Relevant bibliographies by topics / Calculus Mathematics Mathematical analysis

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Calculus Mathematics Mathematical analysis'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Calculus Mathematics Mathematical analysis"

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Altenbach, H. "Some remarks on the paper ‘A unified tensor approach to the analysis of mechanical systems’ by A. A. Fogarasy and M. R. Smith." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 1 (December 1, 2008): 143–55. http://dx.doi.org/10.1243/09544062jmes1141.

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The tensor calculus is a powerful mathematical tool in the analysis of mechanical problems (or generally, of problems in physics). The aim of Fogarasy and Smith's ‘A unified tensor approach to the analysis of mechanical systems’ is to demonstrate this fact considering a problem of dynamical analysis of mechanisms. Fogarasy and Smith are applying the traditional approach in tensor calculus, which comes originally from the mathematics. This implies the a priori introduction of coordinates, which is usual in the analysis of mechanisms. Later the tensor calculus is used for the discussion of the basic equations and their mathematical handling. In this sense, the results obtained by Fogarasy and Smith are mathematically correct, and the interested reader can now have many fruitful and stimulating ideas.
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Пушкарский, Анатолий. "BOUT GEORGE BOOLE’S CALCULUS OF LOGIC." Логико-философские штудии, no. 3 (March 16, 2021): 267–75. http://dx.doi.org/10.52119/lphs.2021.55.34.004.

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Проводится разбор и анализ небольшой статьи Джорджа Буля, опубликованной на следующий год после выхода его знаменитой работы «Математический анализ логики». Исследуется вопрос о том, насколько ее можно рассматривать как адекватный и репрезентативный обзор его логической концепции. Также исследуются математические, экстралогические и философские основания логики Буля. Указывается, что математическим основанием его логической системы послужили его исследования в области линейных дифференциальных уравнений. Кроме того, в основании его пионерских открытий лежали произвольные философско-методологическим допущения, которые напрямую не относились к области логики и математики. Такими допущениями следует признать некоторую оригинальную психологическую теорию сознания, его философию математики, предполагающую существование универсального математического исчисления, и некоторые положения логико-философской концепции И. Канта In the present paper, the small article by George Boole, published the next year after the publication of his famous work The Mathematical Analysis of Logic, is analyzed. We discuss to what extent it can be considered as an adequate and representative overview of his logical views. The mathematical, extralogical and philosophical foundations of Boole’s logic are explored. It is pointed out that the mathematical basis of his logical system was his research in the field of linear differential equations. Moreover, his pioneering discoveries were based on arbitrary philosophical and methodological assumptions that were not directly related to the field of logic and mathematics. Some of the original psychological theory of mind, its philosophy of mathematics, which presupposes the existence of a universal mathematical calculus, and some provisions of Immanuel Kant’s logico-philosophical doctrine should be recognized as such assumptions.
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G.A, Mahayukti, Dantes N, Candiasa I.M, and Marhaeni A.A.I.N. "The effectiveness of using portfolio assessment in lecture by controlling mathematical logical intelligence." SHS Web of Conferences 42 (2018): 00081. http://dx.doi.org/10.1051/shsconf/20184200081.

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The purpose of this research aims to examine the effectiveness of using portfolio assessment in the integral calculus lecture after logical mathematical intelligence is controlled. The population of this research are all students in the department of mathematics education who program integral calculus courses on the 2015/2016 academic year. Samples in this research are 88 students, who were selected randomly. The data were analyzed by one-way covariance analysis. The result of this research showed that student’s learning outcomes of Integral Calculus who were taught Integral Calculus with portfolio assessment, was higher than those of the students who were tought with essay assessment. The findings of this study show that using portfolio assessment is effective to improve student’s learning outcomes of Integral Calculus.
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Jadhav, Ashish A., Abhijeet D. Kalamkar, Pritish A. Gaikwad, Vishwesh Vyawahare, and Navin Singhaniya. "Analysis of GPU Computation of Parabolic, Bessel, Wright and Riemann Zeta Functions." ITM Web of Conferences 40 (2021): 02005. http://dx.doi.org/10.1051/itmconf/20214002005.

