resources Information Center
Liekar, Christine Y.
2012-01-01
Since the time of Sputnik, American educators and policymakers have recognized the need to raise expectations by increasing rigor in high schools across the United States. Copious studies attest to the fact that students who take Advanced Placement coursework experience success in college (Adelman, 1999; Camara, 2003; College Board, 2005;…
ERIC Educational Resources Information Center
Gruman, Daniel H.
2013-01-01
A substantial amount of research examines the benefits of high school college-credit attainment programs against non-participation. The growth in popularity of these programs, particularly Advanced Placement (AP) and dual enrollment (DE), has them competing against one another for student attention. However, students, schools, and policymakers do…
ERIC Educational Resources Information Center
Speroni, Cecilia
2011-01-01
Advanced Placement (AP) and Dual Enrollment (DE) are two programs that allow high school students to earn college credits. The recent growth of these programs has been unprecedented. However, there is little evidence that compares how they fare in terms of improving college access and success. Using data from two cohorts of all high school…
ERIC Educational Resources Information Center
Park, Kelly; Caine, Vera; Wimmer, Randolph
2014-01-01
Enriched high school curricula like the Advanced Placement and International Baccalaureate Diploma programs are endorsed as "pathway programs" for postsecondary-bound students. Program participation is perceived to have benefits that appeal to a broad stakeholder group of universities, administrators, teachers, students, and parents. In…
ERIC Educational Resources Information Center
Krutka, Daniel G.
2012-01-01
Prevalent models of secondary education in the United States have tended to privilege the acquisition of knowledge of scientific disciplines that is often peripheral to the experiences of students. My Advanced Placement Government classes were no different, and this caused me to wonder whether my classes were meeting the often-stated goal of the…
ERIC Educational Resources Information Center
Putti, Alice
2011-01-01
This paper discusses student attitudes and beliefs on using the Science Writing Heuristic (SWH) in an advanced placement (AP) chemistry classroom. During the 2007 school year, the SWH was used in a class of 24 AP chemistry students. Using a Likert-type survey, student attitudes and beliefs on the process were determined. Methods for the study are…
ERIC Educational Resources Information Center
Sadler, Philip M.; Tai, Robert H.
2007-01-01
Honors and advanced placement (AP) courses are commonly viewed as more demanding than standard high school offerings. Schools employ a range of methods to account for such differences when calculating grade point average and the associated rank in class for graduating students. In turn, these statistics have a sizeable impact on college admission…
ERIC Educational Resources Information Center
Ackerman, Phillip L.; Kanfer, Ruth; Calderwood, Charles
2013-01-01
Background/Context: The past few decades have seen an explosive growth in high-school student participation in the Advanced Placement program® (AP), with nearly two million exams completed in 2011. Traditionally, universities have considered AP enrollment as an indicator for predicting academic success during the admission process. However, AP…
ERIC Educational Resources Information Center
Rowland, M. Lance; Shircliffe, Barbara J.
2016-01-01
This study examines educators' perspectives on accountability mandates designed to expand access to the College Board's Advanced Placement (AP) classes to traditionally underserved students at a diverse suburban high school in Florida, Palm Crest High School. Consistent with Elmore (1979), district and site-based administrators focused on the…
ERIC Educational Resources Information Center
Snyder, Scott
2013-01-01
This study investigated the lived experiences of first-generation college students and the perceived influence of taking high school Advanced Placement (AP) courses on their college education. The following research questions were addressed: (a) what motivated students to consider going to college, (b) what was their experience in taking AP…
NASA Astrophysics Data System (ADS)
Crawford, Freda M.
Sixty percent of American high schools offer one or more Advanced Placement courses, and several thousand Advanced Placement teachers serve as Readers or graders of Advanced Placement exams each year. This study was conducted to determine the characteristics of teachers who choose to participate in Advanced Placement Environmental Science Readings and determine how these teachers view the Reading experience as a form of professional development. This study was conducted with teacher participants at the June 2004 Advanced Placement Environmental Science Reading. Sixty of the 114 teacher participants completed a survey regarding their education background, age, experience level, educational philosophy, involvement in professional development opportunities, perceptions of the professional benefits of the Reading, and the influence of the Reading experience on their pedagogical practices. Semi-structured interviews were then conducted with a subset of 18 teacher participants to determine their perceptions regarding the professional benefits of the Reading experience, its potential to serve as a professional development activity, and perceived changes in their pedagogical practices resulting from participation in the Reading process. Results indicate that APES Reading teacher participants are experienced, effective teachers from many parts of the country. These teachers participate in ongoing professional development activities, can delineate components of effective professional development, strongly believe that effective professional development occurs at the APES Reading, and report that their pedagogical practice has improved as a result of participation in the APES Reading. Considering the crucial role teachers play in the educational process, it is important to pursue this additional avenue of professional development in order to further improve APES teacher effectiveness.
Mathematics Placement at the University of Illinois
ERIC Educational Resources Information Center
Ahlgren Reddy, Alison; Harper, Marc
2013-01-01
Data from the ALEKS-based placement program at the University of Illinois is presented visually in several ways. The placement exam (an ALEKS assessment) contains precise item-specific information and the data show many interesting properties of the student populations of the placement courses, which include Precalculus, Calculus, and Business…
ERIC Educational Resources Information Center
Amdahl, Kenn; Loats, Jim
This book, written for students of calculus, is designed to augment the explanations of concepts covered in a calculus class. It consists of an overview of calculus divided into basic ideas and vocabulary, the process of differential calculus, and integral calculus. The book is intended as a resource to explain the concepts of calculus in everyday…
The oral histories of six African American males in their ecology of Advanced Placement Biology
NASA Astrophysics Data System (ADS)
Halasa, Katrina Bassam
The major purpose of this qualitative study was to examine the past in order to understand the complex phenomenon of students engaging in science (Newman, Ridenour, Newman, & DeMarco, 2003) specifically through the oral histories of six self-identified African American males enrolled in a high school Advanced Placement Biology class and the oral histories about events that followed during their post high school experiences. To elucidate an understanding of this phenomenon, this research explored the ecology of African American males' descriptions of their school science, their peer school science community, their lived experiences during and after graduation, and their meso-community (Bronfenbrenner, 1979). Many minority and low-income students are less likely to enroll in rigorous courses during high school (Education Trust, 2006). This study is of utmost importance because capturing the informants' oral histories may improve rigorous science education. Many African American male students are attending urban schools with an ever growing achievement gap among their White counterparts (Norman, Ault, Bentz, & Meskimen, 2001); therefore, they are disengaging in science. As a result, African American males are underrepresented in both science careers and achievements in science (Atwater, 2000; National Science Foundation, 1994). The six oral histories highlighted the ecological factors that affected African American males regarding (1) the impact of their relationship with their mothers, (2) the understanding of personal responsibility, (3) the notion of a scientist, (4) the issue of gender being more of an obstacle than race, (5) the understanding that education is valuable, (6) the interactions and influence of relationships with others on their decisions, (7) the development of integrity through the participation in sports, (8) the ecological neighborhood environment influences an image, (9) the enrollment of Advanced Placement Biology course helped the transition
ERIC Educational Resources Information Center
Kerr, Roberta
2014-01-01
The purpose of this study was to obtain an accurate picture of minority student enrollment in honors and advanced placement (AP) classes at Wichita (Kansas) High School East and to develop a plan of action to close the achievement gap between White and non-White students. Prior to this study there was no clear, concise data to move this discussion…
ERIC Educational Resources Information Center
Cirillo, Michelle
2007-01-01
In this article, the author explores the history and the mathematics used by Newton and Leibniz in their invention of calculus. The exploration of this topic is intended to show students that mathematics is a human invention. Suggestions are made to help teachers incorporate the mathematics and the history into their own lessons. (Contains 3…
ERIC Educational Resources Information Center
McGivney-Burelle, Jean; Xue, Fei
2013-01-01
In this paper we discuss flipping pedagogy and how it can transform the teaching and learning of calculus by applying pedagogical practices that are steeped in our understanding of how students learn most effectively. In particular, we describe the results of an exploratory study we conducted to examine the benefits and challenges of flipping a…
Calculus with a quaternionic variable
NASA Astrophysics Data System (ADS)
Schwartz, Charles
2009-01-01
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn in trying to extend our reach to include quaternions. The noncommutativity of the quaternion algebra poses obstacles for the usual manipulations of calculus, but we show in this paper how many of those obstacles can be overcome. The surprising result is that the first order term in the expansion of F(x +δ) is a compact formula involving both F'(x) and [F(x )-F(x∗)]/(x -x∗). This advance in the differential calculus for quaternionic variables also leads us to some progress in studying integration.
Individualized additional instruction for calculus
NASA Astrophysics Data System (ADS)
Takata, Ken
2010-10-01
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 student's performance. Our study compares two calculus classes, one taught with mandatory remedial IAI and the other without. The class with mandatory remedial IAI did significantly better on comprehensive multiple-choice exams, participated more frequently in classroom discussion and showed greater interest in theorem-proving and other advanced topics.
NASA Astrophysics Data System (ADS)
Heglund, Brian
Educators recognize the importance of reasoning ability for development of critical thinking skills, conceptual change, metacognition, and participation in 21st century society. There is a recognized need for students to improve their skills of argumentation, however, argumentation is not explicitly taught outside logic and philosophy---subjects that are not part of the K-12 curriculum. One potential way of supporting the development of argumentation skills in the K-12 context is through incorporating Computer-Assisted Argument Mapping to evaluate arguments. This quasi-experimental study tested the effects of such argument mapping software and was informed by the following two research questions: 1. To what extent does the collaborative use of Computer-Assisted Argumentation Mapping to evaluate competing theories influence the critical thinking skill of argument evaluation, metacognitive awareness, and conceptual knowledge acquisition in high school Advanced Placement physics, compared to the more traditional method of text tables that does not employ Computer-Assisted Argumentation Mapping? 2. What are the student perceptions of the pros and cons of argument evaluation in the high school Advanced Placement physics environment? This study examined changes in critical thinking skills, including argumentation evaluation skills, as well as metacognitive awareness and conceptual knowledge, in two groups: a treatment group using Computer-Assisted Argumentation Mapping to evaluate physics arguments, and a comparison group using text tables to evaluate physics arguments. Quantitative and qualitative methods for collecting and analyzing data were used to answer the research questions. Quantitative data indicated no significant difference between the experimental groups, and qualitative data suggested students perceived pros and cons of argument evaluation in the high school Advanced Placement physics environment, such as self-reported sense of improvement in argument
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.…
ERIC Educational Resources Information Center
Irvin, Matthew J.; Hannum, Wallace H.; Farmer, Thomas W.; de la Varre, Claire; Keane, Julie
2009-01-01
This paper examines the need for interventions to support students who are taking advanced placement courses in small rural districts and describes the Facilitator Preparation Program (FPP) as a strategy to address this need. Issues in the delivery of Online Distance Education (ODE) in small rural schools are summarized and the conceptual…
ERIC Educational Resources Information Center
Jin, Qiushuang; Shi, Qian
2008-01-01
This study investigated the association between sleep deprivation and enrollment in Advanced Placement (AP) and/or college courses among high school students. Approximately 4,000 surveys were distributed, and 2,197 completed surveys were returned from students in Grades 9 to 12 at 15 high schools in Iowa. Findings indicated the majority of high…
ERIC Educational Resources Information Center
Poole, Kerry D.
2014-01-01
Florida has experienced some of the greatest growth of Advanced Placement (AP) programs in recent years and student scores on the AP exams have evolved into a highly significant metric in evaluating student proficiency and teacher and school effectiveness. Despite this growth, it is not well known how AP teachers make decisions about the content…
ERIC Educational Resources Information Center
Patterson, Brian F.; Packman, Sheryl; Kobrin, Jennifer L.
2011-01-01
The purpose of this study was to examine the effects of Advanced Placement[R] (AP[R]) exam participation and performance on college grades for courses taken in the same subject area as students' AP Exam(s). Students' first-year college subject area grade point averages (SGPAs) were examined in nine subject areas: mathematics, computer science,…
ERIC Educational Resources Information Center
Buck, Gary; Kostin, Irene; Morgan, Rick
2002-01-01
The purpose of this study is to examine the content of the questions in a number of Advanced Placement Examinations and to attempt to identify content that is related to gender-based performance differences. Free-response questions for ten forms of the AP® Exams in U.S. History, European History, Biology, Microeconomics, and Macroeconomics were…
ERIC Educational Resources Information Center
Patterson, Brian F.; Packman, Sheryl; Kobrin, Jennifer L.
2011-01-01
The purpose of this study was to examine the effects of Advanced Placement (AP) exam participation and performance on college grades for courses taken in the same subject area as students' AP Exam(s). Students' first-year college subject area grade point averages (SGPAs) were examined in nine subject areas: mathematics, computer science,…
ERIC Educational Resources Information Center
Gillenwater, Cary
2014-01-01
This phenomenological case study attempts to understand the phenomenon of intertextuality of traditional novels and graphic novels, and how it may or may not contribute to transference of one mode of literacy to another. The study's sample was seven Grade 12 Advanced Placement English/language arts students and their teacher. I conducted my…
ERIC Educational Resources Information Center
Foust, Regan Clark; Hertberg-Davis, Holly; Callahan, Carolyn M.
2009-01-01
Using qualitative methods, the researchers explored student perceptions of the social and emotional advantages and disadvantages of Advanced Placement (AP) and International Baccalaureate (IB) program participation, differences between the AP and IB programs in those perceptions, and whether or not students report experiencing a "forced-choice…
ERIC Educational Resources Information Center
Lanni, Laura M.
2014-01-01
A guided-inquiry lab, suitable for first-year general chemistry or high school advanced placement chemistry, is presented that uses only inexpensive, store-bought materials. The reaction of sodium bicarbonate (baking soda) with aqueous acetic acid (vinegar), under the constraint of the challenge to completely fill a sealable plastic bag with the…
ERIC Educational Resources Information Center
Sanderson, Geoffrey T.
2014-01-01
The continuing emphasis by Montgomery County (Maryland) Public Schools (MCPS) on rigorous course taking resulted in MCPS students taking a record-setting 33,662 Advanced Placement (AP) exams in 2014. Additionally, the percentage of AP exams taken by MCPS students who attained scores of 3 or higher (73.9 percent) was 13.0 and 16.7 percentage points…
ERIC Educational Resources Information Center
Handwerk, Phil
2007-01-01
Online high schools are growing significantly in number, popularity, and function. However, little empirical data has been published about the effectiveness of these institutions. This research examined the frequency of group work and extended essay writing among online Advanced Placement Program® (AP®) students, and how these tasks may have…
ERIC Educational Resources Information Center
Sanderson, Geoffrey T.
2013-01-01
This memorandum provides data on the participation and performance of Advanced Placement (AP) exams taken by students in the Montgomery County (Maryland) Public Schools (MCPS) in the 2012-2013 school year as compared with those by public school students in Maryland and the nation. Generally, the number of AP exams taken by MCPS students in 2013…
Advanced L2 Learners and Reading Placement: Self-Assessment, CBT, and Subsequent Performance
ERIC Educational Resources Information Center
Brantmeier, Cindy
2006-01-01
There is a dearth of research involving advanced second language (L2) learners in the USA [Brantmeier, C., 2001. Second language reading research on passage content and gender: challenges for the intermediate level curriculum, Foreign Language Annals 34, 325-333; Young, D.J., 2003. Workshop on overcoming anxiety in the foreign language classroom.…
NASA Astrophysics Data System (ADS)
Persin, Ronald C.
The purpose of this study was to investigate whether statistically significant differences existed between high school Honors Physics websites and those of Advanced Placement (AP) Physics in terms of Web-design, National Science Education Standards (NSES) Physics content, and NSES Science Process standards. The procedure began with the selection of 152 sites comprising two groups with equal sample sizes of 76 for Honors Physics and for Advanced Placement Physics. The websites used in the study were accumulated using the Google(TM) search engine. To find Honors Physics websites, the search words "honors physics high school" were entered as the query into the search engine. To find sites for Advanced Placement Physics, the query, "advanced placement physics high school," was entered into the search engine. The evaluation of each website was performed using an instrument developed by the researcher based on three attributes: Web-design, NSES Physics content, and NSES Science Process standards. A "1" was scored if the website was found to have each attribute, otherwise a "0" was given. This process continued until all 76 websites were evaluated for each of the two types of physics websites, Honors and Advanced Placement. Subsequently the data were processed using Excel functions and the SPSS statistical software program. The mean and standard deviation were computed individually for the three attributes under consideration. Three, 2-tailed, independent samples t tests were performed to compare the two groups of physics websites separately on the basis of Web Design, Physics Content, and Science Process. The results of the study indicated that there was only one statistically significant difference between high school Honors Physics websites and those of AP Physics. The only difference detected was in terms of National Science Education Standards Physics content. It was found that Advanced Placement Physics websites contained more NSES physics content than Honors
ERIC Educational Resources Information Center
Cassuto, Leonard
2012-01-01
The practical goal of graduate education is placement of graduates. But what does "placement" mean? Academics use the word without thinking much about it. "Placement" is a great keyword for the graduate-school enterprise. For one thing, its meaning certainly gives a purpose to graduate education. Furthermore, the word is a portal into the way of…
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.
