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)
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…
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…
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…
Advanced Placement: Access Not Exclusion.
ERIC Educational Resources Information Center
Camara, Wayne; Dorans, Neil J.; Morgan, Rick; Myford, Carol
2000-01-01
Refutes the assertion by W. Lichten (2000) that increased access to advanced placement (AP) courses in high school has led to a decline in AP quality. Suggests that increased access exposes students to college-level course material, encourages teachers to expand their knowledge domains, increases curriculum rigor, and give students new challenges.…
Advanced Placement Course Description. Statistics.
ERIC Educational Resources Information Center
College Entrance Examination Board, New York, NY.
The Advanced Placement (AP) program is a cooperative educational effort of secondary schools, colleges, and the College Board that consists of 30 college-level courses and examinations in 17 academic disciplines for highly motivated students in secondary schools. AP courses are offered in more than 11,000 high schools and are recognized by nearly…
Advanced Placement: More than a Test.
ERIC Educational Resources Information Center
Colwell, Richard
1990-01-01
Encourages music teachers to work with students interested in advanced placement (AP) music courses. Discusses the logistics and advantages of placing students in these courses. Describes the Advanced Placement Listening and Literature and the Advanced Placement Theory courses and examinations. Outlines the examination scoring method and looks at…
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 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…
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.
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…
Literary Archetypes. Advanced Placement English Curriculum Guide.
ERIC Educational Resources Information Center
Anne Arundel County Public Schools, Annapolis, MD.
Providing students with the opportunity to earn college credit while still in high school, the Advanced Placement English course described in this guide is designed to help students (1) want to choose from a wide range of literature for independent reading; (2) develop a critical awareness about literature; (3) recognize connections among works of…
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…
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. 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,…
Introduction. Teaching Advanced Placement Human Geography.
ERIC Educational Resources Information Center
Murphy, Alexander B.
2000-01-01
Introduces this special issue of "Journal of Geography" focusing on the teaching of Advanced Placement (AP) human geography. States that essays were developed by members of the AP Human Geography Development Committee focusing on areas in the human geography course outline which are included in the appendix. (CMK)
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.…
Modern Agriculture in Advanced Placement Human Geography.
ERIC Educational Resources Information Center
Lanegran, David A.
2000-01-01
Discusses the four sections of the Advanced Placement (AP) human geography course focusing on agriculture: (1) development and diffusion of agriculture; (2) major agricultural production regions; (3) rural land use and change; and (4) impacts of modern agricultural change. Includes references and a resource list. (CMK)
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…
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…
Predicting success on the Advanced Placement Biology Examination
NASA Astrophysics Data System (ADS)
Shepherd, Lesa Hanlin
Four hundred sixty students in four public high schools were used as subjects to determine which of eleven academic and demographic factors studied were significant predictors of success for the Advanced Placement Biology Examination. Factors studied were attendance, class rank, gender, grade level at the time of the examination, grade point average, level of prerequisite biology course, number of Advanced Placement Examinations taken in the year prior to the Advanced Placement Biology Examination, number of Advanced Placement Examinations taken in the same year as the Advanced Placement Biology Examination, proposed major in college, race, and SAT mathematics, verbal, and combined score. Significant relationships were found to exist between the Advanced Placement Biology Examination score and attendance, class rank, gender, grade level at the time of the Advanced Placement Biology Examination, grade point average, number of Advanced Placement Examinations taken in the year prior to the Advanced Placement Biology Examination, number of Advanced Placement Examinations taken in the same year as the Advanced Placement Biology Examination, race, and SAT scores. Significant relationships were not found to exist between Advanced Placement Biology Examination score and level prerequisite biology course and Advanced Placement Biology Examination score and proposed major in college. A multiple regression showed the best combination of predictors to be attendance, SAT verbal score, and SAT mathematics score. Discriminant analysis showed the variables in this study to be good predictors of whether the student would pass the Advanced Placement Biology Examination (score a 3, 4, or 5) or fail the Advanced Placement Biology Examination (score a 1 or 2). These results demonstrated that significant predictors for the Advanced Placement Biology Examination do exist and can be used to assist in the prediction of scores, prediction of passing or failing, the identification of
Advanced tow placement of composite fuselage structure
NASA Technical Reports Server (NTRS)
Anderson, Robert L.; Grant, Carroll G.
1992-01-01
The Hercules NASA ACT program was established to demonstrate and validate the low cost potential of the automated tow placement process for fabrication of aircraft primary structures. The program is currently being conducted as a cooperative program in collaboration with the Boeing ATCAS Program. The Hercules advanced tow placement process has been in development since 1982 and was developed specifically for composite aircraft structures. The second generation machine, now in operation at Hercules, is a production-ready machine that uses a low cost prepreg tow material form to produce structures with laminate properties equivalent to prepreg tape layup. Current program activities are focused on demonstration of the automated tow placement process for fabrication of subsonic transport aircraft fuselage crown quadrants. We are working with Boeing Commercial Aircraft and Douglas Aircraft during this phase of the program. The Douglas demonstration panels has co-cured skin/stringers, and the Boeing demonstration panel is an intricately bonded part with co-cured skin/stringers and co-bonded frames. Other aircraft structures that were evaluated for the automated tow placement process include engine nacelle components, fuselage pressure bulkheads, and fuselage tail cones. Because of the cylindrical shape of these structures, multiple parts can be fabricated on one two placement tool, thus reducing the cost per pound of the finished part.
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…
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)
African American Educators' Perspectives on the Advanced Placement Opportunity Gap
ERIC Educational Resources Information Center
Taliaferro, Jocelyn DeVance; DeCuir-Gunby, Jessica T.
2008-01-01
This study examines perspectives of educators on the advanced placement opportunity gap for African American students. Using interviews with 11 educators from 10 high schools, we explored their perceptions regarding the impact of a local academic achievement program on the enrollment of African American students in honors and advanced placement…
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…
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…
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…
Advanced Placement Course Enrollment and School-Level Characteristics
ERIC Educational Resources Information Center
Barnard-Brak, Lucy; McGaha-Garnett, Valerie; Burley, Hansel
2011-01-01
The current study examined access to Advanced Placement (AP) courses as a function of these school characteristics (e.g., percentage of ethnic minority and lower socioeconomic status) and then examined AP course enrollment as a function of both access to AP courses and these school characteristics. Using structural equation modeling techniques,…
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)
Advanced Placement Human Geography: The First Five Years
ERIC Educational Resources Information Center
Gray, Paul T., Jr.; Hidlebrant, Barbara S.; Strauss, Tim R.
2006-01-01
Advanced Placement Human Geography (APHG) has grown steadily from 3,272 tests at the first test administration in 2001 to 14,139 tests in 2005. This paper examines the dynamics of growth throughout the United States through numbers of students and numbers of high schools involved in the program. APHG is discussed relative to the establishment of…
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...
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,…
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…
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…
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…
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…
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;…
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…
ERIC Educational Resources Information Center
Vidrine, Brent
2013-01-01
The purpose of the study was to investigate participation rates of minorities and economically disadvantaged students in Advanced Placement programs in selected high schools in Northeast Louisiana. Advanced Placement programs in high schools generally promote higher level education courses. The focus of the investigation was perceptions held by…
Advanced Placement Report to the Nation, 2007
ERIC Educational Resources Information Center
College Board, 2007
2007-01-01
American educators are achieving much success in their efforts to enable a wider and more diverse group of U.S. students than ever before to succeed in college-level studies in high school. Yet individuals must also gaze clear-eyed at the inequities that remain and the challenges that accompany success in expanding access to the Advanced Placement…
ERIC Educational Resources Information Center
Bremer, James Walter
In Spring 1967, the "Leadership Group of High School Teachers of Economics" in Orange County, California, expressed interest in developing an Advanced Placement Program (APP) in Economics. They were concerned that students from the stronger secondary school economics programs would find introductory college economics repetitive. This concern…
ERIC Educational Resources Information Center
Ramsey, Susan Brady
2012-01-01
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…
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.…
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…
ERIC Educational Resources Information Center
Eisner, Caroline, Ed.
This is the first comprehensive study to examine Advanced Placement (AP) course-taking patterns and subject test results in the nation's urban schools. This study investigates both Great City Schools' (GCS) AP scores and scores for a national sample of test takers. The GCS data set includes 58 large urban public school districts. The primary…
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
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…
Policy to Practice: A Case Study of Advanced Placement Open Enrollment Programs in New Mexico
ERIC Educational Resources Information Center
McIlroy, Ann Lynn
2010-01-01
This case study explored Advanced Placement open enrollment programs in New Mexico in an attempt to identify mechanisms embedded within the implementation practices which possibly prevent the equitable enrollment of students of color. Advanced Placement (AP) courses have become a gate-keeper in competitive college admissions. Therefore, a study of…
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...
Progress in Advanced Placement and International Baccalaureate in SREB States. Challenge to Lead
ERIC Educational Resources Information Center
Kaye, Rebecca Daugherty
2006-01-01
Southern Regional Education Board (SREB) states lead the nation in student participation in Advanced Placement and International Baccalaureate Programs. SREB states know that getting students engaged in a challenging high school curriculum is the most important step they can take to promote college readiness. Advanced Placement (AP) courses and…
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…
Exemplary Advanced Placement Programs: Comparing AP Test Scores by Subject and School.
ERIC Educational Resources Information Center
Hoven, John
This study compared performance of seniors at 21 Montgomery County (Maryland) high schools on the Advanced Placement (AP) Tests. The schools were ranked by the percentage of college-educated adults within the school boundaries, and the ranking was compared to Advanced Placement test results (the average number of students, per 100 seniors, who…
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…
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…
ERIC Educational Resources Information Center
Barham, Mary Ann
2009-01-01
The purpose of this study was to investigate the low participation rate among high school students 18 years of age or older in Advanced Placement courses. The subjects in this study were 129 Advanced Placement Students and 129 non-Advanced Placement high school students 18 years of age or older in five high schools in two Louisiana parishes.…
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…
ERIC Educational Resources Information Center
Docimo, Chelsey L.
2013-01-01
The purpose of this eleventh grade Advanced Placement (AP) program study was to determine factors associated with AP placement and subsequent student performance. This research was considered to be a mixed methods case study with elements of arrested action research. One hundred and twenty-four students, four guidance counselors, three AP…
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
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)
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.)
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…
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
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…
ERIC Educational Resources Information Center
Burney, Virginia H.