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This paper deals with GPU computing of special mathematical functions that are used in Fractional Calculus. The graphics processing unit (GPU) has grown to be an integral part of nowadays’s mainstream computing structures. The special mathematical functions are an integral part of Fractional Calculus. This paper deals with a novel parallel approach for computing special mathematical functions used in Fractional Calculus. NVIDIA’s GPU hardware is used to speed up the parallel algorithm. A comparison of the sequential code, vectorized code and GPU code is performed. We have successfully reduced the computation time of special mathematical functions using the parallel computing capabilities of GPU.
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Wang, Long-Fei, Xiao-Jun Yang, Dumitru Baleanu, Carlo Cattani, and Yang Zhao. "Fractal Dynamical Model of Vehicular Traffic Flow within the Local Fractional Conservation Laws." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/635760.

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Guce, Ive K. "Mathematical Writing Errors in Expository Writings of College Mathematics Students." International Journal of Evaluation and Research in Education (IJERE) 6, no. 3 (September 1, 2017): 233. http://dx.doi.org/10.11591/ijere.v6i3.8549.

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<p>Despite the efforts to confirm the effectiveness of writing in learning mathematics, analysis on common errors in mathematical writings has not received sufficient attention. This study aimed to provide an account of the students’ procedural explanations in terms of their commonly committed errors in mathematical writing. Nine errors in mathematical writing were pre-defined namely, misuse of mathematical terms, misuse of mathematical symbols, incorrect notation, incorrect grammar, incorrect capitalization, no or incorrect punctuation, vague term, incorrect term, and lack of term or phrase. This study used qualitative method of research to keep a record of errors in mathematical writing. Conducted in the College of Education Arts and Sciences of De La Salle Lipa, the study involved twelve BS Mathematics students enrolled in Advanced Calculus 1 class as respondents. Results revealed that the most committed errors done in mathematical writing are incorrect grammar and misuse of mathematical symbols. Certainly, intervention programs on mathematics writing will bring favorable outcomes. Language courses in the students’ curriculum which tackle proper grammar usage may be integrated with writing about mathematics as part of the student activities. Such will provide the students with writing experiences fitted to their discipline.</p><p> </p>
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Rusyda, N. A., D. Ahmad, R. Rusdinal, and F. Dwina. "Analysis of students’ mathematical communication skill in calculus course." Journal of Physics: Conference Series 1554 (May 2020): 012043. http://dx.doi.org/10.1088/1742-6596/1554/1/012043.

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Siddiqui, Nida. "Mathematical Intuition: impact on non-math major undergraduates." Bolema: Boletim de Educação Matemática 35, no. 70 (May 2021): 727–44. http://dx.doi.org/10.1590/1980-4415v35n70a09.

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Abstract The research question being investigated in this paper is how to improve the learning of calculus for non-math major students whose interests are primarily non mathematical. The study explores the impact of an intuitive approach applied to the concepts of limits and integration. The survey was carried on 1st year engineering students taking the Calculus-1 course. The students had already had a brief encounter with the topics in high school. They were surveyed about their outlook towards the concepts of limits and integration using the same pre and post inquiry form. The post analysis was conducted after introducing both the topics through an intuitive approach. The survey was analyzed for statistical significance using the Mc Nemar’s statistical test, which studies the impact of an intervention. Survey analysis indicated an improved understanding for the students and a positive change in their approach towards the topics.
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Pujilestari, Pujilestari, and Yuntawati Yuntawati. "PENGARUH PEMBELAJARAN PROBLEM POSING TERHADAP KOMUNIKASI MATEMATIKA MAHASISWA." Media Pendidikan Matematika 6, no. 2 (December 30, 2018): 50. http://dx.doi.org/10.33394/mpm.v6i2.1690.

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Type of this research is experimental research which aims to determine the effect of problem posing learning on mathematical communication of students prospective mathematics teacher at IKIP Mataram by calculus I module. This module developed by a problem posing approach that meets the criteria of being feasible, practical, and effective. The experimental design used was the type of Quasi Experimental Design and the design used was Nonequivalent Control Group Design. Data collection instruments included tests of mathematical communication skills, student response questionnaires, and lecturer response questionnaires. Based on the results of the hypothesis test analysis obtained a value with a significantlevel or is . So that it is rejected and accepted. So it can be concluded that Problem Posing Learning by using problem posing based I calculus module influences student mathematics communication and is effectively used in lectures
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Volkova, Elena Sergeevna, and Vladimir Borisovich Gisin. "On the assessment of formation of the system of main concepts of mathematical analysis." Современное образование, no. 2 (February 2020): 12–27. http://dx.doi.org/10.25136/2409-8736.2020.2.32942.