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 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…
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…
Iwai, Toshinori; Fuwa, Nobukazu; Hirota, Makoto; Mitsudo, Kenji; Tohnai, Iwai
2014-06-01
We describe secure surgical method for catheter placement using ultrasonic scalpel via the occipital artery to achieve retrograde superselective intra-arterial chemotherapy for advanced oral cancer, as alternative to approach via the superficial temporal artery. PMID:24822164
Hermeneutic operative calculus
NASA Astrophysics Data System (ADS)
Ramakrishnan, Sivakumar; Isawasan, Pradeep; Mohanan, Vasuky
2014-07-01
The predicate calculus used currently by mathematical logic in computer science, philosophy and linguistic was found to be too restrictive and inadequate for describing the grammar of natural and artificial language. Therefore many higher order logics have been developed to overcome the limitation of predicate calculus. In this paper a new representation of logic using mathematical principles has been developed for the natural language called Hermeneutic Operative Calculus. This Hermeneutic Operative Calculus is a new language interpretive calculus developed to account for the syntactic, semantic and pragmatic features of natural language and allows removing the restrictions of any particular natural language in the semantic field its map out. The logic of Hermeneutic Operative Calculus capable of represent the syntactic and semantic of factual information of a natural language precisely in any language. The logic of this Hermeneutic Operative Calculus has two different forms of operations called object and meta-operations. The object operation allow for listing the various objects, picturing the various propositions and so forth. The meta-operation would specify what cannot be specified by the object operation like semantical stances of a proposition. The basic operative processes of linguistics and cognitive logic will be mathematically conceptualized and elaborated in this paper.
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…
NASA Astrophysics Data System (ADS)
Campbell, D. Michael
The lack of preparation, participation, and equal access of students in mathematics and the science education continues to afflict America's high school system (Ratliff, 2001). Additionally, gender and ethnic status have become significant factors as females and minority subgroups such as African Americans and Hispanics continue to be underrepresented in these two subject fields. Recognizing and understanding these trends is extremely important for the future of this country. As fewer minorities and females become involved in advanced mathematics and science curriculum there will be a continued lack of minorities and females in mathematics and science careers. Additionally, this insufficient representation leads to fewer numbers of females and minorities in industry and educational leadership positions in mathematics and science to promote participation and equality in these fields. According to Brainard and Carlin (2003) as trends currently stand, these two groups will be under-represented in the fields of math and science and will continue to be denied economic and social power. Thus, a better understanding of these trends in participation in mathematics and science among these groups of students is warranted. This study is intended to accomplish four objectives. The first objective is to identify the extent to which opportunities are increasing or decreasing for students in high schools taking mathematics and science Advanced Placement exams by examining six years of student testing data from the College Board. A second objective is to identify features of high schools that relate to greater expansion in Advanced Placement test taking for females and minority groups in the areas of both math and science. A third objective is to explore whether, and to what extent, any social or educational features such as economic status, regional school and living locations, and ethnic backgrounds have enhanced or reduced Advanced Placement testing in these schools. Lastly
NASA Astrophysics Data System (ADS)
Rasmussen, Natalie D.
The academic achievement gap between African American and White students has gained much attention in recent years. Much has been written about the causes of and reasons for this problem ranging from the vestigial effects of slavery to poor parenting. Much less has been written or understood about its solution. While it is impossible for educators to change the pasts of their African American students, it is possible to effect change for the few minutes in which they are in direct contact with them each day. If African American science students are taught effective study skills and habits, then perhaps they might have the tools to close the achievement gap themselves. The participants in this phenomenologically based interpretive study were five African American Advanced Placement Chemistry students from an inner-city high school. Three in-depth interviews were conducted with each of the participants during the beginning, middle and end of a semester. The purpose of the interviews was to locate the students in terms of their thought processes, experiences and perceived barriers concerning the nature and practice of effective study and retention of chemistry content. The interviews were recorded and transcribed. The texts were then analyzed for common themes. Five common themes emerged from the interviews. These were: (1) Homework vs. Study: a distinction between homework---which students knew how to approach; and study---which they did not. (2) Student Effort: their changing perception of adequate and effective study practices while in a rigorous course. (3) Teacher Rigor: they perceived high expectations and challenging work as a sign of respect from their teachers. (4) Parental Involvement: students' admission that they desired more input from parents regarding their academic performance. (5) Racial Considerations: their need to disprove negative stereotypes and their personal observations regarding racial differences in studying. A discussion of the themes and
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.
Krishnaswami, Ashok; Kiley, Mary-Lou; Anthony, Faith F; Chen, Yuexin; Chen, Jason; Rajagopal, Sumanth; Liu, Taylor I; Young, Charlie; Paxton, Elizabeth W
2016-01-01
Context: There is insufficient information on the effect that advancing age and multiple chronic conditions (MCC) have on mortality after placement of an implantable cardioverter-defibrillator in patients with end-stage renal disease (ESRD) vs non-ESRD. Objective: To assess whether a differential effect of age and MCC exists between ESRD and non-ESRD. Design: Population-based, retrospective cohort study using data from the national Kaiser Permanente Cardiac Device Registry of patients who underwent placement of an implantable cardioverter-defibrillator between January 1, 2007, and December 31, 2013. Main Outcome Measures: All-cause mortality. Results: Of 7825 patients with implantable cardioverter-defibrillator placement, ESRD-affected patients constituted 4.0% of the cohort (n = 311), were similar in age (p = 0.91), and presented with a larger comorbidity burden (3.3 ± 1.3 vs 2.4 ± 1.5, p < 0.001). The effect of advancing age (every 5 years) on mortality in the ESRD cohort (hazard ratio [HR] = 1.11, 95% confidence interval [CI] = 1.03–1.20) was less than in the non-ESRD cohort (HR = 1.28, 95% CI = 1.25–1.32). Similarly, the effect of each additional comorbidity in the ESRD cohort was less (HR = 1.04, 95% CI = 0.91–1.19) than in the non-ESRD group (HR = 1.20, 95% CI = 1.16–1.25). Lastly, ESRD was independently associated with a 3-fold greater hazard of mortality. Conclusions: Advancing age and increasing number of MCC have a differential effect on mortality risk in patients with ESRD compared with their non-ESRD counterparts. Future studies should focus on assessment of nonlinear relationships of age, MCC, and naturally occurring clusters of MCC on mortality. PMID:26562307
NASA Astrophysics Data System (ADS)
Depalma, Darlene M.
A problem within science education in the United States persists. U.S students rank lower in science than most other students from participating countries on international tests of achievement (National Center for Education Statistics, 2003). In addition, U.S. students overall enrollment rate in high school Advanced Placement (AP) physics is still low compared to other academic domains, especially for females. This problem is the background for the purpose of this study. This investigation examined cognitive and motivational variables thought to play a part in the under-representation of females in AP physics. Cognitive variables consisted of mathematics, reading, and science knowledge, as measured by scores on the 10th and 11th grade Florida Comprehensive Assessment Tests (FCAT). The motivational factors of attitude, stereotypical views toward science, self-efficacy, and epistemological beliefs were measured by a questionnaire developed with questions taken from previously proven reliable and valid instruments. A general survey regarding participation in extracurricular activities was also included. The sample included 12th grade students from two high schools located in Seminole County, Florida. Of the 106 participants, 20 girls and 27 boys were enrolled in AP physics, and 39 girls and 20 boys were enrolled in other elective science courses. Differences between males and females enrolled in AP physics were examined, as well as differences between females enrolled in AP physics and females that chose not to participate in AP physics, in order to determine predictors that apply exclusively to female enrollment in high school AP physics and predictors of an anticipated science related college major. Data were first analyzed by Exploratory Factor Analysis, followed by Analysis of Variance (ANOVA), independent t-tests, univariate analysis, and logistic regression analysis. One overall theme that emerged from this research was findings that refute the ideas that
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.
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…
Multiplicative Calculus and Student Projects.
ERIC Educational Resources Information Center
Campbell, Duff
1999-01-01
Multiplicative calculus is based on a multiplicative rate of change whereas the usual calculus is based on an additive rate of change. Describes some student investigations into multiplicative calculus, including an original student idea about multiplicative Euler's Method. (Author/ASK)
Dental Calculus and the Evolution of the Human Oral Microbiome.
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. PMID:27514153
Dental Calculus and the Evolution of the Human Oral Microbiome.
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.
Tangent Lines without Calculus
ERIC Educational Resources Information Center
Rabin, Jeffrey M.
2008-01-01
This article presents a problem that can help high school students develop the concept of instantaneous velocity and connect it with the slope of a tangent line to the graph of position versus time. It also gives a method for determining the tangent line to the graph of a polynomial function at any point without using calculus. (Contains 1 figure.)
Software Review: "Interactive Calculus."
ERIC Educational Resources Information Center
Connors, Edward A.
1995-01-01
An interactive, multimedia text for calculus instruction that contains the entire contents of a corresponding textbook is evaluated and found to have features that enhance concepts with dynamic examples of graphs and problems that make good use of animation, audio, and video. Its design accommodates diverse student abilities and educational…
ERIC Educational Resources Information Center
Fletcher, T. J.
1971-01-01
Non-traditional methods of presenting and solving calculus problems in high school mathematics classes are presented. All problems deal with the principle that the maximum product of two numbers whose sum is constant is obtained if the numbers are equal (i.e., the arithmetic mean of n numbers is greater than or equal to the geometric mean). (JG)
NASA Astrophysics Data System (ADS)
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 original foundation. It is necessary to present the information along with other methods one might employ now in common use; avoiding these principles of the Calculus can cloud its simplicity. The nature and significance of integration and differentiation are clarified, including the power and chain rules, logarithmic differentiation, and the fundamental relationships between integrals and derivatives. By considering in detail the graphical areas covered by a thin thread under a continuous smooth function along its course, the Fundamental Theorems of the Calculus may be proven. Any function f(x) is both the derivative of and the integrand of its integral F(x). The area traced out by any f(x) has ordinal values that are the slopes of F(x) because the function is the derivative of the integral. Differences in ordinal values of an integral, F(b) - F(a), calculate the total of all dy variations along the integral and equal the exact net area of thin vertical f(x)dx threads between the derivative function and the horizon from a to b. Unique features of the sine function, including its line integral arc length and its area, demonstrate the power of the Fundamental Theorems of the Calculus.
Fractional calculus in bioengineering.
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
Fractional calculus in bioengineering.
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
Astrophysical Applications of Fractional Calculus
NASA Astrophysics Data System (ADS)
Stanislavsky, Aleksander A.
The paradigm of fractional calculus occupies an important place for the macroscopic description of subdiffusion. Its advance in theoretical astrophysics is expected to be very attractive too. In this report we discuss a recent development of the idea to some astrophysical problems. One of them is connected with a random migration of bright points associated with magnetic fields at the solar photosphere. The transport of the bright points has subdiffusive features that require the fractional generalization of the Leighton's model. Another problem is related to the angular distribution of radio beams, being propagated through a medium with random inhomogeneities. The peculiarity of this medium is that radio beams are trapped because of random wave localization. This idea can be useful for the diagnostics of interplanetary and interstellar turbulent media.
Calculus fragmentation in laser lithotripsy.
Welch, A J; Kang, H W; Lee, H; Teichman, J M H
2004-03-01
The intracorporeal treatment of urinary calculi with lasers is presented, which describes laser-calculus interactions associated with lithotripsy. Reliable fragmentation of calculi with diverse compositions and minimal collateral tissue damage are primarily contingent upon laser parameters (wavelength, pulse duration, and pulse energy) and physical properties of calculi (optical, mechanical, and chemical). The pulse duration governs the dominant mechanism in calculi fragmentation, which is either photothermal or photoacoustical/photomechanical. Lasers with long pulse durations (i.e. > tens of micros) induce a temperature rise in the laser-affected zone with minimal acoustic waves; material is removed by means of vaporization, melting, mechanical stress, and/or chemical decomposition. Short-pulsed laser ablation (i.e. < 10 micros), on the other hand, produces shock waves, and the resultant mechanical energy fragments calculi. Work continues throughout the world to evaluate the feasibility of advanced lasers in lithotripsy and to optimize laser parameters and light delivery systems pertinent to efficient fragmentation of calculi.
Bozec, Alexandre; Benezery, Karen; Chamorey, Emmanuel; Ettaiche, Marc; Vandersteen, Clair; Dassonville, Olivier; Poissonnet, Gilles; Riss, Jean-Christophe; Hannoun-Lévi, Jean-Michel; Chand, Marie-Eve; Leysalle, Axel; Saada, Esma; Sudaka, Anne; Haudebourg, Juliette; Hebert, Christophe; Falewee, Marie-Noelle; Demard, François; Santini, José; Peyrade, Frédéric
2016-09-01
The objective of the study is to evaluate the nutritional status and determine its impact on clinical outcomes in patients with locally advanced hypopharyngeal cancer included in an induction chemotherapy (ICT)-based larynx preservation program without prophylactic feeding-tube placement. All patients with locally advanced (T3/4, N0-3, M0) hypopharyngeal squamous cell carcinoma, technically suitable for total pharyngolaryngectomy, treated by docetaxel, cisplatin and 5-fluorouracil (TPF)-ICT for larynx preservation at our institution between 2004 and 2013, were included in this retrospective study. Patients' nutritional status was closely monitored. Enteral nutrition was used if and when a patient was unable to sustain per-oral nutrition and hydration. The impact of nutritional status on clinical outcomes was investigated in univariate and multivariate analysis. A total of 53 patients (42 men and 11 women, mean age = 58.6 ± 8.2 years) were included in this study. Six (11.3 %) patients had lost more than 10 % of their usual body weight before therapy. Compared with patients' usual weight, the mean maximum patient weight loss during therapeutic management was 8.7 ± 4.5 kg. Enteral nutrition was required in 17 patients (32 %). We found no influence of the tested nutritional status-related factors on response to ICT, toxicity of ICT, overall, cause-specific and recurrence-free survival, and on post-therapeutic swallowing outcome. Maximum weight loss was significantly associated with a higher risk of enteral tube feeding during therapy (p = 0.03) and of complications (grade ≥3, p = 0.006) during RT. Without prophylactic feeding-tube placement, approximately one-third of the patients required enteral nutrition. There was no significant impact of nutritional status on oncologic or functional outcomes.
Student understanding of calculus within physics and mathematics classrooms
NASA Astrophysics Data System (ADS)
Christensen, Warren; Thompson, John
2010-03-01
The earliest results in Physics Education Research demonstrated the challenges facing students in understanding the graphical interpretations of slope, derivative, and area under curves in the context of kinematics. As part of ongoing research on mathematical challenges that may underlie documented physics difficulties, we developed and administered a brief survey on single- and multivariable calculus concepts to students within physics and mathematics classrooms at both the introductory and advanced levels. Initial findings among students in multivariable calculus show that as many as one in five students encounter some type of difficulty when asked to rank the slopes at five different points along a single path. We will present further data on the extent to which students in a first semester calculus course and an introductory calculus-based physics course encounter similar challenges.
NASA Technical Reports Server (NTRS)
Tucker, Jerry H.; Tapia, Moiez A.; Bennett, A. Wayne
1988-01-01
The concept of Boolean integration is developed, and different Boolean integral operators are introduced. Given the changes in a desired function in terms of the changes in its arguments, the ways of 'integrating' (i.e. realizing) such a function, if it exists, are presented. The necessary and sufficient conditions for integrating, in different senses, the expression specifying the changes are obtained. Boolean calculus has applications in the design of logic circuits and in fault analysis.
ERIC Educational Resources Information Center
Department of Education, Washington, DC.
This transcript reproduces a Department of Education/College Board sponsored discussion on ways to expand advanced placement (AP) opportunities in high schools. The deliberations opened with a presentation by Phil Chavez, an assistant principal in San Antonio, Texas, who outlined the genesis and development of the AP program in his predominantly…
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.
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.)
ERIC Educational Resources Information Center
Sharp, Helen M.; Shega, Joseph W.
2009-01-01
Purpose: To describe the beliefs and practices of speech-language pathologists (SLPs) about the use of percutaneous endoscopic gastrostomy (PEG) among patients with advanced dementia and dysphagia. Method: A survey was mailed to a geographically stratified random sample of 1,050 medical SLPs. Results: The response rate was 57%, and 326 surveys met…
ERIC Educational Resources Information Center
Meagher, Michael; Ozgun-Koca, Asli; Edwards, Michael Todd
2011-01-01
This paper reports on a study of 22 preservice teachers enrolled in a first-semester mathematics teaching methods course. Course activities included participation in two separate field experiences in neighboring school districts. The methods class placed considerable emphasis on the use of advanced digital technologies in the teaching and learning…
ERIC Educational Resources Information Center
Hare, Angela; Phillippy, Doug
2004-01-01
A program on calculus is conducted, which helps students learn about inherent differentiation through a study of mathematical functions, while simultaneously reinforcing their understanding of functional concepts. This process develops their mathematical experience in the field of calculus and in other advanced quantitative programs.
A Mixed-Methods Explanatory Study of the Failure Rate for Freshman STEM Calculus Students
ERIC Educational Resources Information Center
Worthley, Mary R.; Gloeckner, Gene W.; Kennedy, Paul A.