2010-01-01
The purpose of the study was to identify school- and district-level variables that relate to advanced academic achievement, as defined by the ratio of number of scores of 3, 4, or 5 on Advanced Placement exams to school enrollment. The study initially included 46 variables for 339 public high schools in one Midwestern state. Hierarchical linear…
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…
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
Power, David; Stevens, Ken; Boone, Wilbert; Barry, Maurice
In partnership with the Memorial University of Newfoundland, the Vista School District, 1 of 10 districts in Newfoundland, Canada, established the Vista School District Digital Intranet (VSDDI) to deliver Web-based advanced placement courses to rural students. Advanced placement mathematics, physics, biology, and chemistry courses are delivered…
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…
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)
Barriers to Advanced Placement for Latino Students at the High-School Level
ERIC Educational Resources Information Center
Walker, Susan A.; Pearsall, Laura D.
2012-01-01
In order to gain a better understanding about Latino student underrepresentation in advanced placement (AP) coursework, this investigation explored the factors that inhibit and/or encourage Latino student enrollment in AP coursework at one suburban public high school in the Western United States. Latino high-school students and their parents…
A Multi-Year Analysis of Asian Gender Differences on Advanced Placement Exams
ERIC Educational Resources Information Center
Moore, George; Slate, John R.
2011-01-01
The performance of Asian boys and girls on Advanced Placement (AP) exam overall scores across the United States for the past 14 years was analyzed. For each of the 14 years of data analyzed, Asian boys had statistically significant higher percentages of overall AP exam scores of 5 than did Asian girls. In addition, the gap between the mean…
ERIC Educational Resources Information Center
Chandler Unified Schools, AZ.
The honors program at Chandler High School (Arizona) which combines the International Baccalaureate (IB) and Advanced Placement (AP) programs is described in this brochure. Following a general overview of IB and AP programs, several benefits of this combined program are listed: (1) small classes with superior students; (2) the opportunity to earn…
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 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…
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…
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…
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…
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
Sublett, Michael D.
2007-01-01
Members of the National Council for Geographic Education have been instrumental in the creation, launch, and early success of Advanced Placement Human Geography. Annual meetings of the Council have served as a forum for spreading the word about the course and its follow-up national examination and in helping teachers develop content confidence and…
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…
Ethnic and Gender Differences in Advanced Placement Exam Performance: A Multiyear National Analysis
ERIC Educational Resources Information Center
Holmes, Maria Alexander
2013-01-01
Purpose: The purpose of this study was to analyze ethnic and gender differences in Advanced Placement (AP) exam performance of U.S. high school students. Specifically, the extent to which differences exist in overall AP exam performance scores within and between four ethnic groups (i.e., Asian, Black, Hispanic, and White) was investigated. Within…
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…
The Relationship between Advanced Placement and College Graduation. 2005 AP Study Series, Report 1
ERIC Educational Resources Information Center
Dougherty, Chrys; Mellor, Lynn; Jian, Shuling
2006-01-01
This study explores the relationship between college graduation rates and student participation and success in Advanced Placement (AP) courses and exams. We reviewed three approaches to examining this relationship: 1) comparing the college graduation rates of AP and non-AP students; 2) comparing the college graduation rate of AP and non-AP…
The Challenge of Advanced Placement Partnerships in the South Texas Border Classroom
ERIC Educational Resources Information Center
Blackwell, Deborah L.; Pisani, Jana S.; Pisani, Michael J.
2007-01-01
In the year 2000, the Texas Education Agency and the Texas A&M University System teamed up to create an initiative called the University Faculty Fellows Program. Spearheaded by Texas A&M International University in Laredo, the program paired up faculty from the university with area Advanced Placement (AP) teachers in a variety of disciplines.…
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…
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
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…
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,…
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…
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…
Advanced Placement and International Baccalaureate Exam Results for 2003-2004
ERIC Educational Resources Information Center
Connolly, Faith; Powell, Marilyn
2005-01-01
Goal 1 of the Montgomery County Public Schools (MCPS) Strategic Plan, "Our Call to Action: Pursuit of Excellence" (MCPS, 2004), is to "Ensure Success for Every Student." One measure of success for students who plan to attend college is their preparation for college-level course work. The Advanced Placement (AP) program offers MCPS students an…
ERIC Educational Resources Information Center
Collins, Crystal; Lenard, Matthew
2007-01-01
Advanced Placement (AP) and International Baccalaureate (IB) courses continue to receive national recognition for their rigorous curricula, and many colleges and universities award credit to students who score well on end-of-course exams in AP classes. Research suggests that students are better prepared for college if they take these courses and…
Credit Policies for Courses in Minnesota Colleges & Universities: Advanced Placement, 2004-2005.
ERIC Educational Resources Information Center
Minnesota State Department of Education, 2004
2004-01-01
This guide is intended to aid high school students in their educational planning. Colleges and universities state their policies in granting college credit for successful completion of Advanced Placement (AP) examinations in high school. The guide also represents certification of these policies to the Department of Education and to the Minnesota…
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…
How Colleges and Universities Employ Credit and Placement for Advanced Academic Studies.
ERIC Educational Resources Information Center
Alder, Henry L.
The University of California's grading/credit policy for advanced placement (AP) courses taken by high school students is discussed. The university traditionally has encouraged high school students to take AP courses if they are prepared and mature enough to benefit from them. The university grants credit for scores of 3, 4, or 5 earned on AP…
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…
The Lowest Quartile African Americans Taking Advanced Placement Language and Literature
ERIC Educational Resources Information Center
Hale, David P.
2007-01-01
As the lead Advanced Placement (AP) English teacher at Suncoast High School, a magnet school, the author started a pilot program teaching the lowest quartile group of African American students the AP English Literature and Composition course their senior year. Their educational background was limited, and several were not able to write a complete…
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…
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…
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…
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…
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…
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…
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…
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…
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…
Federal Register 2010, 2011, 2012, 2013, 2014
2010-09-01
... From the Federal Register Online via the Government Publishing Office DEPARTMENT OF EDUCATION Office of Elementary and Secondary Education Overview Information; Advanced Placement (AP) Test Fee... academic credit is awarded. Program Authority: 20 U.S.C. 6531-6537. Applicable Regulations: The...
ERIC Educational Resources Information Center
Dutkowsky, Donald H.; Evensky, Jerry M.; Edmonds, Gerald S.
2009-01-01
This article provides an explicit framework for evaluating the expected benefit to college-bound students of courses offered by Advanced Placement (AP) versus concurrent enrollment programs (CEP). District personnel can use it to assess the relative merits of these programs, given the characteristics of their students, in deciding which model to…
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
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 Effects of Advanced Placement and International Baccalaureate Programs on Student Achievement
ERIC Educational Resources Information Center
Luo, Samia Merza
2013-01-01
This study compared student academic achievement in two college readiness programs, Advanced Placement (AP) and International Baccalaureate (IB) and attempted to determine how well program participation predict student performance compared to variables such as SES, parent education level, GPA, gender, and SAT II scores. Finally, the research…
Advanced Placement in Studio Art and Secondary Art Education Policy: Countering the Null Curriculum
ERIC Educational Resources Information Center
Graham, Mark A.; Sims-Gunzenhauser, Alice
2009-01-01
Because of education reform policy and misconceptions about artistry and artistic assessment, visual art education remains in the margins of high school education. One response to the lack of supportive arts education policy is the Advanced Placement (AP) Studio Art Program, a visual arts assessment at the high school level that engages large…
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…
A Study of the Advanced Placement Program in High School Biology.
ERIC Educational Resources Information Center
Luckey, James H., Jr.
Principals, teachers and students of 12 Memphis city high schools provided attitudinal data concerning the Advanced Placement Biology Program. Test score data were obtained from the students and compared to national norms for the Lorge-Thorndike Intelligence Tests and the Cooperative Test Battery in English and Biology. The program was strongly…
ERIC Educational Resources Information Center
Jeong, Dong Wook
2009-01-01
Many states provide incentives to students, teachers, and schools for the participation and success of students on Advanced Placement (AP) examinations administered by the College Board. The purpose of this article is to examine whether these incentives help students enroll and succeed in AP exams. An analysis of nationally representative AP exam…
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…
Advanced image placement performance for the current EPL masks
NASA Astrophysics Data System (ADS)
Eguchi, Hideyuki; Sugimura, Hiroshi; Koike, Kaoru; Sakaue, Hiroshi; Arimoto, Hiroshi; Ogawa, Kentaro; Susa, Takashi; Kunitani, Shinji; Kurosu, Toshiaki; Yoshii, Takashi; Itoh, Kojiro; Tamura, Akira
2006-03-01
We examined two EPL mask fabrication processes to control precisely image placement (IP) on the EPL masks. One is a wafer process using an electrostatic chuck during an e-beam write and another is a membrane process using a mechanical chuck during the e-beam write. In the wafer process, the global IP is corrected during the e-beam write on the basis of the IP data taken with x-y metrology tool. In the membrane process, the global IP is corrected during the e-beam write on the basis of the data taken with the x-y metrology tool and taken in situ with the e-beam writer. The resist and final global IP (3s) of the wafer process is 7.2 nm and 10.6 nm. For the average local IP errors (3s), the local IP of 5.7 nm at the resist step increases to 14.7 nm at the final step due to process-induced distortions. The local IP could be reduced to 6.0 nm by applying the constant scale value to the mask process. In the membrane process, the resist and final global IP (3s) is 15.3 nm and 17.1 nm. With more detectable alignment marks, it would be possible to improve the global IP. For the average local IP errors (3s) of the membrane process, the average resist and final local IP are 6.7 and 7.1 nm which shows no PID. The two approaches proved to control IP more accurately than the conventional one.
The impact of taking a college pre-calculus course on students' college calculus performance
NASA Astrophysics Data System (ADS)
Sonnert, Gerhard; Sadler, Philip M.
2014-11-01
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 four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.
Chavalitdhamrong, Disaya; DiMaio, Christopher J.; Siersema, Peter D.; Wagh, Mihir S.