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The object of this research is the results of experimental use of the test for inventory of the concepts of mathematical analysis (Calculus Concept Inventory, CCI), which is aimed at assessment of the key concepts of mathematical analysis, such as function, limit and derivative. The test was conducted in the period from 2016 to 2020 and involved Bachelor&rsquo;s degree students of Financial University under the Government of the Russian Federation on the discipline &ldquo;Applied Mathematics and Informatics&rdquo;. &ldquo;Mathematical Analysis&rdquo; is one of the key disciplines in formation of mathematical competencies of students majoring &ldquo;Applied Mathematics and Informatics&rdquo;. Test was developed by the leading experts from the United States in the area of mathematics and teaching mathematics in the universities, and was implemented in Russian practice for the first time. For quality assessment of the test was applied Cronbach's alpha coefficient, and the results were evaluated based on the Item Response Theory. Although in universities of the United States the implementation of this test showed relatively low effectiveness, for the students of Financial University the coefficient values were significantly higher and allow making an unequivocal conclusion on the informativeness of results. The article also applies the values of discriminant coefficient. Their fluctuation allows using the test not only for assessing the achievement in learning mathematical analysis of students in groups, but also individual results. The results demonstrate that the traditional approach in teaching the principles of mathematical analysis that is widely recognized in the Russian universities is ineffective, which underlines the need to rearrange the content and methods of teaching mathematical analysis in a university.
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Dissertations / Theses on the topic "Calculus Mathematics Mathematical analysis"

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Teuscher, Dawn. "Two paths to advanced placement calculus an examination of secondary students' mathematical understanding emerging from integrated and single-subject curricula /." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/5530.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2008.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 17, 2009) Vita. Includes bibliographical references.
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Charoenphon, Sutthirut. "Green's Functions of Discrete Fractional Calculus Boundary Value Problems and an Application of Discrete Fractional Calculus to a Pharmacokinetic Model." TopSCHOLAR®, 2014. http://digitalcommons.wku.edu/theses/1327.

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Fractional calculus has been used as a research tool in the fields of pharmacology, biology, chemistry, and other areas [3]. The main purpose of this thesis is to calculate Green's functions of fractional difference equations, and to model problems in pharmacokinetics. We claim that the discrete fractional calculus yields the best prediction performance compared to the continuous fractional calculus in the application of a one-compartmental model of drug concentration. In Chapter 1, the Gamma function and its properties are discussed to establish a theoretical basis. Additionally, the basics of discrete fractional calculus are discussed using particular examples for further calculations. In Chapter 2, we use these basic results in the analysis of a linear fractional difference equation. Existence of solutions to this difference equation is then established for both initial conditions (IVP) and two-point boundary conditions (BVP). In Chapter 3, Green's functions are introduced and discussed, along with examples. Instead of using Cauchy functions, the technique of finding Green's functions by a traditional method is demonstrated and used throughout this chapter. The solutions of the BVP play an important role in analysis and construction of the Green's functions. Then, Green's functions for the discrete calculus case are calculated using particular problems, such as boundary value problems, discrete boundary value problems (DBVP) and fractional boundary value problems (FBVP). Finally, we demonstrate how the Green's functions of the FBVP generalize the existence results of the Green's functions of DVBP. In Chapter 4, different compartmental pharmacokinetic models are discussed. This thesis limits discussion to the one-compartmental model. The Mathematica FindFit command and the statistical computational techniques of mean square error (MSE) and cross-validation are discussed. Each of the four models (continuous, continuous fractional, discrete and discrete fractional) is used to compute the MSE numerically with the given data of drug concentration. Then, the best fit and the best model are obtained by inspection of the resulting MSE. In the last Chapter, the results are summarized, conclusions are drawn, and directions for future work are stated.
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Cass, Thomas Richard. "Applications of Malliavin calculus in stochastic analysis and mathematical finance." Thesis, University of Cambridge, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.612064.

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Houchens, Jesse P. "Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis." Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1365705311.