2016-01-01
In this study we aimed to understand who was struggling in freshman calculus courses, and why. Concentrating on the Fall sections of the class, the best predictors for success (R[superscript 2] = 0.4) were placement test results, the student's own appraisal of the quality of mathematics teaching they received in high school, and the Motivated…
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 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…
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…
Jin, Qiushuang; Shi, Qian
2008-12-01
This study investigated the association between sleep deprivation and enrollment in Advanced Placement (AP) and/or college courses among high school students. Approximately 4,000 surveys were distributed, and 2,197 completed surveys were returned from students in Grades 9 to 12 at 15 high schools in Iowa. Findings indicated the majority of high school students were sleep deprived. Sleep deprivation was significantly associated with enrollment in AP/college courses. Results indicated that enrollment in AP/college courses had a greater impact on younger students than older students. Compared with non-AP/college course takers, AP/college course takers slept approximately 20 minutes less per night. Specifically, 9th- and 10th-grade AP/college course takers slept approximately 1 hour less and 40 minutes less, respectively. In addition, students enrolled in two or more AP/college classes received 1 hour less and 30 minutes less among 10th and 11th graders, respectively. These results provide useful information on adolescent sleep patterns for school nurses. PMID:19114472
NASA Astrophysics Data System (ADS)
Markus, Doron J.
Test anxiety is one of the most debilitating and disruptive factors associated with underachievement and failure in schools (Birenbaum, Menucha, Nasser, & Fadia, 1994; Tobias, 1985). Researchers have suggested that interventions that combine multiple test-anxiety reduction techniques are most effective at reducing test anxiety levels (Ergene, 2003). For the current study, involving 62 public high school students enrolled in advanced placement science courses, the researcher designed a multimodal intervention designed to reduce test anxiety. Analyses were conducted to assess the relationships among test anxiety levels, unit examination scores, and irregular multiple-choice error patterns (error clumping), as well as changes in these measures after the intervention. Results indicate significant, positive relationships between some measures of test anxiety and error clumping, as well as significant, negative relationships between test anxiety levels and student achievement. In addition, results show significant decreases in holistic measures of test anxiety among students with low anxiety levels, as well as decreases in Emotionality subscores of test anxiety among students with high levels of test anxiety. There were no significant changes over time in the Worry subscores of test anxiety. Suggestions for further research include further confirmation of the existence of error clumping, and its causal relationship with test anxiety.
Nishimura, Junya; Kubo, Naoshi; Lee, Tomohiro; Shinto, Osamu; Sakurai, Katsunobu; Toyokawa, Takahiro; Tanaka, Hiroaki; Muguruma, Kazuya; Shibutani, Masatsune; Yamazoe, Sadaaki; Nagahara, Hisashi; Kimura, Kenjiro; Amano, Ryosuke; Ohtani, Hiroshi; Yashiro, Masakazu; Maeda, Kiyoshi; Ohira, Masaichi; Hirakawa, Kosei
2013-11-01
The patient was a 68-year-old man who complained of hoarseness and dyspnea. Upper gastrointestinal endoscopy revealed a type 3 tumor located in the middle thoracic esophagus at 30 cm from the incisor tooth that involved one-fourth of the circumference of the esophagus. Histopathological examination revealed moderately differentiated squamous cell carcinoma. Chest computed tomography( CT) revealed severe tracheal stenosis due to compression by a metastatic lymph node along the left recurrent laryngeal nerve. The patient was diagnosed as having cT4( 106recL-trachea), N2( 101L, 106recL, 106recR), M0, Stage IVa unresectable esophageal carcinoma. After insertion of a tracheal stent tube( spiral Z stent: diameter, 18 mm; length, 80 mm) to improve dyspnea, combination chemotherapy with 5-fluorouracil( 5-FU) plus nedaplatin was administered. Subsequent CT and endoscopy showed that the main tumor and the metastatic lymph node had significantly reduced in size and that complete response (CR) had been achieved. Thirty months after the initial treatment, the patient showed no sign of disease recurrence, after completion of 19 cycles of chemotherapy. The patient did not experience any severe adverse events. We report a case of a patient with locally advanced squamous cell carcinoma of the esophagus successfully treated with 5-FU/nedaplatin combination chemotherapy following tracheal stent tube placement.
Open Calculus: A Free Online Learning Environment
ERIC Educational Resources Information Center
Korey, Jane; Rheinlander, Kim; Wallace, Dorothy
2007-01-01
Dartmouth College mathematicians have developed a free online calculus course called "Open Calculus." Open Calculus is an exportable distance-learning/self-study environment for learning calculus including written text, nearly 4000 online homework problems and instructional videos. The paper recounts the evaluation of course elements since 2000 in…
A Simple Acronym for Doing Calculus: CAL
ERIC Educational Resources Information Center
Hathaway, Richard J.
2008-01-01
An acronym is presented that provides students a potentially useful, unifying view of the major topics covered in an elementary calculus sequence. The acronym (CAL) is based on viewing the calculus procedure for solving a calculus problem P* in three steps: (1) recognizing that the problem cannot be solved using simple (non-calculus) techniques;…
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.
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.
Classroom Integral Calculus: Some Useful Digressions When Teaching Integral Calculus.
ERIC Educational Resources Information Center
Acosta, Daniel J.; Wills, Randall
2002-01-01
Outlines ideas and exercises for two topics that accompany the standard treatment of integral calculus. Emphasizes intuition to help facilitate student comprehension of the definite integral as a limit of Riemann Sums. (Author/MM)
Algorithmic Differentiation for Calculus-based Optimization
NASA Astrophysics Data System (ADS)
Walther, Andrea
2010-10-01
For numerous applications, the computation and provision of exact derivative information plays an important role for optimizing the considered system but quite often also for its simulation. This presentation introduces the technique of Algorithmic Differentiation (AD), a method to compute derivatives of arbitrary order within working precision. Quite often an additional structure exploitation is indispensable for a successful coupling of these derivatives with state-of-the-art optimization algorithms. The talk will discuss two important situations where the problem-inherent structure allows a calculus-based optimization. Examples from aerodynamics and nano optics illustrate these advanced optimization approaches.
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.…
Insights from the MAA National Study of College Calculus
ERIC Educational Resources Information Center
Bressoud, David
2015-01-01
Over the past five years, the Mathematical Association of America, with support from the National Science Foundation, has explored the teaching of mainstream Calculus 1 at the postsecondary level, where by "mainstream" we mean those courses that can be used as part of the prerequisite stream to more advanced postsecondary mathematics. We…
Dynamic Visualizations of Calculus Ideas.
ERIC Educational Resources Information Center
Embse, Charles Vonder
2001-01-01
Presents three fundamental ideas of calculus and explains using the coordinate plane geometrically. Uses Cabri Geometry II to show how computer geometry systems can facilitate student understanding of general conic objects and its dynamic algebraic equations. (KHR)
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.
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)
NASA Technical Reports Server (NTRS)
Venkatapathy, Ethiraj; Arnold, James O.; Peterson, K. H.; Blosser, M. L.
2013-01-01
This paper describes aerothermodynamic and thermal structural testing that demonstrate the viability of three dimensional woven carbon cloth and advanced carbon-carbon (ACC) ribs for use in the Adaptive Deployable Entry Placement Technology (ADEPT). ADEPT is an umbrella-like entry system that is folded for stowage in the launch vehicle's shroud and deployed prior to reaching the atmeopheric interface. A key feature of the ADEPT concept is a lower ballistic coefficient for delivery of a given payload than seen with conventional, rigid body entry systems. The benefits that accrue from the lower ballistic coefficient incllude factor-of-ten reductions of deceleration forces and entry heating. The former enables consideration of new classes of scientific instruments for solar system exploration while the latter enables the design of a more efficient thermal protection system. The carbon cloth base lined for ADEPT has a dual use in that it serves as the thermal protection system and as the "skin" that transfers aerdynamic deceleration loads to its umbrella-like substructure. Arcjet testing described in this paper was conducted for some of the higher heating conditions for a future Venus mission using the ADEPT concept, thereby showing that the carbon cloth can perform in a relevant entry environment. Recently completed the thermal structural testing of the cloth attached to a representative ACC rib design is also described. Finally, this paper describes a preliminary engineering level code, based on the arcjet data, that can be used to estimate cloth thickness for future ADEPT missions and to predict carbon cloth performance in future arcjet tests.
Integral calculus problem solving: an fMRI investigation.
Krueger, Frank; Spampinato, Maria Vittoria; Pardini, Matteo; Pajevic, Sinisa; Wood, Jacqueline N; Weiss, George H; Landgraf, Steffen; Grafman, Jordan
2008-07-16
Only a subset of adults acquires specific advanced mathematical skills, such as integral calculus. The representation of more sophisticated mathematical concepts probably evolved from basic number systems; however its neuroanatomical basis is still unknown. Using fMRI, we investigated the neural basis of integral calculus while healthy participants were engaged in an integration verification task. Solving integrals activated a left-lateralized cortical network including the horizontal intraparietal sulcus, posterior superior parietal lobe, posterior cingulate gyrus, and dorsolateral prefrontal cortex. Our results indicate that solving of more abstract and sophisticated mathematical facts, such as calculus integrals, elicits a pattern of brain activation similar to the cortical network engaged in basic numeric comparison, quantity manipulation, and arithmetic problem solving. PMID:18596607
Integral calculus problem solving: an fMRI investigation.
Krueger, Frank; Spampinato, Maria Vittoria; Pardini, Matteo; Pajevic, Sinisa; Wood, Jacqueline N; Weiss, George H; Landgraf, Steffen; Grafman, Jordan
2008-07-16
Only a subset of adults acquires specific advanced mathematical skills, such as integral calculus. The representation of more sophisticated mathematical concepts probably evolved from basic number systems; however its neuroanatomical basis is still unknown. Using fMRI, we investigated the neural basis of integral calculus while healthy participants were engaged in an integration verification task. Solving integrals activated a left-lateralized cortical network including the horizontal intraparietal sulcus, posterior superior parietal lobe, posterior cingulate gyrus, and dorsolateral prefrontal cortex. Our results indicate that solving of more abstract and sophisticated mathematical facts, such as calculus integrals, elicits a pattern of brain activation similar to the cortical network engaged in basic numeric comparison, quantity manipulation, and arithmetic problem solving.
``Riemann equations'' in bidifferential calculus
NASA Astrophysics Data System (ADS)
Chvartatskyi, O.; Müller-Hoissen, F.; Stoilov, N.
2015-10-01
We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a semi-discrete and a fully discrete version of the matrix Riemann equation. A corresponding universal solution-generating method then either yields a (continuous or discrete) Cole-Hopf transformation, or leaves us with the problem of solving Riemann equations (hence an application of the hodograph method). If the bidifferential calculus extends to second order, solutions of a system of "Riemann equations" are also solutions of an equation that arises, on the universal level of bidifferential calculus, as an integrability condition. Depending on the choice of bidifferential calculus, the latter can represent a number of prominent integrable equations, like self-dual Yang-Mills, as well as matrix versions of the two-dimensional Toda lattice, Hirota's bilinear difference equation, (2+1)-dimensional Nonlinear Schrödinger (NLS), Kadomtsev-Petviashvili (KP) equation, and Davey-Stewartson equations. For all of them, a recent (non-isospectral) binary Darboux transformation result in bidifferential calculus applies, which can be specialized to generate solutions of the associated "Riemann equations." For the latter, we clarify the relation between these specialized binary Darboux transformations and the aforementioned solution-generating method. From (arbitrary size) matrix versions of the "Riemann equations" associated with an integrable equation, possessing a bidifferential calculus formulation, multi-soliton-type solutions of the latter can be generated. This includes "breaking" multi-soliton-type solutions of the self-dual Yang-Mills and the (2+1)-dimensional NLS equation, which are parametrized by solutions of Riemann equations.
Investigating the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Johnson, Heather L.
2010-01-01
The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were…
The Power of Investigative Calculus Projects
ERIC Educational Resources Information Center
Perrin, John Robert; Quinn, Robert J.
2008-01-01
This article describes investigative calculus projects in which students explore a question or problem of their own construction. Three exemplary pieces of student work are showcased. Investigative calculus projects are an excellent way to foster student understanding and interest in calculus. (Contains 4 figures.)
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.…
ERIC Educational Resources Information Center
Hughes, Chris
2010-01-01
The primary method of placement at Portland CC (PCC) is the Compass Placement test. For the most part, students are placed correctly, but there are cases when students feel that they have been placed too low. In such cases we use our newly created Placement Advisory Test (PAT) to help us place them appropriately. (Contains 2 figures.)
ERIC Educational Resources Information Center
Los Angeles Unified School District, CA. Div. of Career and Continuing Education.
Designed to serve as a guide for job placement personnel, this handbook is written from the point of view of a school or job preparation facility, based on methodology applicable to the placement function in any setting. Factors identified as critical to a successful placement operation are utilization of a systems approach, establishment of…
ERIC Educational Resources Information Center
Atlanta Public Schools, GA.
Directed to school systems initiating a job placement program, the Atlanta Public Schools (Georgia) job placement manual discusses how a job placement program can provide a transition from school to work for all students leaving the public schools, as well as place students in paid and non-paid part-time work experiences as a part of their…
Calculus of twisted vertex operators
Lepowsky, J.
1985-01-01
Starting from an arbitrary isometry of an arbitrary even lattice, twisted and shifted vertex operators are introduced. Under commutators, these operators provide realizations of twisted affine Lie algebras. This construction, generalizing a number of known ones, is based on a self-contained “calculus.” PMID:16593635
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…
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…
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,…
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…
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)
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…
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…
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…
A Study of Placement and Grade Prediction in First College Mathematics Courses
ERIC Educational Resources Information Center
Madison, Bernard L.; Linde, Cassandra S.; Decker, Blake R.; Rigsby, E. Myron; Dingman, Shannon W.; Stegman, Charles E.
2015-01-01
A college mathematics placement test with 25 basic algebra items and 15 calculus readiness items was administered to 1572 high school seniors, and first college mathematics course grades were obtained for 319 of these students. Test results indicated that more than two thirds of the high school graduates were not college ready, and the test…
Trumm, Christoph Gregor; Rubenbauer, Bianca; Piltz, Stefan; Reiser, Maximilian F.; Hoffmann, Ralf-Thorsten
2011-02-15
We present a case of combined surgical screw placement and osteoplasty guided by computed tomography-fluoroscopy (CTF) in a 68-year-old man with unilateral osteolytic destruction and a pathological fracture of the iliosacral joint due to a metastasis from renal cell carcinoma. The patient experienced intractable lower back pain that was refractory to analgesia. After transarterial particle and coil embolization of the tumor-feeding vessels in the angiography unit, the procedure was performed under general anesthesia by an interdisciplinary team of interventional radiologists and trauma surgeons. Under intermittent single-shot CTF, two K wires were inserted into the left iliosacral joint from a lateral transiliac approach at the S1 level followed by two self-tapping surgical screws. Continuous CTF was used for monitoring of the subsequent polymethylmethacrylate injection through two vertebroplasty cannulas for further stabilization of the screw threads within the osteolytic sacral ala. Both the screw placement and cement injection were successful, with no complications occurring during or after the procedure. With additional nonsteroidal anti-inflammatory and opioid medication, the patient reported a marked decrease in his lower back pain and was able to move independently again at the 3-month follow-up assessment. In our patient with intolerable back pain due to tumor destruction and consequent pathological fracture of the iliosacral joint, CTF-guided iliosacral screw placement combined with osteoplasty was successful with respect to joint stabilization and a reduction in the need for analgesic therapy.
Strategies for Controlled Placement of Nanoscale Building Blocks
2007-01-01
The capability of placing individual nanoscale building blocks on exact substrate locations in a controlled manner is one of the key requirements to realize future electronic, optical, and magnetic devices and sensors that are composed of such blocks. This article reviews some important advances in the strategies for controlled placement of nanoscale building blocks. In particular, we will overview template assisted placement that utilizes physical, molecular, or electrostatic templates, DNA-programmed assembly, placement using dielectrophoresis, approaches for non-close-packed assembly of spherical particles, and recent development of focused placement schemes including electrostatic funneling, focused placement via molecular gradient patterns, electrodynamic focusing of charged aerosols, and others. PMID:21794185
Calculus: The Dynamics of Change. MAA Notes Number 39.
ERIC Educational Resources Information Center
Roberts, A. Wayne, Ed.
This book discusses the calculus reform effort. The first essay captures the basic themes that should characterize a calculus course that is modern in its vision as well as its pedagogy and content. The next section contains essays on the vision of calculus reform: "Visions of Calculus" (Sharon Cutler Ross); "Nonalgebraic Approaches to Calculus"…
[Calculus index (OHI-S) and periodontal condition in diabetes mellitus].
Fett, K D
1977-01-01
The calculus (OHI-S) index according to Greene and Vermillion and the periodontal disease index of Kötzschke were determined in 209 male diabetics. The calculus index (CI) was significantly lower in diabetics with healthy gingivae (CI=0.40) than in diabetics with pathological periodontal findings (CI=1.40). Diabetics with advanced periodontal diseases (gingival recession, periodontitis and pockets), such as parodontopathia inflammata profunda, showed the highest CI value (1.88) which also differed significantly from the CI values for diabetics with healthy gingivae or with parodontopathia inflammata superficialis. 91% of our diabetics with pathological findings showed also concretions of calculus, subgingival concretions being detectable in 47.4% of these patients. It is concluded from results obtained that calculus formation is surely a sequela but not the only cause of periodontal diseases.
Schulsinger, D A; Sosa, R E
1998-03-01
We have seen an explosion in technical innovations for the management of urolithiasis. Today, the endourologist possesses an assortment of minimally invasive tools to treat renal stones. Most patients receive fast, safe and effective treatment in the outpatient setting. Despite the many technical advances, however, anatomical malformations and complex stones still provide significant challenges in diagnosis, access to a targeted stone, fragmentation, and clearance of the resulting fragments. This review examines a variety of urinary stone presentations and treatment strategies for cost-effective management.