2015-01-01
Radiation therapy has an important role in the treatment of locally advanced or metastatic pancreatic cancer and can be used alone or in conjunction with surgery and/or systemic chemotherapy. Because of the challenge of delivering an accurate and optimal radiation dose, image-guided radiation therapy can be used to improve targeting. Fiducial markers can be placed in the tumor and used for localization in patients undergoing image-guided radiation therapy. The safety and feasibility of endoscopic ultrasound (EUS)-guided placement of fiducials has been assessed and reported for the management of pancreatic cancer. We herein review the technique, efficacy, and safety profile of EUS-guided fiducial placement. In addition, we highlight recent advances and technological upgrades in EUS-guided fiducial delivery systems for pancreatic cancer most relevant to practicing gastroenterologists and interventional endoscopists. PMID:26355267
Chavalitdhamrong, Disaya; DiMaio, Christopher J; Siersema, Peter D; Wagh, Mihir S
2015-08-01
Radiation therapy has an important role in the treatment of locally advanced or metastatic pancreatic cancer and can be used alone or in conjunction with surgery and/or systemic chemotherapy. Because of the challenge of delivering an accurate and optimal radiation dose, image-guided radiation therapy can be used to improve targeting. Fiducial markers can be placed in the tumor and used for localization in patients undergoing image-guided radiation therapy. The safety and feasibility of endoscopic ultrasound (EUS)-guided placement of fiducials has been assessed and reported for the management of pancreatic cancer. We herein review the technique, efficacy, and safety profile of EUS-guided fiducial placement. In addition, we highlight recent advances and technological upgrades in EUS-guided fiducial delivery systems for pancreatic cancer most relevant to practicing gastroenterologists and interventional endoscopists. PMID:26355267
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…
The role of gastrostomy tube placement in advanced dementia with dysphagia: a critical review
Goldberg, Leanne S; Altman, Kenneth W
2014-01-01
Purpose Over 4.5 million people in North America had a diagnosis of dementia in the year 2000, and more than half had advanced disease with potential aspiration risk. There is much controversy regarding the use and timing of enteral feeding support in these patients with dysphagia. The management of dysphagia is far more complex when considering quality of life, “comfort care” hand feeding, the use of percutaneous endoscopic gastrostomy tube (PEG), and associated mortality rates. This study seeks to critically review the literature that evaluates PEG placement in this population. Methods A systematic literature review of PubMed, from 1995–2012, was conducted to identify studies relating to PEG placement in dementia patients with dysphagia. The principal outcomes and related survival rates for this population were compared. Results In total, 100 articles were identified in the search. Of these, ten met the search criteria and were analyzed. There was one study with a 2b level of evidence, one with 3b, and the remainder had level 4. All studies discussed long-term survival in the PEG versus non-PEG populations. No studies showed definitive evidence to suggest long-term survival rates improved in patients who underwent PEG placement as compared to those who did not. Two studies documented median survival worse in patients over age 80 with dementia and PEG placement. Conclusion There is presently no evidence to suggest long-term survival rates improved in patients with advanced dementia who underwent PEG placement for dysphagia. Relevance to quality of life, need for nutrition and hydration, and ethical considerations in the decision process are discussed. PMID:25342891
Gastrostomy tube placement in patients with advanced dementia or near end of life.
Schwartz, Denise Baird; Barrocas, Albert; Wesley, John R; Kliger, Gustavo; Pontes-Arruda, Alessandro; Márquez, Humberto Arenas; James, Rosemarie Lembo; Monturo, Cheryl; Lysen, Lucinda K; DiTucci, Angela
2014-12-01
Based on current scientific literature, gastrostomy tube (G-tube) placement or other long-term enteral access devices should be withheld in patients with advanced dementia or other near end-of-life conditions. In many instances healthcare providers are not optimally equipped to implement this recommendation at the bedside. Autonomy of the patient or surrogate decision maker should be respected, as should the patient's cultural, religious, social, and emotional value system. Clinical practice needs to address risks, burdens, benefits, and expected short-term and long-term outcomes in order to clarify practice changes. This paper recommends a change in clinical practice and care strategy based on the results of a thorough literature review and provides tools for healthcare clinicians, particularly in the hospital setting, including an algorithm for decision making and a checklist to use prior to the placement of G-tubes or other long-term enteral access devices. Integrating concepts of patient-centered care, shared decision making, health literacy, and the teach-back method of education enhances the desired outcome of ethical dilemma prevention. The goal is advance care planning and a timely consensus among health team members, family members, and significant others regarding end-of-life care for patients who do not have an advance directive and lack the capacity to advocate for themselves. Achieving this goal requires interdisciplinary collaboration and proactive planning within a supportive healthcare institution environment. PMID:25293595
ERIC Educational Resources Information Center
Vaughn, E. Sidney, III
2010-01-01
According to Arthur Powell "Advanced Placement courses have probably brought more challenging academic experiences to more students than any other single reform in recent American high school history" ("Lessons from Privilege: The American Prep School Tradition", p. 243). To this end, there has been a significant increase in Advanced Placement…
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)
The Advanced Placement Physics Examinations: Test Development and Free-Response Section Readings
NASA Astrophysics Data System (ADS)
McMurray, Terri; Cain, L. S.
2003-11-01
The Advanced Placement Physics B and C Examinations are developed by a Test Development Committee consisting of both high school and college teachers appointed by The College Board. We will discuss the creation of the tests from their conception to their administration to more than 60,000 high school students each year. We will also discuss the reading of the free response sections for each exam. A group of readers, consisting of interested and motivated high school AP physics teachers and college instructors who teach comparable courses, is appointed to read the free response sections during June of each year. Two experienced readers, one of whom is a member of the Test Development Committee, will share information in this talk on becoming involved with the AP program as a reader.
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
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
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
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
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
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…
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;…
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
Zarate, Maria Estela; Pachon, Harry P.
2006-01-01
Analysis by researchers of the Tomas Rivera Policy Institute (TRPI) on Advanced Placement (AP) courses in California public high schools in the mid-1990s concluded that although high school AP programs offered talented youngsters the opportunity to stretch their mental horizons and preview the challenges of college-level coursework, the programs…
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
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
Flowers, Lamont A.
2008-01-01
Despite the wealth of information generated in recent years regarding the benefits for students who participate in Advanced Placement (AP) programs on educational outcomes, limited research exists contrasting and comparing the differential effects of AP program participation on educational and labor market outcomes by race. However, research…
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
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
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
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
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…
ERIC Educational Resources Information Center
Kutchner, Wendy
2012-01-01
This quantitative study examined the impact that Advanced Placement (AP) coursework had on students attending college with specific emphasis on those who failed the exam. The study comprised four years of entering freshmen students between the academic years 2006-2009. The study was comprehensive in that it revealed all AP attempts regardless of…
ERIC Educational Resources Information Center
National Center for Educational Achievement, 2010
2010-01-01
Many policymakers and education leaders have embraced the Advanced Placement (AP) Program as a tool to strengthen the high school curriculum and prepare students for college. The popularity of the AP program among these policy leaders reflects their belief that the traditional high school curriculum has often failed to provide rigorous courses…
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…
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
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
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
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
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…
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…
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.
NASA Astrophysics Data System (ADS)
Herr, Norman Edward
These are two major models for advanced science instruction in American high schools, the traditional honors program and the Advanced Placement (AP) program of the College Entrance Examination Board. Using the self-reports of teachers who were experienced in teaching honors and AP courses to students of similar academic preparation and ability, the author examined the perceived influences of program format upon the use of basic teaching techniques, the laboratory experience, the pace of the course, curricular freedom, and student creativity. One of the most notable aspects of the AP program is the speed at which teachers move through the curriculum. In the rush to prepare students for the exam, most AP teachers adopt a strong lecture format and minimize student-centered activities such as laboratory experimentation, student projects, and student presentations. When laboratory work is not assessed on the national AP examination, such experiences are sacrificed to provide time for lecture. When laboratory experiments are assessed, however, teachers respond by allocating more time for laboratory work, and by upgrading their exercises to make them more quantitative and experimental than those used previously or those used in honors classes. Although AP is associated with a loss in curricular freedom and flexibility, teachers perceive no clear influence of program format upon student creativity.
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…
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.
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.
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
Kotkar, Kunal; Thakkar, Ravi; Songra, MC
2011-01-01
Primary urethral calculus is rarely seen and is usually encountered in men with urethral stricture or diverticulum. We present a case of giant urethral calculus secondary to a urethral stricture in a man. The patient was treated with calculus extraction with end to end urethroplasty. PMID:24950400
ERIC Educational Resources Information Center
2003
Math Sense consists of five books that develop from basic to more advanced math skills. This document contains a placement test used with Math Sense to help students and their teachers decide into which Math Sense book to begin working. The placement test is divided into six parts, each consisting of 10 to 22 problems, and is based on exit skill…
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
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
Balint, Marilyn
A study was conducted to evaluate the effect of integrating advanced placement licensed vocational nursing (APLVN) students with generic students in the second year of the registered nursing program at Long Beach City College. It was hypothesized that the academic achievement of the APLVN students who were taught as a separate group for the first…
ERIC Educational Resources Information Center
de la Varre, Claire
2012-01-01
This study used a social presence construct derived from the Community of Inquiry (COI) framework, with cohesive, affective, and interactive components, to explore online discussion in an Advanced Placement course for rural high school students. The COI is based on the underlying theoretical framework of social constructivism, where interaction is…
ERIC Educational Resources Information Center
Camara, Wayne J.; Millsap, Roger
1998-01-01
This study reports that student performance on the PSAT/NMSQT can be useful in identifying additional students who may be successful in Advanced Placement Program (AP) courses. PSAT/NMSQT scores can identify students who may not have been initially considered for an AP course through teacher nomination, self-nomination, or other local procedures.…
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
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
Breland, Hunter M.; Oltman, Philip K.
2001-01-01
Advanced Placement Program® (AP®) Examinations in Macroeconomics, Microeconomics, and Comparative Government and Politics were studied to examine college course performance and gender differences. It was concluded that students who had received college credit for AP performed as well or better in higher-level college courses in Macroeconomics and…
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
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
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
Hansen, Kristine; Reeve, Suzanne; Gonzalez, Jennifer; Sudweeks, Richard R.; Hatch, Gary L.; Esplin, Patricia; Bradshaw, William S.
2006-01-01
This study was conducted to obtain empirical data to inform policy decisions about exempting incoming students from a first-year composition (FYC) course on the basis of Advanced Placement (AP) English exam scores. It examined the effect of avoiding first-year writing on the writing abilities of sophomore undergraduates. Two three-page writing…
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
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
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)
Arons-Polan, Bonnie
This study examined the effect of three schedule types on student achievement in Advanced Placement Biology classes. AP Biology test scores from students on three types of full-year schedules were analyzed to assess the impact schedule type had on student achievement. The three schedules included the block and traditional schedules, and the rotating/hybrid, a blend of the former two schedules. The results indicated the variable most closely associated with success on the AP Biology exam was the length of experience the teachers had teaching the course, regardless of schedule type. Although significant differences were seen in mean AP Biology test scores among the three schedule types, this could be explained by the relationship between instructors' experience and schedule type. Regression analysis determined the two strongest predictors of successful performance on the AP Biology exam were instructors' experience and perceived teaching style, regardless of schedule type. It appears that the economically developed suburbs, had teachers with the largest amount of experience teaching AP Biology, and these teachers reported using a direct approach to teaching, using lecture greater than 50% of the time. The results of this study also suggest when restructuring to improve student achievement, educators should examine other variables in addition to the high school schedule. Restructuring the day to allow for longer classes must be accompanied by professional staff development to allow teachers to develop new teaching methods. Most of the teachers in the survey reported using lecture a great deal of the time, regardless of schedule type. Comments from the teachers from the various schedules revealed that the ability to add student centered, inquiry based activities and labs were dependent on adequate class time. No information on whether or not the teachers were given professional development to expand their repertoire of teaching methods when the school adopted a block
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
Rathod, Rajiv; Bansal, Prashant; Gutta, Srinivas
2013-01-01
Ureteric stones are usually small and symptomatic. We present a case of a 35-year old female who presented with minimally symptomatic right distal ureteric calculus with proximal hydroureteronephrosis. Laparoscopic right ureterolithotomy was performed and a giant ureteric calculus measuring 11 cm Χ 1.5 cm, weighing 40 g was retrieved. PMID:24082453
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…
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.