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Gibson, Kathleen Renae. "Nonstandard analysis based calculus." CSUSB ScholarWorks, 1994. https://scholarworks.lib.csusb.edu/etd-project/915.

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In the first part of the project the elementary development of an extended number system called Hyperreals is discussed. The second half of this project develops the basics of Nonstandard Analysis, including the theory of ultrafilters, and the formal construction of the Hyperreals.
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Ho, Theang. "Analysis of an online placement exam for calculus." Kansas State University, 2010. http://hdl.handle.net/2097/4650.

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Master of Science
Department of Mathematics
Andrew G. Bennett
An online mathematics placement exam was administered to new freshmen enrolled at Kansas State University for the Fall of 2009. The purpose of this exam is to help determine which students are prepared for a college Calculus I or Calculus II course. Problems on the exam were analyzed and grouped together using different techniques including expert analysis and item response theory to determine which problems were similar or even relevant to placement. Student scores on the exam were compared to their performance on the final exam at the end of the course as well as ACT data. This showed how well the placement exam indicated which students were prepared. A model was created using ACT information and the new information from the placement exam that improved prediction of success in a college calculus course. The new model offers a significant improvement upon what the ACT data provides to advisers. Suggestions for improvements to the test and methodology are made based upon the analysis.
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Kimeu, Joseph M. "Fractional Calculus: Definitions and Applications." TopSCHOLAR®, 2009. http://digitalcommons.wku.edu/theses/115.

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Arora, Raman. "Analysis of Economic Models Through Calculus of Variations." TopSCHOLAR®, 2005. http://digitalcommons.wku.edu/theses/453.

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This thesis is a combination of two science fields: Mathematics and Economics. Mathematics is often used to formulate a clear and concise solution to economic problems. In my observation calculus of variation has often been used in various macroeconomic problems. This mathematical method deals with maximizing or minimizing of various objective functions given a set of constraints. This topic brings out one of the best ways to show the relationship between mathematics and economics. My thesis consists of three parts: The first chapter contains a review of the calculus of variations. Basic definitions and important conditions have been stated. The aim of this chapter was to set the groundwork for understanding calculus of variations so that it can be used in solving various economics models. In the second chapter we study an economic model from which calculus of variations has been used to solve it. The macroeconomic model deals with optimizing the social welfare function. The entire working of the model has been discussed and documented in the thesis report. The third chapter deals with the analysis of the Lucas model which concentrated on how the accumulation of human capital impacts the growth rate of the economy. Lucas assumes that the growth rate of the human capital is linearly related to its level. If we abandon this assumption, will the optimal value of the time devoted to education in the steady state exist? If it exists, will it be same or different? So we introduced a new model in which the only modification we made to the Lucas model was in the equation that describes the process of human accumulation by introducing a nonlinear component. On investigation of this new model we have shown that it is possible that optimal behavior for an individual can be not to educate himself.
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Karlsson, Olle. "Analysis and Algebraic Structures of q-Analysis and its Generalizations." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-48847.

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In this thesis we explore the concept of q-calculus and its generalisation. We begin by defining q-combinatorics which uses a real number to define a new set of numbers and then use these numbers to get classic combinatoric elements. These results have use when we work on our algebra that are related with this specific real number. We then work out some results involving one of the operators in the algebra. This operator together with a similar operator produces some special differential equations that we explore. Then we go on to define integrals as the inverse operator to the one used for our differential equations. In the last chapter we try to generalise everything we have explored until then.
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Eriksson, Olle. "Hodge Decomposition for Manifolds with Boundary and Vector Calculus." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-328318.

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Books on the topic "Calculus Mathematics Mathematical analysis"

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Channon, Sarah. Calculus. Chandni Chowk, Delhi: Global Media, 2009.

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1941-, Davies Joan, ed. Calculus. Cambridge, UK ; New York, NY, USA: Cambridge University Press, 2001.

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Schinazi, Rinaldo B. From calculus to analysis. New York: Birkhäuser/Springer, 2012.

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Convolutional calculus. 2nd ed. Dordrecht: Kluwer Academic, 1990.

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Advanced calculus with applications in statistics. New York: Wiley, 1993.

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Khuri, André I. Advanced calculus with applications in statistics. 2nd ed. Hoboken, N.J: Wiley-Interscience, 2003.

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1962-, Escher Joachim, ed. Analysis. Basel: Birkhäuser Verlag, 1998.