Fractal calculus involving gauge function
NASA Astrophysics Data System (ADS)
Golmankhaneh, Alireza K.; Baleanu, Dumitru
2016-08-01
Henstock-Kurzweil integral or gauge integral is the generalization of the Riemann integral. The functions which are not integrable because of singularity in the senses of Lebesgue or Riemann are gauge integrable. In this manuscript, we have generalized Fα-calculus using the gauge integral method for the integrating of the functions on fractal set subset of real-line where they have singularities. The suggested new method leads to the wider class of functions on the fractal subset of real-line that are *Fα-integrable. Using gauge function we define *Fα-derivative of functions their Fα-derivative is not exist. The reported results can be used for generalizing the fundamental theorem of Fα-calculus.
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)
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.
Dental Calculus Arrest of Dental Caries
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
ERIC Educational Resources Information Center
Wampler, Elizabeth C.
The publication presents guidelines to assist secondary schools in developing and implementing a job placement service within an existing guidance program. The need for and the goals of a school placement program are given. Areas to be considered in developing a program according to one of three organizational patterns (decentralized, centralized,…
ERIC Educational Resources Information Center
Devlin, Thomas; And Others
1984-01-01
Describes computerized placement programs at three colleges. Cornell University developed a microcomputer program while Virginia Polytechnic Institute and State University used the university's mainframe system. College of Lake County found that computerized job placement meant a stronger link with the business community. (JAC)
Study on bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis.
Wan, Tien-Chun; Cheng, Fu-Yuan; Liu, Yu-Tse; Lin, Liang-Chuan; Sakata, Ryoichi
2009-12-01
The purpose of the study was to investigate bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis obtained as valuable by-products from animals used for meat production. The results showed that the components of natural Calculus Bovis were rich in bilirubin and biliverdin and had higher content of essential amino acids. The major amino acids of in vitro cultured Calculus Suis were identified as glycine, alanine, glutamic acid and aspartic acid, and those for natural Calculus Bovis were found to be glutamic acid, aspartic acid, proline, and arginine. The methionine and cysteine contents of precursors for glutathione in natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The mineral contents of zinc, iron and manganese of natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The major bile acids in both products were cholic acid and dehydrocholic acid, respectively. The chenodeoxycholic and ursodeoxycholic acid content of in vitro cultured Calculus Suis was significantly higher than that of natural Calculus Bovis.
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…
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…
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.
Plotting Pots: Archaeological Exercises in Introductory Calculus.
ERIC Educational Resources Information Center
Meier, John; Thorme, Trisha
1997-01-01
Outlines a pair of projects used in introductory calculus that are inspired by techniques archaeologists use in the analysis of pottery. These real-world application problems appeal to students who are not necessarily interested in the standard application of calculus. (Author/DDR)
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…
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…
Top-Down Calculus: A Concise Course.
ERIC Educational Resources Information Center
Williamson, S. Gill
This textbook was designed for a first course in differential and integral calculus, and is directed toward students in engineering, the sciences, mathematics, and computer science. Its major goal is to bring students to a level of technical competence and intuitive understanding of calculus that is adequate for applying the subject to real world…
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…
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…
Calculus: An Active Approach with Projects.
ERIC Educational Resources Information Center
Hilbert, Stephen; And Others
1993-01-01
Discusses a pedagogical approach to calculus based on the question: What kinds of problems should students be able to solve? Includes a discussion of types of problems and curriculum threads for such a course. Describes a projects-based calculus with examples of projects and classroom activities. (Author/MDH)
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…
NASA Astrophysics Data System (ADS)
Crombie, William
2013-04-01
We take a second look at Saletan's American Journal of Physics article (1973) which describes a method, appropriate to elementary physics courses, for defining the instantaneous velocity of a moving object and for computing derivatives without recourse to limits. The mathematics behind our extended method enters at the level of College Algebra and provides an alternative formulation to the Calculus based on either infinitesimals or limits. This approach holds the promise of providing access to Calculus and those quantitative disciplines that depend upon Calculus to a larger pool of students than is presently engaged in the advanced study of STEM disciplines.
Computer-Oriented Calculus Courses Using Finite Differences.
ERIC Educational Resources Information Center
Gordon, Sheldon P.
The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been…
Using Dynamic Software to Address Common College Calculus Stumbling Blocks
ERIC Educational Resources Information Center
Seneres, Alice W.; Kerrigan, John A.
2014-01-01
There are specific topics in college calculus that can be major stumbling blocks for students. Having taught college calculus for four years to over a thousand students, we observed that even the students who have already taken pre-calculus or calculus during their high school careers had common misunderstandings. Students may remember a technique…
Callahan, Rebecca; Wilkinson, Lindsey; Muller, Chandra; Frisco, Michelle
2010-01-01
In this study, the authors explore English as a Second Language (ESL) placement as a measure of how schools label and process immigrant students. Using propensity score matching and data from the Adolescent Health and Academic Achievement Study and the National Longitudinal Study of Adolescent Health, the authors estimate the effect of ESL placement on immigrant achievement. In schools with more immigrant students, the authors find that ESL placement results in higher levels of academic performance; in schools with few immigrant students, the effect reverses. This is not to suggest a one-size-fits-all policy; many immigrant students, regardless of school composition, generational status, or ESL placement, struggle to achieve at levels sufficient for acceptance to a 4-year university. This study offers several factors to be taken into consideration as schools develop policies and practices to provide immigrant students opportunities to learn. PMID:20617111
Teaching calculus with Wolfram|Alpha
NASA Astrophysics Data System (ADS)
Dimiceli, Vincent E.; Lang, Andrew S. I. D.; Locke, LeighAnne
2010-12-01
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 Wolfram|Alpha in our differential and integral calculus labs, together with the positive results from our experience. We also discuss the current limitations of Wolfram|Alpha, including a discussion on why we still use a CAS for our multivariate calculus labs.
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.
Fractional-calculus diffusion equation
2010-01-01
Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677
ERIC Educational Resources Information Center
Barnett, M.D.; Sonnert, G.; Sadler, P.M.
2014-01-01
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…
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…
Generalized Laplace Transforms and Extended Heaviside Calculus
ERIC Educational Resources Information Center
Deakin, Michael A. B.
2008-01-01
An extended Heaviside calculus proposed by Peraire in a recent paper is similar to a generalization of the Laplace transform proposed by the present author. This similarity will be illustrated by analysis of an example supplied by Peraire.
Applying Change of Variable to Calculus Problems
ERIC Educational Resources Information Center
Kachapova, Farida; Kachapov, Ilias
2011-01-01
This article describes the technique of introducing a new variable in some calculus problems to help students master the skills of integration and evaluation of limits. This technique is algorithmic and easy to apply.
Renal calculus complicated with squamous cell carcinoma of renal pelvis: Report of two cases.
Xiao, Jiantao; Lei, Jun; He, Leye; Yin, Guangming
2015-01-01
Longstanding renal calculus is a risk factor of squamous cell carcinoma (SCC) of the renal pelvis. It is highly aggressive and usually diagnosed at advanced stages with a poor prognosis. We present two cases of kidney stone complications with renal pelvic SCC. These two patients had a radical nephrectomy and the dissected tissues were renal pelvic SCC. Our cases further emphasize that renal pelvic SCC should be considered in patients with longstanding renal calculus. These cases contribute greatly to an early diagnosis and early treatment, both of which will significantly minimize the damage of, and markedly improve the prognosis of, renal pelvic SCC.
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.
Generalized Cartan Calculus in general dimension
NASA Astrophysics Data System (ADS)
Wang, Yi-Nan
2015-07-01
We develop the generalized Cartan Calculus for the groups 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 Poincaré lemmas in this new differential geometry is also discussed. Finally we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.
Generalized Cartan Calculus in general dimension
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.
Non-commutative functional calculus: Unbounded operators
NASA Astrophysics Data System (ADS)
Colombo, Fabrizio; Gentili, Graziano; Sabadini, Irene; Struppa, Daniele C.
2010-02-01
In a recent work, Colombo (in press) [1], we developed a functional calculus for bounded operators defined on quaternionic Banach spaces. In this paper we show how the results from the above-mentioned work can be extended to the unbounded case, and we highlight the crucial differences between the two cases. In particular, we deduce a new eigenvalue equation, suitable for the construction of a functional calculus for operators whose spectrum is not necessarily real.
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.
Atasoy, Beste M; Yonal, Oya; Demirel, Birsen; Dane, Faysal; Yilmaz, Yusuf; Kalayci, Cem; Abacioglu, Ufuk; Imeryuz, Nese
2012-01-01
To investigate the impact of early insertion of percutaneous endoscopic gastrostomy-tube on nutritional status and completeness of concurrent chemotherapy in locally advanced head and neck cancer patients treated with chemoradiotherapy. Twenty-three patients were enrolled into this prospective study. Gastrostomy-tube was inserted in patients before the initiation of chemoradiotherapy. There was not any significant change in nutritional parameters of patients that used their tube during treatment. Despite the grade 3 mucositis, the planned concurrent chemotherapy could be given in 70% of the patients. However, nine patients had weak compliance and their body weight (P = 0.01) and body mass index (P = 0.01) deteriorated in the first 4 weeks of chemoradiotherapy. The completeness of concurrent chemo-rate was 44% in these patients. Toxicity, requiring aggressive supportive care, may limit the chemotherapy part of curative concomitant chemoradiotherapy. By providing adequate enteral nutrition the insertion of gastrostomy-tube can increase the completeness rate of concurrent chemotherapy.
Mechanistic explanation of integral calculus
NASA Astrophysics Data System (ADS)
Sauerheber, Richard D.
2015-04-01
The anatomic features of filaments, drawn through graphs of an integral F(x) and its derivative f(x), clarify why integrals automatically calculate area swept out by derivatives. Each miniscule elevation change dF on an integral, as a linear measure, equals the magnitude of square area of a corresponding vertical filament through its derivative. The sum of all dF increments combine to produce a range ΔF on the integral that equals the exact summed area swept out by the derivative over that domain. The sum of filament areas is symbolized ∫f(x)dx, where dx is the width of any filament and f(x) is the ordinal value of the derivative and thus, the intrinsic slope of the integral point dF/dx. dx displacement widths, and corresponding dF displacement heights, along the integral are not uniform and are determined by the intrinsic slope of the function at each point. Among many methods that demonstrate why integrals calculate area traced out by derivatives, this presents the physical meaning of differentials dx and dF, and how the variation in each along an integral curve explicitly computes area at any point traced by the derivative. This area is the filament width dx times its height, the ordinal value of the derivative function f(x), which is the tangent slope dF/dx on the integral. This explains thoroughly but succinctly the precise mechanism of integral calculus.
ERIC Educational Resources Information Center
Fredericksen, Marlene; Slark, Julie
Following the implementation of a matriculation plan at Rancho Santiago College (RSC), a study was conducted to examine the appropriateness of student course placement as assessed by faculty and students and to investigate faculty's perceptions of changes in students' skill level preparation over the past few years. Questionnaires were completed…
Research: Hyperactivity, Placement Centers
ERIC Educational Resources Information Center
Nation's Schools and Colleges, 1975
1975-01-01
A diet that emphasizes the elimination of food containing artificial coloring and flavoring from meals served to hyperactive children has met with success in preliminary studies; college placement centers are advised to shift their emphasis from job research and counseling. (Author/MLF)
"Unilateral" Placements Face Review
ERIC Educational Resources Information Center
Samuels, Christina A.
2007-01-01
The U.S. Supreme Court has agreed to step into one of the most contentious and costly areas of special education law by accepting a case involving a parent's efforts to seek public reimbursement for a private school placement of his child. In this article, the author talks about the case entitled, "New York City Board of Education vs. Tom F."…
Anti-calculus and whitening toothpastes.
van Loveren, Cor; Duckworth, Ralph M
2013-01-01
In terms of novel formulations, there seems to have been a shift in emphasis from anti-caries/anti-gingivitis to anti-calculus/whitening toothpastes in recent years. The anti-calculus and whitening effects of toothpastes are to some extent based on the same active ingredients: compounds of high affinity for tooth mineral. Due to this affinity, crystal growth may be hindered (anti-calculus) and chromophores be displaced (whitening). Besides these common ingredients, both types of toothpaste may contain agents specifically aimed at each condition. Clinical studies have shown that these active ingredients can be successfully formulated in fluoride toothpastes to give significant reductions in supragingival calculus and stain formation and facilitate their removal. Some of the ingredients are formulated in toothpastes that additionally contain anti-plaque and anti-gingivitis ingredients, making these toothpastes (together with the fluoride) truly multi-functional. The development of these products is not straightforward because of interaction between formulation components and because the active ingredients must maintain their beneficial characteristics during the shelf life of the paste. Neither a therapeutic benefit (in terms of less gingivitis or less caries) nor a societal benefit (in terms of less treatment demand) has been demonstrated as a result of the anti-calculus and whitening effects of toothpastes. PMID:23817060
Ancient DNA analysis of dental calculus.
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.
EARLINET Single Calculus Chain - overview on methodology and strategy
NASA Astrophysics Data System (ADS)
D'Amico, G.; Amodeo, A.; Baars, H.; Binietoglou, I.; Freudenthaler, V.; Mattis, I.; Wandinger, U.; Pappalardo, G.
2015-11-01
In this paper we describe the EARLINET Single Calculus Chain (SCC), a tool for the automatic analysis of lidar measurements. The development of this tool started in the framework of EARLINET-ASOS (European Aerosol Research Lidar Network - Advanced Sustainable Observation System); it was extended within ACTRIS (Aerosol, Clouds and Trace gases Research InfraStructure Network), and it is continuing within ACTRIS-2. The main idea was to develop a data processing chain that allows all EARLINET stations to retrieve, in a fully automatic way, the aerosol backscatter and extinction profiles starting from the raw lidar data of the lidar systems they operate. The calculus subsystem of the SCC is composed of two modules: a pre-processor module which handles the raw lidar data and corrects them for instrumental effects and an optical processing module for the retrieval of aerosol optical products from the pre-processed data. All input parameters needed to perform the lidar analysis are stored in a database to keep track of all changes which may occur for any EARLINET lidar system over the time. The two calculus modules are coordinated and synchronized by an additional module (daemon) which makes the whole analysis process fully automatic. The end user can interact with the SCC via a user-friendly web interface. All SCC modules are developed using open-source and freely available software packages. The final products retrieved by the SCC fulfill all requirements of the EARLINET quality assurance programs on both instrumental and algorithm levels. Moreover, the manpower needed to provide aerosol optical products is greatly reduced and thus the near-real-time availability of lidar data is improved. The high-quality of the SCC products is proven by the good agreement between the SCC analysis, and the corresponding independent manual retrievals. Finally, the ability of the SCC to provide high-quality aerosol optical products is demonstrated for an EARLINET intense observation
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.
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…
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…
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…
Partial nephrectomy: an option in calculus disease?
Timoney, A G; Payne, S R; Walmsley, B H; Vinnicombe, J; Abercrombie, G F
1988-12-01
Thirty-seven patients treated by partial nephrectomy for calculus disease between 1971 and 1986 were reviewed retrospectively. Of the 25 patients available for analysis, 20% developed immediate surgical complications, 20% had residual post-operative stone and 33% developed true ipsilateral stone recurrence during the period of follow-up. Our results from partial nephrectomy for calculus disease are compared with the results of treatment by percutaneous nephrolithotomy and extracorporeal shockwave lithotripsy. It was concluded that partial nephrectomy should be reserved for situations where stone disease is associated with anatomical abnormalities which cannot be treated by the newer modalities of stone management.
Generalized Cartan Calculus in general dimension
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.
Dynamical Regge calculus as lattice gravity
NASA Astrophysics Data System (ADS)
Hagura, Hiroyuki
2001-03-01
We propose a hybrid approach to lattice quantum gravity by combining simultaneously the dynamical triangulation with the Regge calculus, called the dynamical Regge calculus (DRC). In this approach lattice diffeomorphism is realized as an exact symmetry by some hybrid ( k, l) moves on the simplicial lattice. Numerical study of 3D pure gravity shows that an entropy of the DRC is not exponetially bounded if we adopt the uniform measure Π idli. On the other hand, using the scale-invariant measure Π idli/ li, we can calculate observables and observe a large hysteresis between two phases that indicates the first-order nature of the phase transition.
Impacted material placement plans
Hickey, M.J.
1997-01-29
Impacted material placement plans (IMPP) are documents identifying the essential elements in placing remediation wastes into disposal facilities. Remediation wastes or impacted material(s) are those components used in the construction of the disposal facility exclusive of the liners and caps. The components might include soils, concrete, rubble, debris, and other regulatory approved materials. The IMPP provides the details necessary for interested parties to understand the management and construction practices at the disposal facility. The IMPP should identify the regulatory requirements from applicable DOE Orders, the ROD(s) (where a part of a CERCLA remedy), closure plans, or any other relevant agreements or regulations. Also, how the impacted material will be tracked should be described. Finally, detailed descriptions of what will be placed and how it will be placed should be included. The placement of impacted material into approved on-site disposal facilities (OSDF) is an integral part of gaining regulatory approval. To obtain this approval, a detailed plan (Impacted Material Placement Plan [IMPP]) was developed for the Fernald OSDF. The IMPP provides detailed information for the DOE, site generators, the stakeholders, regulatory community, and the construction subcontractor placing various types of impacted material within the disposal facility.
Is Calculus Really That Different from Algebra? A More Logical Way To Understand and Teach Calculus.
ERIC Educational Resources Information Center
Elk, Seymour B.