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…
Rathod, Rajiv; Bansal, Prashant; Gutta, Srinivas
2013-07-01
Ureteric stones are usually small and symptomatic. We present a case of a 35-year old female who presented with minimally symptomatic right distal ureteric calculus with proximal hydroureteronephrosis. Laparoscopic right ureterolithotomy was performed and a giant ureteric calculus measuring 11 cm Χ 1.5 cm, weighing 40 g was retrieved. PMID:24082453
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…
ERIC Educational Resources Information Center
Zehr, Mary Ann
2006-01-01
When Susan Richman called the College Board in 1992 to ask if her son Jesse could take Advanced Placement tests as a home schooler, a staff member responded that no one had ever asked him that question, but then assured her that home schoolers were welcome to take the tests. Ms. Richman went on to coach Jesse for so many AP exams that he started…
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.
Stochastic calculus in physics
Fox, R.F.
1987-03-01
The relationship of Ito-Stratonovich stochastic calculus to studies of weakly colored noise is explained. A functional calculus approach is used to obtain an effective Fokker-Planck equation for the weakly colored noise regime. In a smooth limit, this representation produces the Stratonovich version of the Ito-Stratonovich calculus for white noise. It also provides an approach to steady state behavior for strongly colored noise. Numerical simulation algorithms are explored, and a novel suggestion is made for efficient and accurate simulation of white noise equations.
Discovering a Geometric Volume Relationship in Calculus.
ERIC Educational Resources Information Center
Morriss, Patrick
1998-01-01
Outlines the discovery of an advanced calculus class based on the generalization of the relationship between the volume of a right circular cone and the volume of a right cylinder with same height and base radius while studying solids of revolution. Relates the course of discovery and concludes with plans to use it to try to generate the same…
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 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.
Cui, Helen; Thomas, Johanna; Kumar, Sunil
2013-01-01
We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging. PMID:23580676
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
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
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.
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
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…
NASA Astrophysics Data System (ADS)
Gionti, S. J. Gabriele
2013-01-01
Recent results in Local Regge Calculus are confronted with Spin Foam Formalism. Introducing Barrett-Crane Quantization in Local Regge Calculus makes it possible to associate a unique Spin jh with an hinge h, fulfilling one of the requirements of Spin Foam definition. It is shown that inter-twiner terms of Spin Foam can follow from the closure constraint in Local Regge Calculus.
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
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.)
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)
ERIC Educational Resources Information Center
Palmaccio, Richard J.
1982-01-01
A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)
Rewriting Calculus: Foundations and Applications
NASA Astrophysics Data System (ADS)
Cirstea, Horatiu
2000-11-01
This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus, which generalizes the first order term rewriting and lambda-calculus, and makes possible the representation of the non-determinism. In our approach the abstraction operator as well as the application operator are objects of calculus. The result of a reduction in the rewriting calculus is either an empty set representing the application failure, or a singleton representing a deterministic result, or a set having several elements representing a not-deterministic choice of results. In this thesis we concentrate on the properties of the rewriting calculus where a syntactic matching is used in order to bind the variables to their current values. We define evaluation strategies ensuring the confluence of the calculus and we show that these strategies become trivial for restrictions of the general rewriting calculus to simpler calculi like the lambda-calculus. The rewriting calculus is not terminating in the untyped case but the strong normalization is obtained for the simply typed calculus. In the rewriting calculus extended with an operator allowing to test the application failure we define terms representing innermost and outermost normalizations with respect to a set of rewriting rules. By using these terms, we obtain a natural and concise description of the conditional rewriting. Finally, starting from the representation of the conditional rewriting rules, we show how the rewriting calculus can be used to give a semantics to ELAN, a language based on the application of rewriting rules controlled by strategies.
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.
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.
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. PMID:26395117
NASA Astrophysics Data System (ADS)
Feinsilver, Philip; Schott, René
2009-09-01
We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.
Rahman, M; Uddin, A; Das, G C; Akanda, N I
2007-07-01
Massive or giant vesical calculus is a rare entity in the recent urological practice. Males are affected more than the females. Vesical calculi are usually secondary to bladder outlet obstruction. These patients present with recurrent urinary tract infection, haematuria or with retention of urine. We report a young male patient who presented with defaecatory problems along with other urinary symptoms. The patient having an average built, non diabetic but hypertensive. The stone could be palpated by physical examination. His urea levels were within normal limits but urine examination shows infection. USG reveals bilateral hydronephrosis with multiple stones in both kidneys along with a giant vesical calculus. After controlling urinary infection and hypertention he underwent an open cystolithotomy. During operation digital rectal help was needed to remove the stone as it was adherent with bladder mucosa. Post operative period was uneventful. His urinary output was quite normal and had no defaecatory problems. Patient left the hospital 10 days after operation. PMID:17917633
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.
Inquiry Calculus and Information Theory
NASA Astrophysics Data System (ADS)
Center, Julian L.
2009-12-01
We consider the relationship between information theory and a calculus of inquiries. We show how an inquiry calculus can be constructed using lattice theory, and how the inquiry calculus relates to information theory. The key idea is to identify both inquiries and variables with partitions of the state space. We also show an approach to extending information theory that deals with the problem of negative entropies on questions that do not correspond to partitions.
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…
ERIC Educational Resources Information Center
Engelhard, George, Jr.; Myford, Carol M.
2003-01-01
The purpose of this study was to examine, describe, evaluate, and compare the rating behavior of faculty consultants who scored essays written for the Advanced Placement English Literature and Composition (AP® ELC) Exam. Data from the 1999 AP ELC Exam were analyzed using FACETS (Linacre, 1998) and SAS. The faculty consultants were not all…
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
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.
Yazawa, Keiichi; Kunisaki, Chikara; Kimura, Jun; Takagawa, Ryo; Minami, Yuta; Makino, Hirochika; Suzuki, Yoshihiro; Tsuburaya, Akira; Akiyama, Hirotoshi; Endo, Itaru
2015-11-01
A 59-year-old man presented with epigastralgia. A diagnosis of advanced gastric cancer MLU, Circ, Type 3, 160 mm, tub2, cT4b (SI: panc), cN1, cM0, cH0, cP0, cCY0, cStage ⅢB was made. Because of difficulty with oral intake due to malignant outlet obstruction and tumor bleeding, endoscopic self-expanding metallic stent placement was performed. We administered chemotherapy involving docetaxel, cisplatin, and S-1(DCS). After 2 courses of chemotherapy, the primary lesion and regional lymph nodes had reduced in size. His response was judged as SD according to the RECIST criteria. The patient elected to undergo explorative laparotomy for assessment of the gastric cancer. The intraoperative findings showed that there was no pancreatic invasion, peritoneal dissemination, or distal metastasis, so a total gastrectomy and D2 lymph node dissection was performed. The pathological findings showed that there were very few cancer cells in the primary lesion, and a lymph node metastasis was found. The final stage was gastric cancer MLU, Circ, Type 3, 100 mm, muc, ypT4a(SE), ypN3a (13/51), ypM0, ypH0, ypP0, ypCY0, ypStage ⅢC. The therapy evaluation was Grade 1b. In summary, we encountered a patient with gastric cancer in whom curative surgery was made possible by undergoing chemotherapy and metallic stent placement. PMID:26805260
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
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
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…
The Basic Principle of Calculus?
ERIC Educational Resources Information Center
Hardy, Michael
2011-01-01
A simple partial version of the Fundamental Theorem of Calculus can be presented on the first day of the first-year calculus course, and then relied upon repeatedly in assigned problems throughout the course. With that experience behind them, students can use the partial version to understand the full-fledged Fundamental Theorem, with further…
Calculus 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…
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;…
Calculus 2, Mathematics: 5297.42.
ERIC Educational Resources Information Center
Gomez, Maria
The second in a four-part sequence for the student seeking Advanced Placement, this booklet emphasizes theory and applications of the derivative and the definite integral. Overall goals and performance objectives are speficied. A course outline, teaching suggestions, and references to state-adopted texts are given for each topic covered. A sample…
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.
Faragò, Giuseppe; Caldiera, Valentina; Tempra, Giovanni; Ciceri, Elisa
2016-02-01
In recent years there has been a progressive increase in interventional neuroradiology procedures, partially due to improvements in devices, but also to the simultaneous development of technologies and radiological images. Cone beam CT (Dyna-CT; Siemens) is a method recently used to obtain pseudo CT images from digital subtraction angiography (DSA) with a flat panel detector. Using dedicated software, it is then possible to merge Dyna-CT images with images from a different source. We report here the usefulness of advanced DSA techniques (Syngo-Dyna CT, three-dimensional DSA iPilot) for the treatment of an intracranial aneurysm with a flow diverter device. Merging MR and Dyna-CT images at the end of the procedure proved to be a simple and rapid additional method of verifying the success of the intervention. PMID:25589548
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.
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
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…
Testicular calculus: A rare case
Sen, Volkan; Bozkurt, Ozan; Demir, Omer; Tuna, Burcin; Yorukoglu, Kutsal; Esen, Adil
2015-01-01
ABSTRACT Background: Testicular calculus is an extremely rare case with unknown etiology and pathogenesis. To our knowledge, here we report the third case of testicular calculus. A 31-year-old man was admitted to our clinic with painful solid mass in left testis. After diagnostic work-up for a possible testicular tumour, he underwent inguinal orchiectomy and histopathologic examination showed a testicular calculus. Case hypothesis: Solid testicular lesions in young adults generally correspond to testicular cancer. Differential diagnosis should be done carefully. Future implications: In young adults with painful and solid testicular mass with hyperechogenic appearance on scrotal ultrasonography, testicular calculus must be kept in mind in differential diagnosis. Further reports on this topic may let us do more clear recommendations about the etiology and treatment of this rare disease. PMID:26200556
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.
Unusual Giant Prostatic Urethral Calculus
Bello, A.; Maitama, H. Y.; Mbibu, N. H.; Kalayi, G. D.; Ahmed, A.
2010-01-01
Giant vesico-prostatic urethral calculus is uncommon. Urethral stones rarely form primarily in the urethra, and they are usually associated with urethral strictures, posterior urethral valve or diverticula. We report a case of a 32-year-old man with giant vesico-prostatic (collar-stud) urethral stone presenting with sepsis and bladder outlet obstruction. The clinical presentation, management, and outcome of the giant prostatic urethral calculus are reviewed. PMID:22091328
Opening up placement opportunities for students.