1998-01-01
Discards the blinders that have hampered the traditional teaching of calculus and reexamines some of the intuitive ideas that underlie this subject matter. Analyzes the various indeterminate forms that arise through the blind application of algebraic operations. (Author/ASK)
Supragingival calculus formation in a group of young adults.
Galgut, P N
1996-12-01
The presence of calculus was assessed on the lingual surfaces of the mandibular anterior teeth in a randomly selected group of 63 young adults. The rate of regrowth of calculus after professional prophylaxis was also observed. Twenty-two individuals had supragingival calculus on the mandibular lingual surfaces of their teeth at baseline. Eleven of these individuals demonstrated regrowth of calculus by the end of the study, in spite of repeated professional prophylaxis. Thus, 17.5% of subjects exhibited rapid regrowth of calculus on the mandibular lingual surfaces of their teeth within 2 weeks of professional prophylaxis.
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.
I Teach Economics, Not Algebra and Calculus
ERIC Educational Resources Information Center
Hey, John D.
2005-01-01
Most people learn to drive without knowing how the engine works. In a similar vein, the author believes that students can learn economics without knowing the algebra and calculus underlying the results. If instructors follow the philosophy of other economics courses in using graphs to illustrate the results, and draw the graphs accurately, then…
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…
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,…
Calculus: The Importance of Precise Notation
ERIC Educational Resources Information Center
Mahavier, William S.; Mahavier, W. Ted
2008-01-01
The careful use of notation and language in the statement of both the definitions and problems of calculus can begin the process of making students mathematically literate while allowing them to enjoy working on challenging problems and applications without the aid of numerous examples. Engaging the students to participate in the precise use of…
Instructional Guide for Calculus, Secondary Mathematics.
ERIC Educational Resources Information Center
Montgomery County Public Schools, Rockville, MD.
The purpose of this instructional guide is to assist teachers of calculus in the organization and presentation of the course content to best meet the needs of the student. The behaviors expected of the student have been organized into eleven units. These units include the topics recommended for those students preparing for the CEEB advanced…
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.
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…
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…
Sharks, Minnows, and Wheelbarrows: Calculus Modeling Projects
ERIC Educational Resources Information Center
Smith, Michael D.
2011-01-01
The purpose of this article is to present two very active applied modeling projects that were successfully implemented in a first semester calculus course at Hollins University. The first project uses a logistic equation to model the spread of a new disease such as swine flu. The second project is a human take on the popular article "Do Dogs Know…
Enabling quaternion derivatives: the generalized HR calculus
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.
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. PMID:26361555
Flipping a Calculus Class: One Instructor's Experience
ERIC Educational Resources Information Center
Palmer, Katrina
2015-01-01
This paper describes one instructor's experiences during a year of flipping four calculus classes. The first exploration attempts to understand student expectations of a math class and their preference towards a flipped classroom. The second examines success of students from a flipped classroom, and the last investigates relationships with student…
Enabling quaternion derivatives: the generalized HR calculus.
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.
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…
ERIC Educational Resources Information Center
Bolt, Mike
2010-01-01
Many optimization problems can be solved without resorting to calculus. This article develops a new variational method for optimization that relies on inequalities. The method is illustrated by four examples, the last of which provides a completely algebraic solution to the problem of minimizing the time it takes a dog to retrieve a thrown ball,…
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…
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.
Fractional calculus in bioengineering, part 3.
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
Fractional calculus in bioengineering, part 3.
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
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.
Customized ATP towpreg. [Automated Tow Placement
NASA Technical Reports Server (NTRS)
Sandusky, Donald A.; Marchello, Joseph M.; Baucom, Robert M.; Johnston, Norman J.
1992-01-01
Automated tow placement (ATP) utilizes robotic technology to lay down adjacent polymer-matrix-impregnated carbon fiber tows on a tool surface. Consolidation and cure during ATP requires that void elimination and polymer matrix adhesion be accomplished in the short period of heating and pressure rolling that follows towpreg ribbon placement from the robot head to the tool. This study examined the key towpreg ribbon properties and dimensions which play a significant role in ATP. Analysis of the heat transfer process window indicates that adequate heating can be achieved at lay down rates as high as 1 m/sec. While heat transfer did not appear to be the limiting factor, resin flow and fiber movement into tow lap gaps could be. Accordingly, consideration was given to towpreg ribbon having uniform yet non-rectangular cross sections. Dimensional integrity of the towpreg ribbon combined with customized ribbon architecture offer great promise for processing advances in ATP of high performance composites.
7. View showing placement of timber deck placement on chord ...
7. View showing placement of timber deck placement on chord and built up construction of top chord and continuous construction through top panel points, eye bar construction on bottom chord - Bridge No. 2.4, Spanning Boiling Fork Creek at Railroad Milepost JC-2.4, Decherd, Franklin County, TN
Fractional calculus in bioengineering, part 2.
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
Fractional calculus in bioengineering, part 2.
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
NASA Astrophysics Data System (ADS)
Rauhala, U. A.
2013-12-01
Array algebra of photogrammetry and geodesy unified multi-linear matrix and tensor operators in an expansion of Gaussian adjustment calculus to general matrix inverses and solutions of inverse problems to find all, or some optimal, parametric solutions that satisfy the available observables. By-products in expanding array and tensor calculus to handle redundant observables resulted in general theories of estimation in mathematical statistics and fast transform technology of signal processing. Their applications in gravity modeling and system automation of multi-ray digital image and terrain matching evolved into fast multi-nonlinear differential and integral array calculus. Work since 1980's also uncovered closed-form inverse Taylor and least squares Newton-Raphson-Gauss perturbation solutions of nonlinear systems of equations. Fast nonlinear integral matching of array wavelets enabled an expansion of the bundle adjustment to 4-D stereo imaging and range sensing where real-time stereo sequence and waveform phase matching enabled data-to-info conversion and compression on-board advanced sensors. The resulting unified array calculus of spacetime sensing is applicable in virtually any math and engineering science, including recent work in spacetime physics. The paper focuses on geometric spacetime reconstruction from its image projections inspired by unified relativity and string theories. The collinear imaging equations of active object space shutter of special relativity are expanded to 4-D Lorentz transform. However, regular passive imaging and shutter inside the sensor expands the law of special relativity by a quantum geometric explanation of 4-D photogrammetry. The collinear imaging equations provide common sense explanations to the 10 (and 26) dimensional hyperspace concepts of a purely geometric string theory. The 11-D geometric M-theory is interpreted as a bundle adjustment of spacetime images using 2-D or 5-D membrane observables of image, string and
Improvement of Job Placement Services.
ERIC Educational Resources Information Center
Mount San Antonio Community Coll. District, Walnut, CA.
The Improvement of Job Placement Services Project was undertaken to examine and strengthen job placement services and programs in the California community colleges. Specific objectives of the project were to: (1) select and convene a 12-member representative advisory committee to oversee project operations working with the California Placement…
Placement: Specific Needs, General Responsibilities.
ERIC Educational Resources Information Center
August, Bonne
The work of the Placement/Progress Subcommittee for the City University of New York (CUNY) system is important. The Freshman Skills Assessment Program (FSAP) comprises one set of instruments used at two points and for two purposes: at initial placement in reading, writing, and math and later at exit from remedial programs. The CUNY Writing…
Placement Decision Dilemmas and Solutions.
ERIC Educational Resources Information Center
Hopf, A. G.
1991-01-01
The director of an agency for the blind and visually impaired examines the service-delivery dilemma of funding versus placement decisions. Three program areas demonstrate this dilemma: (1) Social Security Disability Insurance disincentives to competitive placement; (2) the private agency's role when the educational system falls short; and (3)…
[Developmental Placement.] Collected Research References.
ERIC Educational Resources Information Center
Bjorklund, Gail
Drawing on information and references in the ERIC system, this literature review describes research related to a child's developmental placement. The issues examined include school entrance age; predictive validity, reliability, and features of Gesell School Readiness Assessment; retention; and the effectiveness of developmental placement. A…
Career and Placement Services Survey.
ERIC Educational Resources Information Center
Smith, Shirley H.; Yorke, Deon
This report contains results of a survey at Bronx Community College (New York) that queried career placement counselors on how their field had changed over the past 5 years and what changes they foresaw for the future. Questions were open-ended and directed toward identifying problems and shifts in career planning and placement. More than half of…
On the interpretation of Stratonovich calculus
NASA Astrophysics Data System (ADS)
Moon, W.; Wettlaufer, J. S.
2014-05-01
The Itô-Stratonovich dilemma is revisited from the perspective of the interpretation of Stratonovich calculus using shot noise. Over the long time scales of the displacement of an observable, the principal issue is how to deal with finite/zero autocorrelation of the stochastic noise. The former (non-zero) noise autocorrelation structure preserves the normal chain rule using a mid-point selection scheme, which is the basis Stratonovich calculus, whereas the instantaneous autocorrelation structure of Itô's approach does not. By considering the finite decay of the noise correlations on time scales very short relative to the overall displacement times of the observable, we suggest a generalization of the integral Taylor expansion criterion of Wong and Zakai (1965 Ann. Math. Stat. 36 1560-4) for the validity of the Stratonovich approach.
30 CFR 57.22004 - Category placement or change in placement.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 30 Mineral Resources 1 2012-07-01 2012-07-01 false Category placement or change in placement. 57... placement or change in placement. The Administrator for Metal and Nonmetal Mine Safety and Health (Administrator) shall be responsible for category and subcategory placement, change in placement,...
30 CFR 57.22004 - Category placement or change in placement.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 30 Mineral Resources 1 2011-07-01 2011-07-01 false Category placement or change in placement. 57... placement or change in placement. The Administrator for Metal and Nonmetal Mine Safety and Health (Administrator) shall be responsible for category and subcategory placement, change in placement,...
The Malliavin calculus and hypoelliptic differential operators
NASA Astrophysics Data System (ADS)
Bell, Denis
2015-03-01
This article is intended as an introduction to Malliavin's stochastic calculus of variations and his probabilistic approach to hypoellipticity. Topics covered include an elementary derivation of the basic integration by parts formulae, a proof of the probabilistic version of Hörmander's theorem as envisioned by Malliavin and completed by Kusuoka and Stroock, and an extension of Hörmander's theorem valid for operators with degeneracy of exponential type due to the author and S. Mohammed.
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.
Improved radiographic visualization of calculus in distal ureter.
Amar, A D
1979-10-01
Roentgenographic visualization of a calculus in the distal ureter is often made difficult by gas or bowel contents in the region of the pelvis. Filling the bladder with sterile water raises the bladder dome and displaces the bowel upward. Any calculus in the lower 4 to 5 cm. of the distal ureter is then clearly demonstrated on roentgenograms taken against the water-filled bladder instead of against the bowel filled with gas and feces. This maneuver also aids in differentiation of a calculus in the distal ureter from a phlebolith in the bladder wall, and has improved visualization of distal ureteral calculus in 50 patients during the last six years. PMID:494477
A new proof of the generalized Hamiltonian–Real calculus
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.
Job Placement Regimes in Europe: Trends and Impacts of Changes. IAB Labour Market Research Topics.
ERIC Educational Resources Information Center
Konle-Seidl, Regina; Walwei, Ulrich
Trends in job placement in Europe and the effects of advances in information and communication technologies on job placement practices were examined through case studies of France, Germany, the Netherlands, and the United Kingdom. The case studies revealed that the market shares of public employment services (PES) are generally higher than those…
Validating the Use of AP® Exam Scores for College Course Placement. Research Report 2013-2
ERIC Educational Resources Information Center
Patterson, Brian F.; Ewing, Maureen
2013-01-01
The Advanced Placement Program® (AP®) was created to provide access to rigorous, college-level curricula to motivated and prepared high school students. This study evaluated whether the AP Exam scores from the summative exams associated with 10 courses were valid for the placement of students into higher-level college courses in the subject area…
NASA Astrophysics Data System (ADS)
Thompson, John; Christensen, Warren; Mountcastle, Donald
2010-03-01
In work on student understanding of concepts in advanced thermal physics, we are exploring student understanding of the mathematics required for productive reasoning about the physics. By analysis of student use of mathematics in responses to conceptual physics questions, as well as analogous math questions stripped of physical meaning, we find evidence that students often enter upper-level physics courses lacking the assumed prerequisite mathematics knowledge and/or the ability to apply it productively in a physics context. Our focus is in two main areas: interpretation of P-V diagrams, requiring an understanding of integration, and material properties and the Maxwell relations, involving partial differentiation. We have also assessed these mathematical concepts among students in multivariable calculus. Calculus results support the findings among physics students: some observed difficulties are not just with transfer of math knowledge to physics contexts, but seem to have origins in the understanding of the math concepts themselves.
[Extravasation into a renal sinus cyst due to ureteral calculus: a case report].
Taue, R; Naroda, T; Tamura, M; Kanayama, H; Kagawa, S
1999-07-01
A 71-year-old man who had been treated conservatively for advanced prostate cancer with hormonal therapy presented with complaint of left flank pain. Intravenous urography demonstrated obstruction caused by a left upper ureteral calculus and leakage of contrast medium outside the renal pelvis and calyces. Left percutaneous nephrostomy was performed, and subsequent nephrostography showed extravasation into a parapelvic renal sinus cyst previously recognized on follow-up computed tomography (CT). The left ureteral calculus was treated with extracorporeal shock wave lithotripsy (ESWL), after which obstruction and extravasation disappeared. One month later, abdominal CT demonstrated no left renal nor ureteral calculi, as well as a reduction in the left renal sinus cyst. Urinary extravasation sometimes occurs as a complication of acute urinary obstruction. However, extravasation into a cyst is very rare. We have found only one case reported in the literature, so far.
Schmitt, Todd L; Sur, Roger L
2012-03-01
An adult female bottlenose dolphin (Tursiops truncatus) presented with acute anorexia secondary to progressive azotemia (blood urea nitrogen = 213 mg/dl, creatinine [Cr] = 9.5 mg/dl) and electrolyte abnormalities (K = 7.4 mEq/L). It was later diagnosed with postrenal obstruction secondary to bilaterally obstructing ureteral calculi seen on ultrasound. Treatment of the obstruction required two endoscopic procedures, cystoscopy for ureteral stent placement and ureteroscopy to perform intracorporeal lithotripsy on the obstructing calculi. Before the first procedure, the dolphin's azotemia was stabilized with aggressive fluid therapy, peritoneal dialysis, and treatment for acidosis. Diuresis subsequent to the fluid therapy enabled passage of the right obstructing urolith. For both endoscopic procedures, the dolphin was placed in left lateral recumbency due to the peritoneal dialysis catheter in the right retroperitoneal region. For the first procedure, a 12-French (Fr) flexible cystoscope was inserted retrograde into the bladder via the urethra, whereupon a calculus was seen obstructing the left ureteral orifice. A 4.8-Fr, 26-cm double-pigtail ureteral stent was placed up the left ureter to relieve the postrenal obstruction. Inadvertent proximal migration of the left ureteral stent occurred during the procedure. However, renal parameters (serum Cr = 5.8, K = 5.4) improved significantly by the next day. For the second procedure, 28 hr later, ureteroscopy was performed to treat the calculus and replace the existing stent with a longer stent. The left ureteral calculus was pulverized into tiny fragments by using a holmium:yttrium-aluminum-garnet laser inserted through a 6.9-Fr semirigid ureteroscope. The migrated stent was visualized in the distal left ureter and replaced with a 90-cm single-pigtail ureteral stent that was sutured exterior to the urogenital slit and removed 3 days later. Renal function normalized over the next several days, and the dolphin recovered over
Schmitt, Todd L; Sur, Roger L
2012-03-01
An adult female bottlenose dolphin (Tursiops truncatus) presented with acute anorexia secondary to progressive azotemia (blood urea nitrogen = 213 mg/dl, creatinine [Cr] = 9.5 mg/dl) and electrolyte abnormalities (K = 7.4 mEq/L). It was later diagnosed with postrenal obstruction secondary to bilaterally obstructing ureteral calculi seen on ultrasound. Treatment of the obstruction required two endoscopic procedures, cystoscopy for ureteral stent placement and ureteroscopy to perform intracorporeal lithotripsy on the obstructing calculi. Before the first procedure, the dolphin's azotemia was stabilized with aggressive fluid therapy, peritoneal dialysis, and treatment for acidosis. Diuresis subsequent to the fluid therapy enabled passage of the right obstructing urolith. For both endoscopic procedures, the dolphin was placed in left lateral recumbency due to the peritoneal dialysis catheter in the right retroperitoneal region. For the first procedure, a 12-French (Fr) flexible cystoscope was inserted retrograde into the bladder via the urethra, whereupon a calculus was seen obstructing the left ureteral orifice. A 4.8-Fr, 26-cm double-pigtail ureteral stent was placed up the left ureter to relieve the postrenal obstruction. Inadvertent proximal migration of the left ureteral stent occurred during the procedure. However, renal parameters (serum Cr = 5.8, K = 5.4) improved significantly by the next day. For the second procedure, 28 hr later, ureteroscopy was performed to treat the calculus and replace the existing stent with a longer stent. The left ureteral calculus was pulverized into tiny fragments by using a holmium:yttrium-aluminum-garnet laser inserted through a 6.9-Fr semirigid ureteroscope. The migrated stent was visualized in the distal left ureter and replaced with a 90-cm single-pigtail ureteral stent that was sutured exterior to the urogenital slit and removed 3 days later. Renal function normalized over the next several days, and the dolphin recovered over
Training Special Educators: Sustaining Professional Development in Special School Placements
ERIC Educational Resources Information Center
Peter, Melanie
2013-01-01
With the rapidly changing demographic due to survival rates from medical advances, the need to strengthen training on SEND is now recognised, and special school placements valued, having been previously marginalised within initial teacher training. Practices developed since 2008 at one university to support progression of trainees to gain advanced…
A clinical comparison of two calculus-inhibiting dentifrices.
Conforti, N; Berta, R; Petrone, M E; DeVizio, W; Volpe, A R; Proskin, H M
2000-01-01
The objective of this double-blind clinical study, conducted in harmony with the Volpe-Manhold design for studies of dental calculus, was to compare the effect on supragingival calculus formation of a dentifrice containing pyrophosphate, tripolyphosphate and a copolymer in a 0.243% sodium fluoride/silica base (Test Dentifrice), to that of a commercially available calculus-inhibiting dentifrice containing tetrapotassium pyrophosphate, disodium pyrophosphate and tetrasodium pyrophosphate in a 0.243% sodium fluoride/silica base (Positive Control Dentifrice). Adult male and female subjects from the Buffalo, New York area were entered into the study, provided a full oral prophylaxis, and assigned the use of a placebo (non-calculus-inhibiting) dentifrice for fourteen weeks. At the completion of this initial period, subjects were assessed for baseline Volpe-Manhold Calculus Index scores, provided another full prophylaxis, and stratified into two treatment groups which were balanced for age, sex and baseline calculus. 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 again performed after twelve weeks' use of the study dentifrices. Ninety-one (91) subjects complied with the protocol and completed the entire study. At the three-month examination, the Test Dentifrice group exhibited a statistically significant 27.3% reduction in mean Volpe-Manhold Calculus Index score as compared to the Positive Control Dentifrice group. The results of this clinical study support the conclusion that a new calculus-inhibiting dentifrice, containing pyrophosphate, tripolyphosphate and a copolymer in a 0.243% sodium fluoride/silica base, is efficacious for the control of the development of supragingival calculus, and provides a level of benefit greater than that provided by a commercially available calculus-inhibiting dentifrice containing
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…
ERIC Educational Resources Information Center
Pilgrim, Mary E.
2010-01-01
Data indicate that about 40 percent of students initially enrolled in MATH 160: Calculus for Physical Scientists I finish the course with a grade of D or F, dropped, or withdrew from the course (Reinholz, 2009). The high failure rate let to an intervention course (MATH 180) for students at risk of failing MATH 160. At-risk students were…
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…
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…
Restricted diversity of dental calculus methanogens over five centuries, France
Huynh, Hong T. T.; Nkamga, Vanessa D.; Signoli, Michel; Tzortzis, Stéfan; Pinguet, Romuald; Audoly, Gilles; Aboudharam, Gérard; Drancourt, Michel
2016-01-01
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 14th to 19th 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. PMID:27166431
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…
Use of Technology to Develop Student Intuition in Multivariable Calculus
ERIC Educational Resources Information Center
Kaur, Manmohan
2006-01-01
In order to get undergraduates interested in mathematics, it is essential to involve them in its "discovery". In this paper, we will explain how technology and the knowledge of lower dimensional calculus can be used to help them develop intuition leading to their discovering the first derivative rule in multivariable calculus. (Contains 7 figures.)
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.)
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…
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…
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…
Calculus Students' Early Concept Images of Tangent Lines
ERIC Educational Resources Information Center
Vincent, Brittany; LaRue, Renee; Sealey, Vicki; Engelke, Nicole
2015-01-01
This study explored first-semester calculus students' understanding of tangent lines as well as how students used tangent lines within the context of Newton's method. Task-based interviews were conducted with twelve first-semester calculus students who were asked to verbally describe a tangent line, sketch tangent lines for multiple curves, and…
Calculus Reform and Graphing Calculators: A University View.
ERIC Educational Resources Information Center
Stick, Marvin E.
1997-01-01
Describes the results of a teacher's exploration of the effects of using graphing calculators in calculus instruction in sections other than those that are experimental. Two experimental and two traditional sections of Calculus I and II participated in the study. (DDR)
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…
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…
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…
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…
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…
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…
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 EDITIONS," BY…
How to Enjoy Calculus: With Computer Applications. Revised Edition.
ERIC Educational Resources Information Center
Pine, Eli S.
The author states that this book was written for anyone who wants to know what calculus is all about, and that those with knowledge of some algebra and geometry should be able to understand it. That calculus should be called "slope finding" is discussed, and this term is used extensively. The book is divided into three chapters: (1) the…
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.
Partial Fractions in Calculus, Number Theory, and Algebra
ERIC Educational Resources Information Center
Yackel, C. A.; Denny, J. K.
2007-01-01
This paper explores the development of the method of partial fraction decomposition from elementary number theory through calculus to its abstraction in modern algebra. This unusual perspective makes the topic accessible and relevant to readers from high school through seasoned calculus instructors.
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…
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.
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,…
Restricted diversity of dental calculus methanogens over five centuries, France.
Huynh, Hong T T; Nkamga, Vanessa D; Signoli, Michel; Tzortzis, Stéfan; Pinguet, Romuald; Audoly, Gilles; Aboudharam, Gérard; Drancourt, Michel
2016-01-01
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. PMID:27166431
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…
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…
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…
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 such as…
Our Experiences with Using Visualization Tools in Teaching Calculus.
ERIC Educational Resources Information Center
Kowalczyk, Robert E.; Hausknecht, Adam O.
This paper describes two uses of the software package TEMATH (Tools for Exploring Mathematics) with calculus students: (1) as a demonstration tool in the classroom to visually explore with students the many mathematical models introduced in a first year calculus course; and (2) as a part of a lab where students use a set of laboratory explorations…
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…
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…
The Qualitative Trajectory Calculus on Networks
NASA Astrophysics Data System (ADS)
Bogaert, Peter; van de Weghe, Nico; Cohn, Anthony G.; Witlox, Frank; de Maeyer, Philippe
Moving objects are commonly handled using quantitative methods and information. However, in many cases, qualitative information can be more efficient and more meaningful than quantitative information. A lot of research has been done in generating, indexing, modelling and querying network-based moving objects, but little work has been done in building a calculus of relations between these objects in a qualitative way. In this paper, we introduce a formal definition of how to represent and reason about the relative trajectories of pairs of objects moving along a network.
The Calculus of Responsibility and Commitment
NASA Astrophysics Data System (ADS)
Pollard, Carl
Ever since Montague (1974 [1970]) laid the foundations for formally precise analysis of natural language (hereafter NL) semantics in the late 1960's, the typed lambda calculus (hereafter TLC) and certain of its extensions have been the linguists' tool of choice for representing the meanings of NL expressions. But starting around the turn of the millenium, motivated by a range of linguistic phenomena collectively known as covert movement phenomena, logical grammarians of various persuasions have proposed the use of other semantic term calculi that embody, directly or indirectly, some notion or other of continuation.
Regge calculus and observations. II. Further applications.
NASA Astrophysics Data System (ADS)
Williams, Ruth M.; Ellis, G. F. R.
1984-11-01
The method, developed in an earlier paper, for tracing geodesies of particles and light rays through Regge calculus space-times, is applied to a number of problems in the Schwarzschild geometry. It is possible to obtain accurate predictions of light bending by taking sufficiently small Regge blocks. Calculations of perihelion precession, Thomas precession, and the distortion of a ball of fluid moving on a geodesic can also show good agreement with the analytic solution. However difficulties arise in obtaining accurate predictions for general orbits in these space-times. Applications to other problems in general relativity are discussed briefly.
On the origins of generalized fractional calculus
NASA Astrophysics Data System (ADS)
Kiryakova, Virginia
2015-11-01
In Fractional Calculus (FC), as in the (classical) Calculus, the notions of derivatives and integrals (of first, second, etc. or arbitrary, incl. non-integer order) are basic and co-related. One of the most frequent approach in FC is to define first the Riemann-Liouville (R-L) integral of fractional order, and then by means of suitable integer-order differentiation operation applied over it (or under its sign) a fractional derivative is defined - in the R-L sense (or in Caputo sense). The first mentioned (R-L type) is closer to the theoretical studies in analysis, but has some shortages - from the point of view of interpretation of the initial conditions for Cauchy problems for fractional differential equations (stated also by means of fractional order derivatives/ integrals), and also for the analysts' confusion that such a derivative of a constant is not zero in general. The Caputo (C-) derivative, arising first in geophysical studies, helps to overcome these problems and to describe models of applied problems with physically consistent initial conditions. The operators of the Generalized Fractional Calculus - GFC (integrals and derivatives) are based on commuting m-tuple (m = 1, 2, 3, …) compositions of operators of the classical FC with power weights (the so-called Erdélyi-Kober operators), but represented in compact and explicit form by means of integral, integro-differential (R-L type) or differential-integral (C-type) operators, where the kernels are special functions of most general hypergeometric kind. The foundations of this theory are given in Kiryakova 18. In this survey we present the genesis of the definitions of the GFC - the generalized fractional integrals and derivatives (of fractional multi-order) of R-L type and Caputo type, analyze their properties and applications. Their special cases are all the known operators of classical FC, their generalizations introduced by other authors, the hyper-Bessel differential operators of higher integer
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.
Manufacturing of Smart Structures Using Fiber Placement Manufacturing Processes
NASA Technical Reports Server (NTRS)
Thomas, Matthew M.; Glowasky, Robert A.; McIlroy, Bruce E.; Story, Todd A.
1996-01-01
Smart structures research and development, with the ultimate aim of rapid commercial and military production of these structures, are at the forefront of the Synthesis and Processing of Intelligent Cost-Effective Structures (SPICES) program. As part of this ARPA-sponsored program, MDA-E is using fiber placement processes to manufacture integrated smart structure systems. These systems comprise advanced composite structures with embedded fiber optic sensors, shape memory alloys, piezoelectric actuators, and miniature accelerometers. Cost-effective approaches and solutions to smart material synthesis in the fiber-placement process, based upon integrated product development, are discussed herein.
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…
Graphical calculus for Gaussian pure states
Menicucci, Nicolas C.; Flammia, Steven T.; Loock, Peter van
2011-04-15
We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term 'CV graph state' currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the 'closest' CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.
How Students Use Their Knowledge of Calculus in an Engineering Mechanics Course.
ERIC Educational Resources Information Center
Roddick, Cheryl Stitt
This study investigated students' conceptual and procedural understanding of calculus within the context of an engineering mechanics course. Four traditional calculus students were compared with three students from one of the calculus reform projects, Calculus & Mathematica. Task-based interviews were conducted with each participant throughout the…
Miniature endoscopic optical coherence tomography for calculus detection.
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. PMID:26368780
LC Graphs for the Lambek Calculus with Product
NASA Astrophysics Data System (ADS)
Fowler, Timothy A. D.
This paper introduces a novel graph representation of proof nets for the Lambek calculus that extends the LC graph representation of [13] to include the product connective. This graph representation more clearly specifies the difference between the Lambek calculus with and without product than other proof net representations, which is important to the search for polynomial time among Lambek calculus fragments. We use LC graphs to further the efforts to characterize the boundary between polynomial time and NP-complete sequent derivability by analyzing the NP-completeness proof of [14] and discussing a sequent derivability algorithm.
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.
Extension for prevention: margin placement.
Larson, Thomas D
2012-01-01
This article will review the concept of extension for prevention popularized by G.V. Black around the early 1900s. Concepts of extension and prevention have changed over the years with a more informed knowledge of the caries process, improved materials, cutting instruments, and techniques. The reasons for placement of the outline form relative to the tooth morphology, gingival tissue, relationship to adjacent teeth, and the choice of material will be described for all of the materials used in restorative dentistry. Research will be cited to support the scientific basis for outline form placement. PMID:22662468
VEST: Abstract Vector Calculus Simplification in Mathematica
J. Squire, J. Burby and H. Qin
2013-03-12
We present a new package, VEST (Vector Einstein Summation Tools), that performs abstract vector calculus computations in Mathematica. Through the use of index notation, VEST is able to reduce scalar and vector expressions of a very general type using a systematic canonicalization procedure. In addition, utilizing properties of the Levi-Civita symbol, the program can derive types of multi-term vector identities that are not recognized by canonicalization, subsequently applying these to simplify large expressions. In a companion paper [1], we employ VEST in the automation of the calculation of Lagrangians for the single particle guiding center system in plasma physics, a computation which illustrates its ability to handle very large expressions. VEST has been designed to be simple and intuitive to use, both for basic checking of work and more involved computations. __________________________________________________
Regge calculus models of closed lattice universes
NASA Astrophysics Data System (ADS)
Liu, Rex G.; Williams, Ruth M.
2016-01-01
This paper examines the behavior of closed "lattice universes" wherein masses are distributed in a regular lattice on the Cauchy surfaces of closed vacuum universes. Such universes are approximated using a form of Regge calculus originally developed by Collins and Williams to model closed Friedmann-Lemaître-Robertson-Walker universes. We consider two types of lattice universes, one where all masses are identical to each other and another where one mass gets perturbed in magnitude. In the unperturbed universe, we consider the possible arrangements of the masses in the Regge Cauchy surfaces and demonstrate that the model will only be stable if each mass lies within some spherical region of convergence. We also briefly discuss the existence of Regge models that are dual to the ones we have considered. We then model a perturbed lattice universe and demonstrate that the model's evolution is well behaved, with the expansion increasing in magnitude as the perturbation is increased.
VEST: Abstract vector calculus simplification in Mathematica
NASA Astrophysics Data System (ADS)
Squire, J.; Burby, J.; Qin, H.
2014-01-01
We present a new package, VEST (Vector Einstein Summation Tools), that performs abstract vector calculus computations in Mathematica. Through the use of index notation, VEST is able to reduce three-dimensional scalar and vector expressions of a very general type to a well defined standard form. In addition, utilizing properties of the Levi-Civita symbol, the program can derive types of multi-term vector identities that are not recognized by reduction, subsequently applying these to simplify large expressions. In a companion paper Burby et al. (2013) [12], we employ VEST in the automation of the calculation of high-order Lagrangians for the single particle guiding center system in plasma physics, a computation which illustrates its ability to handle very large expressions. VEST has been designed to be simple and intuitive to use, both for basic checking of work and more involved computations.
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
Teacher Placement Services: An Evaluation.
ERIC Educational Resources Information Center
Edson, William H.; Braun, Frank R.
1984-01-01
Surveyed 215 graduate teachers to examine job search methods and services used. Results indicated 78 percent of the respondents used the vacancy bulletin and 91 percent filed credentials with the career development office. Subjects who consulted with a placement counselor found employment more often than those who did not. (JAC)
Progress with Student Teacher Placements
ERIC Educational Resources Information Center
Her Majesty's Inspectorate of Education, 2006
2006-01-01
This is a report on the progress that has been made since HMIE published "Student Teacher Placements within Initial Teacher Education" in October 2005 in response to a request by the Minister for Education and Young People. The report was based on extensive fieldwork and consultation over session 2004/2005, activity which itself contributed to…
Student Placement Folders and Accountability
ERIC Educational Resources Information Center
Moore, Gary E.
1974-01-01
To improve accountability in its vocational agriculture program, Fort Frye High School, Beverly, Ohio, developed a student placement folder. It includes the student's picture, autobiography, information sheet, equipment and skills sheet, references, letters of recommendation, and a copy of his high school transcript. The confidentiality of the…
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.
Ants, Tunnels, and Calculus: An Exercise in Mathematical Modeling.
ERIC Educational Resources Information Center
Winkel, Brian J.
1994-01-01
Discusses an activity which models the building of a tunnel by ants using the definitions of derivative and indefinite integral from calculus. Includes a discussion of reasonableness and interpretation of the problem. (MKR)
Relational Semantics for the Lambek-Grishin Calculus
NASA Astrophysics Data System (ADS)
Kurtonina, Natasha; Moortgat, Michael
We study ternary relational semantics for LG: a symmetric version of the Lambek calculus with interaction principles due to Grishin [10]. We obtain completeness on the basis of a Henkin-style weak filter construction.
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.
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.
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].
Dynamic Compartments in the Imperative π-Calculus
NASA Astrophysics Data System (ADS)
John, Mathias; Lhoussaine, Cédric; Niehren, Joachim
Dynamic compartments with mutable configurations and variable volumes are of basic interest for the stochastic modeling of biochemistry in cells. We propose a new language to express dynamic compartments that we call the imperative π -calculus. It is obtained from the attributed π -calculus by adding imperative assignment operations to a global store. Previous approaches to dynamic compartments are improved in flexibility or efficiency. This is illustrated by an appropriate model of osmosis and a correct encoding of bioambBioAmbients.
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.
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…
The Placement Continuum: What Place Work?
ERIC Educational Resources Information Center
Grantham, Robert J.
1979-01-01
Because of changes in mental health and rehabilitation services to mentally disabled persons, the primacy of vocational placement has come under scrutiny. Residential placement plays an important role in the client's coping. A new view of the prominence of vocational placement in the context of community adjustment is provided. (Author)
28 CFR 551.24 - Child placement.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 28 Judicial Administration 2 2010-07-01 2010-07-01 false Child placement. 551.24 Section 551.24 Judicial Administration BUREAU OF PRISONS, DEPARTMENT OF JUSTICE INSTITUTIONAL MANAGEMENT MISCELLANEOUS Birth Control, Pregnancy, Child Placement, and Abortion § 551.24 Child placement. (a) The Warden may...