Hill, Phillipa; Bullpitt, Samantha; Dean, Sharon; O'Flanagan, Sheryl; Fishburn, Nicky
Student nurses need a variety of high-quality practice placements to prepare them for qualification yet, in reality, this can be difficult to achieve. A practice placement allocation model has enabled one university and its partner healthcare organisations to shift from a traditional, process-led system to a robust, proactive, student-focused approach. The model is based on partnership concepts including advance planning of student placements and clear lines of communication. It has resulted in 100% of first-year students taking part in a new fundamentals of care placement and received positive feedback from students and mentors. PMID:26012012
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.
``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.
A Discrete Approach to the Calculus.
ERIC Educational Resources Information Center
Gordon, Sheldon P.
1979-01-01
The calculus of finite differences and finite sums is used to create a context in which the computer can be incorporated into calculus courses. Analyses of the experimental implementations are included. (MP)
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.…
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.)
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…
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 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…
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…
The Pendulum and the Calculus.
ERIC Educational Resources Information Center
Sworder, Steven C.
A pair of experiments, appropriate for the lower division fourth semester calculus or differential equations course, are presented. The second order differential equation representing the equation of motion of a simple pendulum is derived. The period of oscillation for a particular pendulum can be predicted from the solution to this equation. As a…
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…
Constructivized Calculus in College Mathematics
ERIC Educational Resources Information Center
Lawrence, Barbara Ann
2012-01-01
The purpose of this study is to present some of the classical concepts, definitions, and theorems of calculus from the constructivists' point of view in the spirit of the philosophies of L.E.J. Brouwer and Errett Bishop. This presentation will compare the classical statements to the constructivized statements. The method focuses on giving…
A "Model" Multivariable Calculus Course.
ERIC Educational Resources Information Center
Beckmann, Charlene E.; Schlicker, Steven J.
1999-01-01
Describes a rich, investigative approach to multivariable calculus. Introduces a project in which students construct physical models of surfaces that represent real-life applications of their choice. The models, along with student-selected datasets, serve as vehicles to study most of the concepts of the course from both continuous and discrete…
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,…
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…
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…
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
Toward lattice fractional vector calculus
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2014-09-01
An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.
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.
Variational calculus on Banach spaces
Uglanov, A V
2000-10-31
The problem of variational calculus is considered in a (variable) subdomain of a Banach space. Analogues of the basic principles of the finite-dimensional theory are derived: the main formula for variations of a functional, necessary conditions of an extremum, Noether's theorem. All the results obtained are dimension-invariant and become the classical ones in the finite-dimensional setting. The main tool of the analysis is the theory of surface integration in Banach spaces.
Schubert calculus and singularity theory
NASA Astrophysics Data System (ADS)
Gorbounov, Vassily; Petrov, Victor
2012-02-01
Schubert calculus has been in the intersection of several fast developing areas of mathematics for a long time. Originally invented as the description of the cohomology of homogeneous spaces, it has to be redesigned when applied to other generalized cohomology theories such as the equivariant, the quantum cohomology, K-theory, and cobordism. All this cohomology theories are different deformations of the ordinary cohomology. In this note, we show that there is, in some sense, the universal deformation of Schubert calculus which produces the above mentioned by specialization of the appropriate parameters. We build on the work of Lerche Vafa and Warner. The main conjecture these authors made was that the classical cohomology of a Hermitian symmetric homogeneous manifold is a Jacobi ring of an appropriate potential. We extend this conjecture and provide a simple proof. Namely, we show that the cohomology of the Hermitian symmetric space is a Jacobi ring of a certain potential and the equivariant and the quantum cohomology and the K-theory is a Jacobi ring of a particular deformation of this potential. This suggests to study the most general deformations of the Frobenius algebra of cohomology of these manifolds by considering the versal deformation of the appropriate potential. The structure of the Jacobi ring of such potential is a subject of well developed singularity theory. This gives a potentially new way to look at the classical, the equivariant, the quantum and other flavors of Schubert calculus.
Jet-calculus approach including coherence effects
Jones, L.M.; Migneron, R.; Narayanan, K.S.S.
1987-01-01
We show how integrodifferential equations typical of jet calculus can be combined with an averaging procedure to obtain jet-calculus-based results including the Mueller interference graphs. Results in longitudinal-momentum fraction x for physical quantities are higher at intermediate x and lower at large x than with the conventional ''incoherent'' jet calculus. These results resemble those of Marchesini and Webber, who used a Monte Carlo approach based on the same dynamics.
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.
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. PMID:20163661
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 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…
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…
[Pharmacological action of cultured calculus bovis].
Yuan, H
1991-02-01
By means of comparative pharmacological study, the main pharmacodynamics and toxicity of cultured calculus bovis and natural calculus bovis were compared under the same conditions. The results show that both drugs possess sedative, antispasmodic, antipyretic, antiinflammatory, cardiotonic and hypotensive effects, the strength of effect and toxicity being similar. PMID:1872960
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 Snapshot of the Calculus Classroom
ERIC Educational Resources Information Center
Weathers, Tony D.; Latterell, Carmen M.
2003-01-01
Essentially a focus group to discuss textbook related issues, a meeting of calculus instructors from a wide variety of environments was convened and sponsored by McGraw Hill to provide feedback on the current state of the calculus classroom. This paper provides a description of the group's discussions.
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…
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…
Can We Learn Calculus from a Jerk?
ERIC Educational Resources Information Center
Kenyon, Paula L.; Bardzell, Michael J.
2001-01-01
Summarizes an interdisciplinary undergraduate research project involving experimental physics and calculus and illustrates how mathematics was used to finesse incomplete experimental information and maximize physical quantity known as jerk. Describes how calculus can be applied in the "real world" where functions are not always given by nice…
Some Calculus Affordances of a Graphics Calculator
ERIC Educational Resources Information Center
Kissane, Barry; Kemp, Marian
2008-01-01
Calculus at the secondary school level has traditionally represented the peak of school mathematics in Australia, and has been available only to the most capable students. Until recently, many calculus curricula have focused on developing standard techniques, such as those concerned with differentiation and integration, with an emphasis on…
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…
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.
Attendance and Attainment in a Calculus Course
ERIC Educational Resources Information Center
Meulenbroek, Bernard; van den Bogaard, Maartje
2013-01-01
In this paper the relationship between attendance and attainment in a standard calculus course is investigated. Calculus could in principle be studied without attending lectures due to the wealth of material available (in hardcopy and online). However, in this study we will show that the pass rate of students attending classes regularly (>75%…
A 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…
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)
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)
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,…
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.
Geometric calculus: a new computational tool for Riemannian geometry
Moussiaux, A.; Tombal, P.
1988-05-01
We compare geometric calculus applied to Riemannian geometry with Cartan's exterior calculus method. The correspondence between the two methods is clearly established. The results obtained by a package written in an algebraic language and doing general manipulations on multivectors are compared. We see that the geometric calculus is as powerful as exterior calculus.
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…
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.
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
ERIC Educational Resources Information Center
Segal, Stanley; And Others
1970-01-01
Two part presentation consisting, first, of study of reports indicating lack of imagination on part of placement directors, and second, of a nonstereotyped approach which puts emphasis on operating principles rather than on statistical data. (Author/CJ)
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
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…
Context Problems in Realistic Mathematics Education: A Calculus Course as an Example.
ERIC Educational Resources Information Center
Gravemeijer, Koeno; Doorman, Michiel
1999-01-01
Discusses the role of context problems as they are used in the Dutch approach known as realistic mathematics education (RME). Uses an RME design for a calculus course to illustrate that theory based on the design heuristic using context problems and modeling, which was developed for primary school mathematics, also fits advanced topics such as…
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…
Extending Stochastic Network Calculus to Loss Analysis
Yu, Li; Zheng, Jun
2013-01-01
Loss is an important parameter of Quality of Service (QoS). Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor. PMID:24228019
Null-strut calculus. II. Dynamics
Kheyfets, A.; LaFave, N.J.; Miller, W.A. )
1990-06-15
In this paper, we continue from the preceding paper to develop a fully functional Regge calculus geometrodynamic algorithm from the null-strut-calculus construction. The developments discussed include (a) the identification of the Regge calculus analogue of the constraint and evolution equations on the null-strut lattice, (b) a description of the Minkowski solid geometry for the simplicial blocks of the null-strut lattice, (c) a description of the evolution algorithm for the geometrodynamic scheme and an analysis of its consistency, and (d) a presentation of the dynamical degrees of freedom for a simplicial hypersurface and the description of an initial-value prescription. To demonstrate qualitatively this new approach to geometrodynamics, we present the most simple application of null-strut calculus that we know of---the Friedmann cosmology using the three-boundary of a 600-cell simplicial polytope to model the simplicial hypersurface.
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.
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.
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. PMID:26029303
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. PMID:26029303
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
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.
A phenomenological calculus of Wiener description space.
Richardson, I W; Louie, A H
2007-10-01
The phenomenological calculus is a categorical example of Robert Rosen's modeling relation. This paper is an alligation of the phenomenological calculus and generalized harmonic analysis, another categorical example. Our epistemological exploration continues into the realm of Wiener description space, in which constitutive parameters are extended from vectors to vector-valued functions of a real variable. Inherent in the phenomenology are fundamental representations of time and nearness to equilibrium. PMID:17955459
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.
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.
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.
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. PMID:25476244
Assessment of Field Placement.
ERIC Educational Resources Information Center
Marshood, Nabil
While field placement in human services programs is an extremely important practical phase of training, it has generally not been standardized, and thus can be difficult to assess. A model program and assessment format developed by Hudson County Community College (HCCC), in Jersey City, New Jersey, however, provides a possible framework for…
Technology Transfer Automated Retrieval System (TEKTRAN)
The purpose of this study was to determine the effects on fish production, water quality and economics of concentrating paddlewheel aeration in large commercial ponds, compared to the current method of aerator placement. Ten 17-acre ponds (approximately 600 X 1300 ft) were brought into the study in ...
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)
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
Fractional vector calculus and fractional Maxwell's equations
Tarasov, Vasily E.
2008-11-15
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered.
The giant calculus within the prostatic urethra.
Demir, Omer; Kefi, Aykut; Cahangirov, Asif; Cihan, Ahmet; Obuz, Funda; Esen, Adil Ahmet; Celebi, Ilhan
2011-08-01
The giant calculus within the prostatic urethra is a rare clinical entity in the young population. Most of the calculi within the urethra migrate from the urinary bladder and obliterate the urethra. These stones are often composed of calcium phosphate or calcium oxalate. The decision of treatment strategy is affected by the size, shape and position of the calculus and by the status of the urethra. If the stone is large and immovable, it may be extracted via the perineal or the suprapubic approach. In most cases, the giant calculi were extracted via the transvesical approach and external urethrotomy. Our case is the biggest prostatic calculus, known in the literature so far, which was treated endoscopically by the combination of laser and the pneumatic lithotriptor. PMID:21188583
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.