28 CFR 551.24 - Child placement.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 28 Judicial Administration 2 2014-07-01 2014-07-01 false Child placement. 551.24 Section 551.24 Judicial Administration BUREAU OF PRISONS, DEPARTMENT OF JUSTICE INSTITUTIONAL MANAGEMENT MISCELLANEOUS Birth Control, Pregnancy, Child Placement, and Abortion § 551.24 Child placement. (a) The Warden may...
28 CFR 551.24 - Child placement.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 28 Judicial Administration 2 2011-07-01 2011-07-01 false Child placement. 551.24 Section 551.24 Judicial Administration BUREAU OF PRISONS, DEPARTMENT OF JUSTICE INSTITUTIONAL MANAGEMENT MISCELLANEOUS Birth Control, Pregnancy, Child Placement, and Abortion § 551.24 Child placement. (a) The Warden may...
28 CFR 551.24 - Child placement.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 28 Judicial Administration 2 2013-07-01 2013-07-01 false Child placement. 551.24 Section 551.24 Judicial Administration BUREAU OF PRISONS, DEPARTMENT OF JUSTICE INSTITUTIONAL MANAGEMENT MISCELLANEOUS Birth Control, Pregnancy, Child Placement, and Abortion § 551.24 Child placement. (a) The Warden may...
28 CFR 551.24 - Child placement.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 28 Judicial Administration 2 2012-07-01 2012-07-01 false Child placement. 551.24 Section 551.24 Judicial Administration BUREAU OF PRISONS, DEPARTMENT OF JUSTICE INSTITUTIONAL MANAGEMENT MISCELLANEOUS Birth Control, Pregnancy, Child Placement, and Abortion § 551.24 Child placement. (a) The Warden may...
34 CFR 300.327 - Educational placements.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 34 Education 2 2011-07-01 2010-07-01 true Educational placements. 300.327 Section 300.327... CHILDREN WITH DISABILITIES Evaluations, Eligibility Determinations, Individualized Education Programs, and Educational Placements Development of Iep § 300.327 Educational placements. Consistent with § 300.501(c),...
34 CFR 300.327 - Educational placements.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 34 Education 2 2010-07-01 2010-07-01 false Educational placements. 300.327 Section 300.327... CHILDREN WITH DISABILITIES Evaluations, Eligibility Determinations, Individualized Education Programs, and Educational Placements Development of Iep § 300.327 Educational placements. Consistent with § 300.501(c),...
Water content contribution in calculus phantom ablation during Q-switched Tm:YAG laser lithotripsy
NASA Astrophysics Data System (ADS)
Zhang, Jian J.; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Wang, Hui; Chia, Ray W. J.; Hasenberg, Tom; Kang, Hyun Wook
2015-12-01
Q-switched (QS) Tm:YAG laser ablation mechanisms on urinary calculi are still unclear to researchers. Here, dependence of water content in calculus phantom on calculus ablation performance was investigated. White gypsum cement was used as a calculus phantom model. The calculus phantoms were ablated by a total 3-J laser pulse exposure (20 mJ, 100 Hz, 1.5 s) and contact mode with N=15 sample size. Ablation volume was obtained on average 0.079, 0.122, and 0.391 mm3 in dry calculus in air, wet calculus in air, and wet calculus in-water groups, respectively. There were three proposed ablation mechanisms that could explain the effect of water content in calculus phantom on calculus ablation performance, including shock wave due to laser pulse injection and bubble collapse, spallation, and microexplosion. Increased absorption coefficient of wet calculus can cause stronger spallation process compared with that caused by dry calculus; as a result, higher calculus ablation was observed in both wet calculus in air and wet calculus in water. The test result also indicates that the shock waves generated by short laser pulse under the in-water condition have great impact on the ablation volume by Tm:YAG QS laser.
Noninvasive control of dental calculus removal: qualification of two fluorescence methods
NASA Astrophysics Data System (ADS)
Gonchukov, S.; Sukhinina, A.; Bakhmutov, D.; Biryukova, T.
2013-02-01
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 this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth 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.
An Assessment of Athletic Training Students' Clinical-Placement Hours
Miller, Michael G.; Berry, David C.
2002-01-01
Objective: To establish a time profile to determine how athletic training students use their time in clinical placements and to determine the effects of academic standing, sex, sport type, and risk of injury associated with a sport during athletic training students' clinical placements on instructional, clinical, unengaged, managerial, and active learning time. Design and Setting: Subjects were enrolled in clinical placements within National Collegiate Athletic Association Division I athletics, intramural sports, and a local high school. Students were individually videotaped for approximately 4 hours. Subjects: A total of 20 undergraduate athletic training students (17 women, 3 men) from a Committee on Accreditation of Allied Health Education Programs (CAAHEP)-accredited athletic training education program. Measurements: We created a conceptual behavioral time framework to examine athletic training students' use of clinical-placement time with the performance domains associated with the 1999 National Athletic Trainers' Association Board of Certification Role Delineation Study. Students' use of time was analyzed with the Behavior Evaluation Strategies and Taxonomies software. Results: Students spent 7% of their overall clinical-placement time in instructional activities, 23% in clinical activities, 10% in managerial activities, and 59% in unengaged activities. Using multiple 3 × 3 factorial analyses of variance, we found that advanced students were engaged in significantly more active learning and clinical time compared with novice and intermediate students. Students assigned to sports in which injuries predominately occur in the upper extremities (upper extremity sports) spent significantly more clinical-placement time unengaged compared with students assigned to sports in which injuries predominantly occur in the lower extremities (lower extremity sports) or in both upper and lower extremities (mixed extremity sports). Conclusions: In this exploratory study, we
Humanitarian engineering placements in our own communities
NASA Astrophysics Data System (ADS)
VanderSteen, J. D. J.; Hall, K. R.; Baillie, C. A.
2010-05-01
There is an increasing interest in the humanitarian engineering curriculum, and a service-learning placement could be an important component of such a curriculum. International placements offer some important pedagogical advantages, but also have some practical and ethical limitations. Local community-based placements have the potential to be transformative for both the student and the community, although this potential is not always seen. In order to investigate the role of local placements, qualitative research interviews were conducted. Thirty-two semi-structured research interviews were conducted and analysed, resulting in a distinct outcome space. It is concluded that local humanitarian engineering placements greatly complement international placements and are strongly recommended if international placements are conducted. More importantly it is seen that we are better suited to address the marginalised in our own community, although it is often easier to see the needs of an outside populace.
Generalized Functions for the Fractional Calculus
NASA Technical Reports Server (NTRS)
Lorenzo, Carl F.; Hartley, Tom T.
1999-01-01
Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.
The link between middle school mathematics course placement and achievement.
Domina, Thurston
2014-01-01
The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students' mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth-grade algebra and geometry course placements are academically selective, but considerable between-school variation exists in students' odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness. PMID:24816044
The link between middle school mathematics course placement and achievement.
Domina, Thurston
2014-01-01
The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students' mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth-grade algebra and geometry course placements are academically selective, but considerable between-school variation exists in students' odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness.
Potential of shock waves to remove calculus and biofilm.
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.
Greene, T R; Kuba, C L; Irish, J D
2005-01-01
This paper describes a quantitative approach to the assessment of dental calculus in human archaeological skeletal samples. The approach combines the ranked calculus scoring method described by Buikstra and Ubelaker [1994. Arkansas Archeological Survey Research Series, Arkansas Archeological Survey, Fayetteville, Arkansas] and a modified Simplified Calculus Index, utilized by dental clinicians. We recorded amounts of calculus on the buccal, lingual, and interproximal surface of all extant teeth, and generated an index for the maxillary posterior dentition, maxillary anterior dentition, mandibular posterior dentition, and mandibular anterior dentition for three skeletal samples. They include 145 Egyptian Predynastic individuals from the site of Hierakonpolis, 104 Predynastic individuals from Naqada, Egypt, and 101 Meroitic Nubians from Semna South, present-day Sudan. Mann-Whitney U tests were used to analyze differences between the sexes and among age groups at each site. The results demonstrate that the calculus indices more effectively reveal trends and differences in calculus severity than frequency data can alone. For example, at Hierakonpolis, males (18-35 years) had significantly more calculus in the maxillary posterior dentition than females, while females (50+ years) had significantly more calculus in the maxillary posterior teeth. Frequency data merely showed that 94% of both males and females had calculus. The use of calculus indices can reveal how quickly calculus accumulates with age within the dental arcade and within a sample. Moreover, better understanding of the severity and location of calculus can improve a researcher's knowledge regarding the effect of calculus on dental pathologies, such as carious lesions and periodontal disease.
The F-functional calculus for unbounded operators
NASA Astrophysics Data System (ADS)
Colombo, Fabrizio; Sabadini, Irene
2014-12-01
In the recent years the theory of slice hyperholomorphic functions has become an important tool to study two functional calculi for n-tuples of operators and also for its applications to Schur analysis. In particular, using the Cauchy formula for slice hyperholomorphic functions, it is possible to give the Fueter-Sce mapping theorem an integral representation. With this integral representation it has been defined a monogenic functional calculus for n-tuples of bounded commuting operators, the so called F-functional calculus. In this paper we show that it is possible to define this calculus also for n-tuples containing unbounded operators and we obtain an integral representation formula analogous to the one of the Riesz-Dunford functional calculus for unbounded operators acting on a complex Banach space. As we will see, it is not an easy task to provide the correct definition of the F-functional calculus in the unbounded case. This paper is addressed to a double audience, precisely to people with interests in hypercomplex analysis and also to people working in operator theory.
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.
On the formulations of the quaternionic functional calculus
NASA Astrophysics Data System (ADS)
Colombo, Fabrizio; Sabadini, Irene
2010-10-01
In the paper [F. Colombo, I. Sabadini, On some properties of the quaternionic functional calculus, J. Geom. Anal. 19 (2009) 601-627] the authors treat the quaternionic functional calculus for right linear quaternionic operators whose components do not necessarily commute. This functional calculus is the quaternionic version of the classical Riesz-Dunford functional calculus. When considering quaternionic operators it is natural to also consider the case of left linear operators. Furthermore, one can use left or right slice regular functions to construct a functional calculus for right (or left) linear operators. In this paper we discuss these possibilities, showing that, in all the cases, we can associate to an operator two so-called S-resolvent operators but their interpretation depends on whether we are considering a left or a right linear operator. Also the S-resolvent equations for right or left closed operators do not have the same interpretation. Moreover, we study the bounded perturbations of both the S-resolvent operators.
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.
van Palenstein Helderman, W H; Lembariti, B S; van der Weijden, G A; van 't Hof, M A
1998-02-01
This paper describes the prevalence and severity of gingival recession in Tanzanian adults covering the age range from 20 to 64 years. In addition, it attempts to assess the relationship between the degree of gingival recession and the presence and amount of calculus. In the 20-34 years age group recession occurred in > or = 32% of the buccal, > or = 25% of the lingual, and > or = 13% of the approximal surfaces. These %s increased to > or = 64%, > or = 52%, and > or = 48%, respectively, in the 45-64 years age group. In the 20-34 years age group, lingual surfaces of mandibular incisors and canines followed by buccal surfaces of these teeth were the sites most severely affected with gingival recession. With increasing age, all sites became gradually more severely affected, particularly the buccal and lingual surfaces of the maxillary first molar. The lingual surfaces of mandibular incisors exhibited on an average 1.3 mm, 2.4 mm and 3.2 mm recession in the 20-34 years, 35-44 years and 45-64 years age group, respectively. Most of the correlation coefficients between gingival recession and calculus at the individual tooth surface in three age groups were statistically significant. The highest correlation coefficients (0.50-0.67) were found in the youngest (20-34 years) age group at the lingual surfaces of the mandibular incisors, canine and first premolar and at the buccal surfaces of the mandibular incisors. Based on these findings, the working hypothesis is advanced that longstanding calculus is an important determinant in the onset of gingival recession at sites exhibiting pronounced recession at a young age in populations deprived of prophylactic dental care.
Acadian flycatcher nest placement: Does placement influence reproductive success?
Wilson, R.R.; Cooper, R.J.
1998-01-01
We located 511 Acadian Flycatcher (Empidonax virescens) nests in bottomland hardwood forest of eastern Arkansas. Microhabitat characteristics were measured and their relationship with nest success evaluated. Fifty-two percent of all nesting attempts resulted in predation. Attributes of nest placement were similar between successful and unsuccessful nests, although successful nests were placed higher. Similarly, nonparasitized nests were typically higher than parasitized nests. Nests initiated late in the breeding season were placed in larger trees with higher canopy bases resulting in increased vegetation around the nest. Fifteen different tree species were used for nesting. Acadian Flycatchers chose nest trees in a nonrandom fashion, selecting Nuttall oak (Quercus nuttallii) and possumhaw (Ilex decidua) in greater proportions than their availability. However, there was no relationship between tree species used for nesting and nest success. Nest height was positively correlated with concealment at the nest site, supporting the predator-avoidance theory. No other attribute of nest placement differentiated successful nest sites, suggesting that nest predation is likely a function of random events in space and time.
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.
Bacteria and archaea paleomicrobiology of the dental calculus: a review.
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. PMID:26194817
Golden quantum oscillator and Binet-Fibonacci calculus
NASA Astrophysics Data System (ADS)
Pashaev, Oktay K.; Nalci, Sengul
2012-01-01
The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = φ and Q = -1/φ, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n → ∞ it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated.
Two-dimensional optimal sensor placement
Zhang, H.
1995-05-01
A method for determining the optimal two-dimensional spatial placement of multiple sensors participating in a robot perception task is introduced in this paper. This work is motivated by the fact that sensor data fusion is an effective means of reducing uncertainties in sensor observations, and that the combined uncertainty varies with the relative placement of the sensors with respect to each other. The problem of optimal sensor placement is formulated and a solution is presented in the two dimensional space. The algebraic structure of the combined sensor uncertainty with respect to the placement of sensor is studied. A necessary condition for optimal placement is derived and this necessary condition is used to obtain an efficient closed-form solution for the global optimal placement. Numerical examples are provided to illustrate the effectiveness and efficiency of the solution. 11 refs.
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.
Itô versus Stratonovich calculus in random population growth.
Braumann, Carlos A
2007-03-01
The context is the general stochastic differential equation (SDE) model dN/dt=N(g(N)+sigmaepsilon(t)) for population growth in a randomly fluctuating environment. Here, N=N(t) is the population size at time t, g(N) is the 'average' per capita growth rate (we work with a general almost arbitrary function g), and sigmaepsilon(t) is the effect of environmental fluctuations (sigma>0, epsilon(t) standard white noise). There are two main stochastic calculus used to interpret the SDE, Itô calculus and Stratonovich calculus. They yield different solutions and even qualitatively different predictions (on extinction, for example). So, there is a controversy on which calculus one should use. We will resolve the controversy and show that the real issue is merely semantic. It is due to the informal interpretation of g(x) as being an (unspecified) 'average' per capita growth rate (when population size is x). The implicit assumption usually made in the literature is that the 'average' growth rate is the same for both calculi, when indeed this rate should be defined in terms of the observed process. We prove that, when using Itô calculus, g(N) is indeed the arithmetic average growth rate R(a)(x) and, when using Stratonovich calculus, g(N) is indeed the geometric average growth rate R(g)(x). Writing the solutions of the SDE in terms of a well-defined average, R(a)(x) or R(g)(x), instead of an undefined 'average' g(x), we prove that the two calculi yield exactly the same solution. The apparent difference was due to the semantic confusion of taking the informal term 'average growth rate' as meaning the same average.
Peripheral Stent Placement in Hemodialysis Grafts
Kariya, Shuji Tanigawa, Noboru; Kojima, Hiroyuki; Komemushi, Atsushi; Shomura, Yuzo; Shiraishi, Tomokuni; Kawanaka, Toshiaki; Sawada, Satoshi
2009-09-15
The purpose of the present study was to evaluate the clinical outcome of peripheral stent placement after failed balloon angioplasty in patients with grafts who are on hemodialysis. We examined 30 Wallstents that were placed in 26 patients because balloon angioplasty failed or early restenosis (<3 months) occurred within 3 months. We retrospectively reviewed 267 consecutive balloon angioplasties performed in 71 patients with graft access between August 2000 and March 2007. Stent placements accounted for 30 (11.2%) of the 267 balloon angioplasties. The clinical success rate of stent placement was 93.3% (28 of 30 stent placements). The 3-, 6-, and 12-month primary patency rates were 73.3%, 39.3%, and 17.7%, respectively. The 1-, 2-, and 3-year secondary patency rates were 90.2%, 83.8%, and 83.8%, respectively. Primary patency was significantly prolonged by stent placement after early restenosis compared with previous balloon angioplasty alone (P = 0.0059). Primary patency after stent placement was significantly lower than after successful balloon angioplasty without indications for stent placement (P = 0.0279). Secondary patency rates did not significantly differ between stent placement and balloon angioplasty alone. The mean number of reinterventions required to maintain secondary patency after stent placement was significantly larger than that after balloon angioplasty alone (Mann-Whitney U test, P = 0.0419). We concluded that peripheral stent placement for graft access is effective for salvaging vascular access after failed balloon angioplasty and for prolonging patency in early restenosis after balloon angioplasty. However, reinterventions are required to maintain secondary patency after stent placement. Furthermore, peripheral stent placement for graft access cannot achieve the same primary patency as balloon angioplasty alone.
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…
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…
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…
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,…
NASA Automated Fiber Placement Capabilities: Similar Systems, Complementary Purposes
NASA Technical Reports Server (NTRS)
Wu, K. Chauncey; Jackson, Justin R.; Pelham, Larry I.; Stewart, Brian K.