Early Diagnosis of a Large Vesical Calculus Complicating Pregnancy
Pricilla, Ruby Angeline; David, Kirubah Vasandhi; Venkatesan, Sankarapandian; Benjamin, Santosh Joseph
2013-01-01
Vesical calculus-complicating pregnancy is rare. This is a case report of a large vesical calculus-complicating pregnancy. The early diagnosis and appropriate surgical management of the large vesical calculus prevented complications like recurrent urinary tract infections and obstructed labor. It enabled the mother to have an uneventful vaginal delivery. PMID:24479053
Laparoscopic Ureterolithotomy for Giant Ureteric Calculus: A Case Report.
Magdum, Prasad V; Nerli, Rajendra B; Devaraju, Shishir; Hiremath, Murigendra B
2015-09-01
We present a case of a 21 year old male who presented with symptomatic right upper ureteric calculus measuring 5 cm × 1.5 cm fulfilling the criteria to be named as giant ureteric calculus. Laparoscopic right ureterolithotomy was performed and the giant ureteric calculus was retrieved. PMID:26793529
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…
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…
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 novel guide catheter enabling intracranial placement.
Hurley, Michael C; Sherma, Arun K; Surdell, Daniel; Shaibani, Ali; Bendok, Bernard R
2009-11-15
We describe use of a novel guide, catheter with a soft and pliable, 6-cm or 12-cm distal segment that enables distal, including intracranial, placement--the Neuron guide catheter (Penumbra, San Leandro, CA)--in the treatment of 11 cases with a range of neuroendovascular lesions. We were able to advance the Neuron guide catheter to the intended level in each case and suffered no complications related to catheter spasm, dissection, thrombosis or thromboembolism. PMID:19670314
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.
Connes' calculus for the quantum double suspension
NASA Astrophysics Data System (ADS)
Chakraborty, Partha Sarathi; Guin, Satyajit
2015-02-01
Given a spectral triple (A, H, D) Connes associated a canonical differential graded algebra ΩD• (A) . However, so far this has been computed for very few special cases. We identify suitable hypotheses on a spectral triple that helps one to compute the associated Connes' calculus for its quantum double suspension. This allows one to compute ΩD• for spectral triples obtained by iterated quantum double suspension of the spectral triple associated with a first order differential operator on a compact smooth manifold. This gives the first systematic computation of Connes' calculus for a large family of spectral triples.
Null-strut calculus. I. Kinematics
Kheyfets, A.; LaFave, N.J.; Miller, W.A. )
1990-06-15
This paper describes the kinematics of null-strut calculus---a 3+1 Regge calculus approach to general relativity. We show how to model the geometry of spacetime with simplicial spacelike three-geometries (TET's) linked to earlier'' and later'' momentumlike lattice surfaces (TET{sup *}) entirely by light rays or null struts.'' These three-layered lattice spacetime geometries are defined and analyzed using combinatorial formulas for the structure of polytopes. The following paper in this series describes how these three-layered spacetime lattices are used to model spacetimes in full conformity with Einstein's theory of gravity.
Detection, removal and prevention of calculus: Literature Review
Kamath, Deepa G.; Umesh Nayak, Sangeeta
2013-01-01
Dental plaque is considered to be a major etiological factor in the development of periodontal disease. Accordingly, the elimination of supra- and sub-gingival plaque and calculus is the cornerstone of periodontal therapy. Dental calculus is mineralized plaque; because it is porous, it can absorb various toxic products that can damage the periodontal tissues. Hence, calculus should be accurately detected and thoroughly removed for adequate periodontal therapy. Many techniques have been used to identify and remove calculus deposits present on the root surface. The purpose of this review was to compile the various methods and their advantages for the detection and removal of calculus. PMID:24526823
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.
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,…
Cartan calculus on quantum Lie algebras
Schupp, P.; Watts, P.; Zumino, B.
1993-12-09
A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions au into one big algebra, the ``Cartan Calculus.``
Discrete quantum gravity; The Regge calculus approach
Williams, J.W. )
1992-06-01
After a brief introduction to Regge calculus, some examples of its application is quantum gravity are described in this paper. In particular, the earliest such application, by Ponzano and Regge, is discussed in some detail and it is shown how this leads naturally to current work on invariants of three-manifolds.
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
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
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…
Maple Graphing Tools for Calculus III
ERIC Educational Resources Information Center
Cook, Darwyn
2006-01-01
For those instructors lacking artistic skills, teaching 3-dimensional calculus can be a challenge. Although some instructors spend a great deal of time working on their illustrations, trying to get them just right, students nevertheless often have a difficult time understanding some of them. To address this problem, the author has written a series…
Using the Microcomputer to Enhance Calculus Teaching.
ERIC Educational Resources Information Center
Clayton, Debbie; And Others
1990-01-01
Discusses differences between computer-enhanced learning (CEL) and computer-aided learning (CAL), and describes a microcomputer-based graph-plotting program called Capgraph that was developed for use in a college calculus course. Results of a course evaluation are presented; student attitudes are described; and future considerations are discussed.…
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…
Areas and the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Vajiac, A.; Vajiac, B.
2008-01-01
We present a concise, yet self-contained module for teaching the notion of area and the Fundamental Theorem of Calculus for different groups of students. This module contains two different levels of rigour, depending on the class it used for. It also incorporates a technological component. (Contains 6 figures.)
Using Discovery in the Calculus Class
ERIC Educational Resources Information Center
Shilgalis, Thomas W.
1975-01-01
This article shows how two discoverable theorems from elementary calculus can be presented to students in a manner that assists them in making the generalizations themselves. The theorems are the mean value theorems for derivatives and for integrals. A conjecture is suggested by pictures and then refined. (Author/KM)
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…
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…
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…
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…
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,…
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.
Beliefs about Proof in Collegiate Calculus.
ERIC Educational Resources Information Center
Raman, Manya
The broad aim of this research is to characterize the views of proof held by college calculus students and their two types of teachers mathematics graduate students and professors. The analysis is based on an examination of the ways in which people in all three groups produce and evaluate different types of solutions to a proof-based problem from…
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.
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…
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.
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
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.
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
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
Client-Centered Placement Revisited: A Dialogue on Placement Philosophy
ERIC Educational Resources Information Center
Salomone, Paul R.; Usdane, William M.
1977-01-01
The authors take substantially different philosophical stances concerning placement in the rehabilitation process. Usdane believes that job placement is not given enough attention by rehabilitation counselors early in the rehabilitation process. Salomone advocates a greater emphasis on client growth and independence. (Author)
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
Attendance and attainment in a Calculus course
NASA Astrophysics Data System (ADS)
Meulenbroek, Bernard; van den Bogaard, Maartje
2013-10-01
In this paper the relationship between attendance and attainment in a standard calculus course is investigated. Calculus could in principle be studied without attending lectures due to the wealth of material available (in hardcopy and online). However, in this study we will show that the pass rate of students attending classes regularly (>75% of the classes) is much higher than the pass rate of students attending fewer classes. We use a logistic model to investigate whether this correlation is significant. We will argue why we believe that this correlation between attendance and attainment is causal, i.e. why it is necessary for most students to attend classes in order to (improve their chances to) pass the exam.
Two cosmological solutions of Regge calculus
Lewis, S.M.
1982-01-15
Two cosmological solutions of Regge calculus are presented which correspond to the flat Friedmann-Robertson-Walker and the Kasner solutions of general relativity. By taking advantage of the symmetries that are present, I am able to show explicitly that a limit of Regge calculus does yield Einstein's equations for these cases. The method of averaging these equations when taking limits is important, especially for the Kasner model. I display the leading error term that arises from keeping the Regge equations in discrete form rather than using their continuum limit. In particular, this work shows that for the ''Reggeized'' Friedmann model the minimum volume is a velocity-dominated singularity as in the continuum Friedmann model. However, unlike the latter, the Regge version has a nonzero minimum volume.
Getzler symbol calculus and deformation quantization
NASA Astrophysics Data System (ADS)
Mesa, Camilo
2013-11-01
In this paper we give a construction of Fedosov quantization incorporating the odd variables and an analogous formula to Getzler's pseudodifferential calculus composition formula is obtained. A Fedosov type connection is constructed on the bundle of Weyl tensor Clifford algebras over the cotangent bundle of a Riemannian manifold. The quantum algebra associated with this connection is used to define a deformation of the exterior algebra of Riemannian manifolds.
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.
A new boson calculus for SU(3)
Prakash, J.S.; Sharatchandra, H.S.
1997-09-01
It is shown that the Gelfand-Weyl pattern for SU(3) can be uniquely expressed in terms of four non-negative and one positive or negative free integers. This provides an optimal, albeit non-linear, boson calculus for SU(3) in terms of four harmonic oscillators and one planar rotor. (By optimal it is meant that every irreducible representation is obtained once and once only.) Our techniques can be generalized to other groups. {copyright} {ital 1997 American Institute of Physics.}
MAPP: A Mathematics Placement Program.
ERIC Educational Resources Information Center
Doblin, Stephen A.
1978-01-01
MAPP (A Mathematics Placement Program) uses two COBOL programs to place entering freshmen in mathematics courses which are commensurate with their backgrounds and abilities. Having been used for three years, the program is considered to be a viable alternative to the traditional mathematics placement process. (Author/JKS)
Computerized Placement Tests: Background Readings.
ERIC Educational Resources Information Center
College Entrance Examination Board, Princeton, NJ.
This document is a compilation of background readings for the user of Computerized Placement Tests (CPTs) developed by the College Board for student placement purposes. CPTs are computerized adaptive tests that test the individual abilities and backgrounds of examinees. CPTs are part of the ACCUPLACER student information management system. The…
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…
Job Placement Services Research Study.
ERIC Educational Resources Information Center
McLeod, Pat N.; Tobias, Jeanette
A mailout questionnaire was used in a study which focused on three areas of inquiry: (1) Needs assessment for job placement programs in public schools as viewed by superintendents of school districts and vocational administrators of occupational programs, (2) assessment of the perceived and established benefits of a placement program from the…
30 CFR 57.22004 - Category placement or change in placement.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 30 Mineral Resources 1 2013-07-01 2013-07-01 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, 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,...
30 CFR 57.22004 - Category placement or change in placement.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 30 Mineral Resources 1 2010-07-01 2010-07-01 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, 2014 CFR
2014-07-01
... 30 Mineral Resources 1 2014-07-01 2014-07-01 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,...
Nonnumeric Computer Applications to Algebra, Trigonometry and Calculus.
ERIC Educational Resources Information Center
Stoutemyer, David R.
1983-01-01
Described are computer program packages requiring little or no knowledge of computer programing for college algebra, calculus, and abstract algebra. Widely available computer algebra systems are listed. (MNS)
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
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.