2015-01-01
New automated fiber placement systems at the NASA Langley Research Center and NASA Marshall Space Flight Center provide state-of-art composites capabilities to these organizations. These systems support basic and applied research at Langley, complementing large-scale manufacturing and technology development at Marshall. These systems each consist of a multi-degree of freedom mobility platform including a commercial robot, a commercial tool changer mechanism, a bespoke automated fiber placement end effector, a linear track, and a rotational tool support structure. In addition, new end effectors with advanced capabilities may be either bought or developed with partners in industry and academia to extend the functionality of these systems. These systems will be used to build large and small composite parts in support of the ongoing NASA Composites for Exploration Upper Stage Project later this year.
Maruo, Hirotoshi; Nakamura, Koichi; Higashi, Yukihiro; Shoji, Tsuyoshi; Yamazaki, Masanori; Nishiyama, Raisuke; Koike, Kota; Kubota, Hiroyuki
2015-11-01
The present study investigated the short-term outcomes of 20 patients with obstructive colon cancer who underwent colonic stent placement as a bridge to surgery (BTS) during the 3-year period between April 2012 and March 2015. Subjects comprised 13 men and 7 women, with a mean age of 68.3 years. Placement and decompression were successfully achieved in all of the patients. Oral ingestion became possible from a mean of 2.7 days after placement. No serious complications associated with placement were encountered. Total colonoscopy was performed after placement in 17 patients (85%), and independent advanced cancer was seen in the proximal portion of the colon in 1 patient. Elective surgery was performed for all of the patients after placement. Excluding the 2 patients for whom preoperative chemotherapy or treatment of another disease was prioritized, the mean interval to surgery for the remaining 18 patients was 23.2 days. The operative procedure performed was laparoscopic surgery in 8 patients (40%). Although minor leakage (n=1) and abdominal wall abscess (n=1) were observed as postoperative complications, the patients generally had an uneventful course. Colonic stent placement for obstructive colon cancer is relatively easy and safe, and may be considered as an effective treatment method that enables favorable intestinal decompression preoperatively and one-stage resection. PMID:26805323
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.
Computational physics in the introductory calculus-based course
NASA Astrophysics Data System (ADS)
Chabay, Ruth; Sherwood, Bruce
2008-04-01
The integration of computation into the introductory calculus-based physics course can potentially provide significant support for the development of conceptual understanding. Computation can support three-dimensional visualizations of abstract quantities, offer opportunities to construct symbolic rather than numeric solutions to problems, and provide experience with the use of vectors as coordinate-free entities. Computation can also allow students to explore models in a way not possible using the analytical tools available to first-year students. We describe how we have incorporated computer programming into an introductory calculus-based course taken by science and engineering students.
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.
Adaptable Deployable Entry and Placement Technology (ADEPT)
The Adaptable, Deployable Entry Placement Technology (ADEPT) Project will test and demonstrate a deployable aeroshell concept as a viable thermal protection system for entry, descent, and landing o...
Product placement of computer games in cyberspace.
Yang, Heng-Li; Wang, Cheng-Shu
2008-08-01
Computer games are considered an emerging media and are even regarded as an advertising channel. By a three-phase experiment, this study investigated the advertising effectiveness of computer games for different product placement forms, product types, and their combinations. As the statistical results revealed, computer games are appropriate for placement advertising. Additionally, different product types and placement forms produced different advertising effectiveness. Optimum combinations of product types and placement forms existed. An advertisement design model is proposed for use in game design environments. Some suggestions are given for advertisers and game companies respectively. PMID:18721087
Automated fiber placement: Evolution and current demonstrations
NASA Technical Reports Server (NTRS)
Grant, Carroll G.; Benson, Vernon M.
1993-01-01
The automated fiber placement process has been in development at Hercules since 1980. Fiber placement is being developed specifically for aircraft and other high performance structural applications. Several major milestones have been achieved during process development. These milestones are discussed in this paper. The automated fiber placement process is currently being demonstrated on the NASA ACT program. All demonstration projects to date have focused on fiber placement of transport aircraft fuselage structures. Hercules has worked closely with Boeing and Douglas on these demonstration projects. This paper gives a description of demonstration projects and results achieved.
Product placement of computer games in cyberspace.
Yang, Heng-Li; Wang, Cheng-Shu
2008-08-01
Computer games are considered an emerging media and are even regarded as an advertising channel. By a three-phase experiment, this study investigated the advertising effectiveness of computer games for different product placement forms, product types, and their combinations. As the statistical results revealed, computer games are appropriate for placement advertising. Additionally, different product types and placement forms produced different advertising effectiveness. Optimum combinations of product types and placement forms existed. An advertisement design model is proposed for use in game design environments. Some suggestions are given for advertisers and game companies respectively.
Lee, Ye Jin; Kim, Jin Hyoung Song, Ho-Young; Park, Jung-Hoon; Na, Han Kyu; Kim, Pyeong Hwa; Fan, Yong
2012-10-15
Purpose: To evaluate the clinical effectiveness of self-expandable metallic stents in seven patients with malignant gastroduodenal obstruction caused by inoperable hepatocellular carcinoma (HCC). Methods: Seven patients with gastroduodenal obstruction caused by advanced HCC underwent metallic stent placement from 2003 to 2010. These patients had total dysphagia (n = 5) or were able to eat only liquids (n = 2) before stent placement. Patients had Eastern Cooperative Oncology Group performance scores of 2 or 3, and Child-Pugh classification B or C. Results: Stent placement was technically successful in all seven patients (100%) and clinically successful in six (86%). Five patients could eat a soft diet, and one patient tolerated regular diet after stent placement. Stent-related obstructive jaundice occurred in one patient. One patient had hematemesis 11 days after stent placement. Overall mean survival was 51 days (range, 10-119 days). Stent patency was preserved in six patients with clinical success until death. Conclusion: Placement of a covered self-expandable metallic stent may offer good palliation in patients with gastroduodenal obstruction due to advanced HCC.
Ghorbani, Mahboobeh; Bogdan, Paul
2014-01-01
Healthcare costs in the US are among the highest in the world. Chronic diseases such as diabetes significantly contribute to these extensive costs. Despite technological advances to improve sensing and actuation devices, we still lack a coherent theory that facilitates the design and optimization of efficient and robust medical cyber-physical systems for managing chronic diseases. In this paper, we propose a mathematical model for capturing the complex dynamics of blood glucose time series (e.g., time dependent and fractal behavior) observed in real world measurements via fractional calculus concepts. Building upon our time dependent fractal model, we propose a novel model predictive controller for an artificial pancreas that regulates insulin injection. We verify the accuracy of our controller by comparing it to conventional non-fractal models using real world measurements and show how the nonlinear optimal controller based on fractal calculus concepts is superior to non-fractal controllers in terms of average risk index and prediction accuracy. PMID:25571075
Dynamics of Placement...How to Develop a Successful Career Planning & Placement Program.
ERIC Educational Resources Information Center
Shingleton, John D.; Fitzpatrick, Edwin B.
This document presents college practitioners with a practical guide for establishing, maintaining, expanding, or revitalizing a contemporary career planning and placement center. The introduction to this guide contains a brief history of career planning and placement. Chapter 1, Career Planning and Placement in the Academic Setting, addresses the…
ERIC Educational Resources Information Center
Miller, Howard J.; And Others
This document is a manual for a social work field placement program. The social work field placement is described as a learning experience designed to translate the students' interests, interpersonal abilities, and academic knowledge and theory into the capability of enabling others to solve problems. Expectations of skills to be learned in the…
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.
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…
Contrasting Cases of Calculus Students' Understanding of Derivative Graphs
ERIC Educational Resources Information Center
Haciomeroglu, Erhan Selcuk; Aspinwall, Leslie; Presmeg, Norma C.
2010-01-01
This study adds momentum to the ongoing discussion clarifying the merits of visualization and analysis in mathematical thinking. Our goal was to gain understanding of three calculus students' mental processes and images used to create meaning for derivative graphs. We contrast the thinking processes of these three students as they attempted to…
Holmium laser lithotripsy of a complicated biliary calculus.
Monga, M; Gabal-Shehab, L L; Kamarei, M; D'Agostino, H
1999-09-01
More than 500,000 cholecystectomies are performed annually. Extracorporeal shockwave lithotripsy and endoscopic laser lithotripsy have been used for the management of common bile duct calculi, which complicate 10% of cases. We report the first successful clinical application of the Ho:YAG laser to a complex biliary calculus case.
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…
Calculus of Elementary Functions, Part I, Student Text. Preliminary Edition.
ERIC Educational Resources Information Center
Herriot, Sarah T.; And Others
This is part one of a three-part SMSG calculus text for high school students. The aim of the text is to develop some of the concepts and techniques which will enable the student to obtain important information about graphs of elementary functions. Chapter topics include: (1) polynomial functions; (2) the derivative of a polynomial function; and…
Calculus Students' Understanding of Area and Volume Units
ERIC Educational Resources Information Center
Dorko, Allison; Speer, Natasha
2015-01-01
Units of measure are critical in many scientific fields. While instructors often note that students struggle with units, little research has been conducted about the nature and extent of these difficulties or why they exist. We investigated calculus students' unit use in area and volume computations. Seventy-three percent of students gave…
Airfoil Design in Multivariable Calculus: Tying It All Together
ERIC Educational Resources Information Center
Laverty, Rich; Povich, Timothy; Williams, Tasha
2005-01-01
Near the conclusion of their final term in the calculus sequence at The United States Military Academy, cadets are given a week long group project. At the end of the week, the project is briefed to their instructors, classmates, and superior officers. From a teaching perspective, the goal is to encapsulate as much of the course as possible in one…
Inertial Navigation: A Bridge between Kinematics and Calculus
ERIC Educational Resources Information Center
Sadler, Philip M.; Garfield, Eliza N.; Tremblay, Alex; Sadler, Daniel J.
2012-01-01
Those who come to Cambridge soon learn that the fastest route between Harvard and MIT is by the subway. For many students, this short ride is a quick and easy way to link physics and calculus. A simple, homemade accelerometer provides all the instrumentation necessary to produce accurate graphs of acceleration, velocity, and displacement position…
Using the Pottery Wheel to Explore Topics in Calculus
ERIC Educational Resources Information Center
Farnell, Elin; Snipes, Marie A.
2015-01-01
Students sometimes struggle with visualizing the three-dimensional solids encountered in certain integral problems in a calculus class. We present a project in which students create solids of revolution with clay on a pottery wheel and estimate the volumes of these objects using Riemann sums. In addition to giving students an opportunity for…
Subsequent-Grades Assessment of Traditional and Reform Calculus.
ERIC Educational Resources Information Center
Baxter, Judith Lee; Majumdar, Dibyen; Smith, Stephen D.
1998-01-01
Studies the later course grades of students enrolled in freshman calculus taught using traditional texts through 1994-95 and the Harvard method which was fully adopted starting in 1995-96. Reports that, in some cases, the results were indistinguishable but some statistically significant patterns were found. (Author/ASK)
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.
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…
Evaluating the Performance of Calculus Classes Using Operational Research Tools.
ERIC Educational Resources Information Center
Soares de Mello, Joao Carlos C. B.; Lins, Marcos P. E.; Soares de Mello, Maria Helena C.; Gomes, Eliane G.
2002-01-01
Compares the efficiency of calculus classes and evaluates two kinds of classes: traditional and others that use computational methods in teaching. Applies quantitative evaluation methods using two operational research tools, multicriteria decision aid methods (mainly using the MACBETH approach) and data development analysis. (Author/YDS)
On the Fundamental Theorem of Calculus for Fractal Sets
NASA Astrophysics Data System (ADS)
Bongiorno, Donatella; Corrao, Giuseppa
2015-04-01
The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock-Kurzweil type is introduced.
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…
Multivariate Limits and Continuity: A Survey of Calculus Textbooks.
ERIC Educational Resources Information Center
Thompson, Thomas M.; Wiggins, Kenneth L.
There has been much recent discussion concerning the content of the standard calculus course for students majoring in mathematics and the sciences. Some of this discussion has focused on the available textbooks. One weakness noted in some of these books involves the definitions of limit and continuity for functions of several variables. A…
An Application of Calculus: Optimum Parabolic Path Problem
ERIC Educational Resources Information Center
Atasever, Merve; Pakdemirli, Mehmet; Yurtsever, Hasan Ali
2009-01-01
A practical and technological application of calculus problem is posed to motivate freshman students or junior high school students. A variable coefficient of friction is used in modelling air friction. The case in which the coefficient of friction is a decreasing function of altitude is considered. The optimum parabolic path for a flying object…
a Type of Fractal Interpolation Functions and Their Fractional Calculus
NASA Astrophysics Data System (ADS)
Liang, Yong-Shun; Zhang, Qi
2016-05-01
Combine Chebyshev systems with fractal interpolation, certain continuous functions have been approximated by fractal interpolation functions unanimously. Local structure of these fractal interpolation functions (FIF) has been discussed. The relationship between order of Riemann-Liouville fractional calculus and Box dimension of FIF has been investigated.
Path Integrals, Fourier Transforms, and Feynman's Operational Calculus
Ahn, Byung Moo; Johnson, G. W.
1998-03-15
The disentangling process is the key to Feynman's operational calculus for noncommuting operators. The main result of his heuristic calculations deals with disentangling an exponential factor. We use the Wiener and Feynman integrals to make this disentangling (or time-ordering) mathematically rigorous in the case where the analytic functions from earlier work are replaced by Fourier transforms of complex-valued measures.
A Measurement Activity to Encourage Exploration of Calculus Concepts
ERIC Educational Resources Information Center
McGuffey, William
2015-01-01
This article describes an activity that incorporates measurement in order to lead students to discover and explore fundamental concepts of calculus. Students are provided with an experientially real starting point involving measurement and are encouraged to engage in mathematical discussions in a low-stakes environment. I describe the activity as…
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.
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…
Calculus of One and More Variables with Maple
ERIC Educational Resources Information Center
Samkova, Libuse
2012-01-01
This is a guide to using Maple in teaching fundamental calculus of one, two and three variables (limits, derivatives, integrals, etc.), also suitable for Maple beginners. It outlines one of the ways to effective use of computers in the teaching process. It scans advantages and disadvantages of using Maple in relation to students and teacher. The…
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…
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…
Sharing Teaching Ideas. Giving Meaning to Volume in Calculus.
ERIC Educational Resources Information Center
Rahn, James R.
1991-01-01
Described is an activity that uses the techniques of integral calculus to determine the volume of a bundt cake. The cake is used as an example of a solid of revolution. Included are the procedures and assumptions used by students to solve this problem. (KR)
A Team Taught Interdisciplinary Approach To Physics and Calculus Education.
ERIC Educational Resources Information Center
Johnson, David B.
The Special Intensive Program for Scientists and Engineers (SIPSE) at Diablo Valley College in California replaces the traditional engineering calculus and physics sequences with a single sequence that combines the two subjects into an integrated whole. The project report provides an overview of SIPSE, a section that traces the project from…
Using Origami Boxes to Explore Concepts of Geometry and Calculus
ERIC Educational Resources Information Center
Wares, Arsalan
2011-01-01
The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important concepts of geometry and calculus. This article describes how an origami box can be folded, then it goes on to describe how its volume and surface area can be calculated. Finally, it describes how the box could be folded to…
Designing a Telescope Mirror for Second-Semester Calculus Students
ERIC Educational Resources Information Center
Marchand, Richard J.; Rogers, Robert R.; Parker, Andrew T.
2006-01-01
The purpose of this article is to present an interdisciplinary project, developed as a collaborative effort by the authors, involving the design of a telescope mirror as it was given to second semester calculus students. The goals of the project are to provide an applied setting for the topics typically covered in this type of course including the…
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.
Implementation of Job Placement Services Guidelines.
ERIC Educational Resources Information Center
McGillicuddy (Shirley) & Associates, Sierra Madre, CA.
The Implementation of Job Placement Services Guidelines Project was designed to strengthen placement programs and services for California community college vocational students, and for all students needing part-time employment to realize their educational goals. The project was designed to test the validity and relevance of quality indicators…
Preceptor Handbook: Rural Clinical Nurse Placement Center.
ERIC Educational Resources Information Center
Stuart-Siddall, Sandra; Haberlin, Jean
This handbook provides Rural Clinical Nurse Placement Program (RCNP) preceptors with a program overview and practical suggestions to apply during student placement. An introductory section describes how the program addresses the maldistribution of nurses by raising awareness about the rural experience, adding a needed perspective to the urban bias…
Private Placement Debt Financing for Public Entities
ERIC Educational Resources Information Center
Holman, Lance S.
2010-01-01
Private placement financing is a debt or capital lease obligation arranged between a municipality or a 501(c) (3) not-for-profit organization and a single sophisticated institutional investor. The investor can be a bank, insurance company, finance company, hedge fund, or high-net worth individual. Private placement financing is similar to…
Preparing ESP Learners for Workplace Placement
ERIC Educational Resources Information Center
Wood, David
2009-01-01
Engineering students in North American universities often participate in cooperative education placements in workplaces as part of the requirements for their degrees and professional certification. Students for whom English is an L2 often experience difficulties in these placements due to the fact that while their academic language ability may be…
32 CFR 1656.10 - Job placement.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 32 National Defense 6 2011-07-01 2011-07-01 false Job placement. 1656.10 Section 1656.10 National....10 Job placement. (a) Selective Service will maintain a job bank for the exclusive purpose of placing ASWs in alternative service jobs. (b) An ASW who has identified his own job in accordance with §...