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.
Dietitians and small bowel feeding tube placement.
Marsland, Cheryl
2010-06-01
Some advanced practice nutrition support dietitians have added small bowel feeding tube placement to their scope of responsibility. This is due, in part, to the challenges of gaining early enteral access in patients with functioning GI tracts. Emerging literature supports the practice of skilled practitioners placing feeding tubes at bedside. A variety of methods can be used to place tubes at the bedside. The nutrition support dietitian must understand licensure and liability considerations to perform this invasive procedure. This article will review literature reports of dietitians placing feeding tubes and provide information on the methods used, training and competencies required, and legal issues involved. PMID:20581321
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
Computerized Placement Management Software (CPMS): User Manual, Version 3.0.
ERIC Educational Resources Information Center
College Entrance Examination Board, Princeton, NJ.
This guide is designed to enable the beginner, as well as the advanced user, to understand and use the Computerized Placement Management Software (CPMS). The CPMS is a system for evaluating information about students and recommending their placement into courses best suited for them. It also tracks their progress and maintains their records. The…
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…
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…
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…
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…
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…
Kernel-Based Discriminant Techniques for Educational Placement
ERIC Educational Resources Information Center
Lin, Miao-hsiang; Huang, Su-yun; Chang, Yuan-chin
2004-01-01
This article considers the problem of educational placement. Several discriminant techniques are applied to a data set from a survey project of science ability. A profile vector for each student consists of five science-educational indicators. The students are intended to be placed into three reference groups: advanced, regular, and remedial.…
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…
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.)
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…
Modelling the landing of a plane in a calculus lab
NASA Astrophysics Data System (ADS)
Morante, Antonio; Vallejo, José A.
2012-10-01
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.
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…
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
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…
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…
Visualization and Students' Performance in Technology-Based Calculus.
ERIC Educational Resources Information Center
Galindo, Enrique
The relationship between college students' preferred mode of processing mathematical information--visual or nonvisual--and their performance in calculus classes with and without technology was investigated. Students elected one of three different versions of an introductory differential calculus course: using graphing calculators, using the…
Discovering and Experiencing the Fundamental Theorem of Calculus.
ERIC Educational Resources Information Center
Rosenthal, Bill
1992-01-01
Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…
Calculus, Part 2, Student's Text, Unit No. 67. Revised Edition.
ERIC Educational Resources Information Center
Beck, A.; And Others
This is part two 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…
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.
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…
How Students Use Physics to Reason about Calculus Tasks
ERIC Educational Resources Information Center
Marrongelle, Karen A.
2004-01-01
The present research study investigates how undergraduate students in an integrated calculus and physics class use physics to help them solve calculus problems. Using Zandieh's (2000) framework for analyzing student understanding of derivative as a starting point, this study adds detail to her "paradigmatic physical" context and begins to address…
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…
Using the Finite Difference Calculus to Sum Powers of Integers.
ERIC Educational Resources Information Center
Zia, Lee
1991-01-01
Summing powers of integers is presented as an example of finite differences and antidifferences in discrete mathematics. The interrelation between these concepts and their analogues in differential calculus, the derivative and integral, is illustrated and can form the groundwork for students' understanding of differential and integral calculus.…
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…
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
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…
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…
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…
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…
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…
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.
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)
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…
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…
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…
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.
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…
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…
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…
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…
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…
Heavy quarks in the jet calculus
Jones, L.M.
1983-07-01
In this paper we explore a method for treating heavy quarks such as c and b quarks within the jet calculus. These quarks are differentiated from the more common u, d, and s quarks by the requirement that the gluons never branch into heavy-quark pairs during the jet development. We compute and discuss the charmed-quark ''propagators''; the x distribution of colorless clusters containing a charmed quark, a noncharmed antiquark, and gluons; and the mass distribution of the parent partons giving rise to these colorless clusters.
Equation of motion using fractional calculus
Kihong, Kwon.
1991-01-01
One-dimensional motion of a particle was studied using fractional calculus, which is the differentiation and the integration of arbitrary order. By fractional differentiation, equation of motion could be written in compact form. Fractional parameters were numerically calculated by using the known solutions of general relativistic free fall motion. Also, from the approximate forms for fractional parameters, the physical meanings were found. The fractional parameters depended on the proper time, the mass of gravitating body, and the initial radial coordinate of the particle.
Heisenberg algebra, umbral calculus and orthogonal polynomials
Dattoli, G.; Levi, D.; Winternitz, P.
2008-05-15
Umbral calculus can be viewed as an abstract theory of the Heisenberg commutation relation [P,M]=1. In ordinary quantum mechanics, P is the derivative and M the coordinate operator. Here, we shall realize P as a second order differential operator and M as a first order integral one. We show that this makes it possible to solve large classes of differential and integrodifferential equations and to introduce new classes of orthogonal polynomials, related to Laguerre polynomials. These polynomials are particularly well suited for describing the so-called flatenned beams in laser theory.
An elementary calculus method for evaluating ?
NASA Astrophysics Data System (ADS)
Lee, Tuo Yeong; Xiong, Yuxuan
2014-08-01
We use freshman calculus to prove that
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.
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
Denoising Medical Images using Calculus of Variations
Kohan, Mahdi Nakhaie; Behnam, Hamid
2011-01-01
We propose a method for medical image denoising using calculus of variations and local variance estimation by shaped windows. This method reduces any additive noise and preserves small patterns and edges of images. A pyramid structure-texture decomposition of images is used to separate noise and texture components based on local variance measures. The experimental results show that the proposed method has visual improvement as well as a better SNR, RMSE and PSNR than common medical image denoising methods. Experimental results in denoising a sample Magnetic Resonance image show that SNR, PSNR and RMSE have been improved by 19, 9 and 21 percents respectively. PMID:22606674
Combining Cooperative Education and Placement.
ERIC Educational Resources Information Center
Lentz, Glenda F.
1984-01-01
Suggests that placement, like cooperative education, can function better in academic affairs rather than student affairs. Describes the combination of the two departments at the University of South Florida and discusses advantages and disadvantages of a combined program. (JAC)
Calculus detection technologies: where do we stand now?
Archana, V
2014-01-01
Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data. PMID:25870667
Initialization, conceptualization, and application in the generalized (fractional) calculus.
Lorenzo, Carl F; Hartley, Tom T
2007-01-01
This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions. PMID:19583533
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.
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... Educational Placements Development of Iep § 300.327 Educational placements. Consistent with § 300.501(c), each... makes decisions on the educational placement of their child. (Authority: 20 U.S.C. 1414(e))...
Arcjet Testing of Woven Carbon Fabric Seams for Adapative Deployable Placement Technology
NASA Astrophysics Data System (ADS)
Arnold, J. O.; de Jong, M.; Prabhu, D. K.; Boghozian, T.; Kruger, C.; Cassell, A. M.
2014-06-01
The joining of gores of woven carbon fabric, robust to loading experienced during atmospheric entry is enabling for Advanced Deployable Entry Placement Technology. This paper demonstrates the viability stitched seams for use in ADEPT vehicles.
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…
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.
Calculus and analytic geometry. Second edition
Mizrahi, A.; Sullivan, M.
1986-01-01
This book presents the details of calculus and analytic geometry. The topics covered are: Introduction. Real Numbers. Graphing. The Straight Line. Functions and Their Graphs. Operations on Functions; Types of Functions. Composite Functions. Inverse Functions. Limits from an Intuitive Point of View. Algebraic Techniques for Finding Limits. One-Sided Limits. Continuous Functions. Limit Theorems (If Time Permits). Historical Perspectives. The Derivative. Average Rate of Change. Instantaneous Rate of Change; the Derivative. Two Interpretations of the Derivative Formulas for Finding Derivatives. Formulas for Finding Derivatives (Continued). Higher-Order Derivatives. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Derivative of an Inverse Function; Rational Exponents. Newton's Method of Solving Equations. Functions that are not Differentiable at c., Applications of the Derivative. Related Rates. Differentials. Maxima and Minima. Rolle's Theorem; Mean Value Theorem. Increasing and Decreasing Functions; First Derivative Test. Concavity; Second Derivative Test. Limits at Infinity; Infinite Limits; Asymptotes. Applied Extrema Problems. Antiderivatives. Application to Economics (If Time Permits), The Definite Integral. Area. Evaluation of Area. The Definite Integral. The Fundamental Theorem of Calculus. Properties of the Definite Integral. The Indefinite Integral; Method of Substitution. Historical Perspectives. Applications of the Integral. Area. Volume of a Solid of Revolution: Disk Method. Volume of a Solid of Revolution: Shell Method. Volume by Slicing. Arc Length. Work. Liquid Pressure and Force. Average Value of a Function.
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
Effective conflict resolution strategies for SRAF placement
NASA Astrophysics Data System (ADS)
Ganjugunte, Shashidhara K.; Strecker, Norbert; Jayaram, Srividya; LaCour, Pat; Torunoglu, Ilhami
2015-07-01
Sub-Resolution Assist Features (SRAFs) have emerged as a key technology to enable semiconductor manufacturing for advanced technology nodes. SRAF placement is required to adhere to manufacturability constraints (MRC). MRC specifications are distance and size constraints specified by the user to ensure SRAFs are not detrimental to the final target shapes being printed. Conceptually, SRAF placement can be divided into two steps - SRAF candidate generation and SRAF candidate cleanup or conflict resolution. SRAFs generated as candidates may not adhere to MRC constraints. It is during the cleanup/conflict resolution process that the MRC constraints are enforced. In this paper we focus on the latter phase - cleanup. The goal of the cleanup phase is to retain as much of the initial candidates as possible, and, if necessary, transform them to adhere to MRC conditions. An SRAF is said to be in conflict with another shape if it violates the distance MRC constraint. One can model these conflicts using a conflict graph G=(V,E), whose vertices V correspond to geometric shapes involved in a conflict and an edge is present in E, between two vertices if the corresponding shapes are involved in a conflict. A weight is associated with each vertex that could, for example, correspond to area of the corresponding shape. The goal of conflict resolution then, is to find a transformation of the vertices so that the resulting graph is conflict free while maximizing the weight of vertices retained. This can be viewed as a generalization of the computationally hard problem of finding the largest independent set of candidates, albeit allowing for transformation. The transformations we allow include deletion, splitting, resizing, merge, and bounded translation. In this paper, we describe an approach which classifies the conflicts and apply appropriate transformations to achieve effective SRAF placement. Further, we demonstrate that such a strategy reduces the number of rules to be specified by
Discrete Quantum Gravity in the Regge Calculus Formalism
Khatsymovsky, V.M.
2005-09-01
We discuss an approach to the discrete quantum gravity in the Regge calculus formalism that was developed in a number of our papers. The Regge calculus is general relativity for a subclass of general Riemannian manifolds called piecewise flat manifolds. The Regge calculus deals with a discrete set of variables, triangulation lengths, and contains continuous general relativity as a special limiting case where the lengths tend to zero. In our approach, the quantum length expectations are nonzero and of the order of the Plank scale, 10{sup -33} cm, implying a discrete spacetime structure on these scales.
Constraints from jet calculus on quark recombination
Jones, L.M.; Lassila, K.E.; Sukhatme, U.; Willen, D.
1981-02-01
Within the quantum-chromodynamic jet-calculus formalism, we deduce an equation describing recombination of quarks and antiquarks into mesons within a quark or gluon jet. This equation relates the recombination function R(x/sub 1/,x/sub 2/,x) used in current literature to the fragmentation function for producing that same meson out of the parton initiating the jet. We submit currently used recombination functions to our consistency test, taking as input mainly the u-quark fragmentation ''data'' into ..pi../sup +/ mesons. The qq-bar..--> pi.. recombination functions popular in the literature are consistent with measured fragmentation functions, but they must be supplemented by other contributions to provide the full D..pi../sup +//sub u/. We also discuss the Q/sup 2/ dependence of the resulting fragmentation functions.
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. __________________________________________________
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.
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.
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
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
Problems with the rush toward advanced physics in high schools
NASA Astrophysics Data System (ADS)
Gollub, Jerry
2003-04-01
The Advanced Placement (AP) Program has a major impact on the physics experience of many high school students. It affects admission to college, course choices and performance in college, and subsequent career decisions. A study committee of the National Research Council published a review of these programs in 2002, and concluded that while the program has many positive features, important problems need to be addressed. [1] The programs are not currently consistent with what we have learned about student learning from cognitive research. Students are often poorly prepared for AP courses, because of lack of coordination within schools. The Physics AP-B (non-calculus) program is too broad to allow most high school students to achieve an adequate level of conceptual understanding. Participation by minority students in these programs is far below that of other students. The AP exams need to be re-evaluated to insure that they actually measure conceptual understanding and complex reasoning. The AP exams are sometimes used inappropriately to rate teachers or schools. College and high school courses are poorly coordinated, with the result that students often take an introductory physics survey as many as three times. Policies on college credit for AP courses differ widely. These problems cannot be fixed by the College Board alone. [1] Jerry P. Gollub and Robin Spital, "Advanced Physics in the High Schools", Physics Today, May 2002.
Modified jet calculus of Bassetto, Ciafaloni and Marchesini
Jones, L.M.; Lassila, K.E.
1982-06-01
We reexamine some of the equations derived by Bassetto, Ciafaloni, and Marchesini for the various functions in their extended jet calculus, and derive an alternative set of equations based on the same concepts.
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.
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.
A Discrete Approach to Computer-Oriented Calculus.
ERIC Educational Resources Information Center
Gordon, Sheldon P.
1979-01-01
Some of the implications and advantages of an instructional approach using results from the calculus of finite differences and finite sums, both for motivation and as tools leading to applications, are discussed. (MP)
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.
Candida dubliniensis encrustation of an obstructing upper renal tract calculus
O'Kane, Dermot; Kiosoglous, Anthony; Jones, Kay
2013-01-01
We present the case of a 53-year-old man, with a history of alcohol abuse, requiring intensive care unit admission, with an obstructing right upper renal calculus and Klebsiella pneumoniae urosepsis. Ureteroscopic treatment of this obstruction displayed a small calculus within the renal pelvis completely encapsulated within a fungal bezoar. Laboratory analysis of the fungal mass found it to be Candida dubliniensis. PMID:23975908
Three-plus-one formulation of Regge calculus
Piran, T.; Williams, R.M.
1986-03-15
Following the work of Lund and Regge for homogeneous spaces, we construct the action for Regge calculus in its three-plus-one form for general space-times. This is achieved in two ways: a first-order formalism and a second-order formalism. We describe the Regge-calculus analogue of solving the initial-value equations using conformal transformations. The second-order formalism is used to study the time development of two simple model universes.
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.
Hermeneutics of differential calculus in eighteenth-century northern Germany.
Blanco, Mónica
2008-01-01
This paper applies comparative textbook analysis to studying the mathematical development of differential calculus in northern German states during the eighteenth century. It begins with describing how the four textbooks analyzed presented the foundations of calculus and continues with assessing the influence each of these foundational approaches exerted on the resolution of problems, such as the determination of tangents and extreme values, and even on the choice of coordinates for both algebraic and transcendental curves. PMID:19244874
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.
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 Professional as Marketeer.
ERIC Educational Resources Information Center
Walz, Garry R.
1988-01-01
Discusses resistance of helping professions to marketing. Defines human services marketing. Describes forces that are placing human services in an increasingly competitive position. Makes recommendations to enhance the image of career planning and placement services and increase their usage. Concludes that by adopting a marketeer orientation,…
When Placement People Are Displaced.
ERIC Educational Resources Information Center
Ehrlich, Marianne
1991-01-01
Describes the experiences and insights of five laid-off placement people who discover the trauma of job loss. Discusses grieving a job loss, the emotions involved, the challenge of finding a new job, guilt faced by survivors, and advice to colleagues. (NB)
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.
Water content contribution in calculus phantom ablation during Q-switched Tm:YAG laser lithotripsy.
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. PMID:26662067
Lumbar Catheter Placement Using Paramedian Approach Under Fluoroscopic Guidance
Qureshi, Adnan I.; Khan, Asif A.; Malik, Ahmed A.; Afzal, Mohammad Rauf; Herial, Nabeel A.; Qureshi, Mushtaq H.; Suri, M. Fareed K.
2016-01-01
Background Lumbar catheter placement under fluoroscopic guidance may reduce the rate of technical failures and associated complications seen with insertion guided by manually palpable landmarks. Methods We reviewed our experience with 43 attempted lumbar catheter placements using paramedian approach under fluoroscopic guidance and ascertained rates of technical success, and clinical events. Results Among the 43 patients, 18, 1, and 1 patients were on aspirin (with dipyrimadole in 2), clopidogrel, and combination of both, respectively. Lumbar catheter placement was successful in 42 of 43 attempted placements. Floroscopic guidance was critical in three patients; one patient had severe cerebrospinal fluid (CSF) depletion (empty thecal sac phenomenon) following pituitary surgery leading to no cerebrospinal fluid return despite correct placement confirmation under fluoroscopy. Two patients had spinal needle placement at the junction between epidural and cerebrospinal fluid spaces (junctional position) leading to cerebrospinal fluid return but inability to introduce the lumbar catheter. After confirmation of position by the injection of contrast or radiographic landmarks the needle was advanced by indenting the subcutaneous tissue or reinserting at a spinal level above the first insertion. The lumbar catheter remained in position over a mean period (±standard deviation) of 4.1(±2.3) days. Improvement in hydrocephalus was seen in two patients with intracranial mass lesions. One patient developed cerebrospinal fluid leakage through the insertion track following removal of catheter and required skin suturing at the site of insertion. Conclusions We observed a high technical success rate with low rate of complications even in patients with intracranial mass lesions, those on ongoing antiplatelet medications or in whom insertion would not be possible guided by manually palpable landmarks. PMID:26958156
34 CFR 300.104 - Residential placement
Code of Federal Regulations, 2010 CFR
2010-07-01
... 34 Education 2 2010-07-01 2010-07-01 false Residential placement 300.104 Section 300.104 Education... DISABILITIES State Eligibility Other Fape Requirements § 300.104 Residential placement If placement in a public or private residential program is necessary to provide special education and related services to...
34 CFR 300.104 - Residential placement
Code of Federal Regulations, 2011 CFR
2011-07-01
... 34 Education 2 2011-07-01 2010-07-01 true Residential placement 300.104 Section 300.104 Education... DISABILITIES State Eligibility Other Fape Requirements § 300.104 Residential placement If placement in a public or private residential program is necessary to provide special education and related services to...
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... Birth Control, Pregnancy, Child Placement, and Abortion § 551.24 Child placement. (a) The Warden may not permit the inmate's new born child to return to the institution except in accordance with the Bureau...
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... Birth Control, Pregnancy, Child Placement, and Abortion § 551.24 Child placement. (a) The Warden may not permit the inmate's new born child to return to the institution except in accordance with the Bureau...
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... Birth Control, Pregnancy, Child Placement, and Abortion § 551.24 Child placement. (a) The Warden may not permit the inmate's new born child to return to the institution except in accordance with the Bureau...
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... Birth Control, Pregnancy, Child Placement, and Abortion § 551.24 Child placement. (a) The Warden may not permit the inmate's new born child to return to the institution except in accordance with the Bureau...
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... Birth Control, Pregnancy, Child Placement, and Abortion § 551.24 Child placement. (a) The Warden may not permit the inmate's new born child to return to the institution except in accordance with the Bureau...
Can Placement Tests Inform Instructional Decisions?
ERIC Educational Resources Information Center
Green, Anthony B.; Weir, Cyril J.
2004-01-01
Studies of placement tests are typically narrowly concerned with their validation as instruments for the efficient grouping of students. They rarely explore the assumption that placement test content can be related to classroom tasks and so inform instructional decisions. This study focuses on a trial version of the Global Placement Test (GPT), a…
A Client Centered Approach to Job Placement
ERIC Educational Resources Information Center
Salomone, Paul R.
1971-01-01
A client centered placement approach for handicapped people is proposed as an alternative to the traditional selective placement method. The client centered placement is based on client responsibility and counselor direction and requires the counselor to have an unrealistic but optimistic attitude that the client will get a suitable job.…
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.
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. PMID:20821262
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.
Family ties and child placement.
Colón, F
1978-09-01
The fundamental premise of this paper is the primacy of the child's experience of biological-familial continuity in establishing his sense of self and personal significance. This paper examines the effects of current child placement practices on the child's ties to his biological, foster, and adoptive families. It explores alternative practices that would take into account biological-familial continuity. Comment is invited. PMID:744218
Two-parameter asymptotics in magnetic Weyl calculus
NASA Astrophysics Data System (ADS)
Lein, Max
2010-12-01
This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter ɛ, the case of small coupling λ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hörmander class symbols are proven as (i) ɛ ≪ 1 and λ ≪ 1, (ii) ɛ ≪ 1 and λ = 1, as well as (iii) ɛ = 1 and λ ≪ 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.
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.
Backpropagation and ordered derivatives in the time scales calculus.
Seiffertt, John; Wunsch, Donald C
2010-08-01
Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research. PMID:20615808
Two-parameter asymptotics in magnetic Weyl calculus
Lein, Max
2010-12-15
This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter {epsilon}, the case of small coupling {lambda} to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols are proven as (i) {epsilon}<< 1 and {lambda}<< 1, (ii) {epsilon}<< 1 and {lambda}= 1, as well as (iii) {epsilon}= 1 and {lambda}<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.
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.