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Analysis 2. 5th ed. Berlin: Springer, 2004.

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Belding, David French. Foundations of analysis. 2nd ed. Mineola, N.Y: Dover Publications, 2008.

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Bachman, David. Advanced Calculus Demystified. New York: McGraw-Hill, 2007.

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Book chapters on the topic "Calculus Mathematics Mathematical analysis"

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Römisch, Werner, and Thomas Zeugmann. "The Differential Calculus." In Mathematical Analysis and the Mathematics of Computation, 201–68. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42755-3_5.

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Römisch, Werner, and Thomas Zeugmann. "The Integral Calculus." In Mathematical Analysis and the Mathematics of Computation, 337–420. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42755-3_7.

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Pugh, Charles C. "Multivariable Calculus." In Real Mathematical Analysis, 277–382. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17771-7_5.

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Pugh, Charles Chapman. "Multivariable Calculus." In Real Mathematical Analysis, 267–361. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21684-3_5.

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Römisch, Werner, and Thomas Zeugmann. "Applications of the Differential Calculus." In Mathematical Analysis and the Mathematics of Computation, 269–336. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42755-3_6.

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Giaquinta, Mariano, and Giuseppe Modica. "Further Developments in Calculus." In Mathematical Analysis, 207–59. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0007-9_5.

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Giaquinta, Mariano, and Giuseppe Modica. "The Calculus of Derivatives and of Integrals." In Mathematical Analysis, 145–206. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0007-9_4.

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Giaquinta, Mariano, and Giuseppe Modica. "The Formalism of the Calculus of Variations." In Mathematical Analysis, 149–212. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8310-8_3.

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Kriz, Igor, and Aleš Pultr. "Multivariable Differential Calculus." In Introduction to Mathematical Analysis, 65–95. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0636-7_3.

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Bell, John L. "The Calculus and Mathematical Analysis." In The Western Ontario Series in Philosophy of Science, 153–73. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4209-0_9.

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Conference papers on the topic "Calculus Mathematics Mathematical analysis"

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Sergeyev, Yaroslav D., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Infinity Computer and Calculus." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790118.

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Crouzeix, Michel, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Functional Calculus and Numerical Analysis." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636662.

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Guseinov, Gusein Sh. "Discrete Calculus of Variations." In GLOBAL ANALYSIS AND APPLIED MATHEMATICS: International Workshop on Global Analysis. AIP, 2004. http://dx.doi.org/10.1063/1.1814727.

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Skwara, Urszula, José Martins, Peyman Ghaffari, Maíra Aguiar, João Boto, and Nico Stollenwerk. "Applications of fractional calculus to epidemiological models." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756403.

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Ortigueira, Manuel D. "Preface of the "Symposium on fractional calculus and applications"." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756422.

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Wang, Wei. "Teaching of Mathematical Analysis or Calculus Based on the Thinking of Calculus." In 6th International Conference on Education Reform and Modern Management (ERMM 2021). Paris, France: Atlantis Press, 2021. http://dx.doi.org/10.2991/assehr.k.210513.027.

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Wang, Xiuyan, and Henan Pei. "Analysis of Teaching Strategies for Higher Mathematics Calculus." In Proceedings of the 2018 International Workshop on Education Reform and Social Sciences (ERSS 2018). Paris, France: Atlantis Press, 2019. http://dx.doi.org/10.2991/erss-18.2019.148.

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Jafari, M. A., and A. Aminataei. "Numerical Solution of Problems in Calculus of Variations by Homotopy Perturbation Method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990913.

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Asada, Akira. "Zeta-regularization and calculus on infinite dimensional spaces." In GLOBAL ANALYSIS AND APPLIED MATHEMATICS: International Workshop on Global Analysis. AIP, 2004. http://dx.doi.org/10.1063/1.1814716.

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Khairani, Mukhni, and Faizah Qurrata Aini. "Problems Analysis of Calculus Learning in Higher Educations." In Proceedings of the 2nd International Conference on Mathematics and Mathematics Education 2018 (ICM2E 2018). Paris, France: Atlantis Press, 2018. http://dx.doi.org/10.2991/icm2e-18.2018.19.

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Reports on the topic "Calculus Mathematics Mathematical analysis"

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Roschelle, Jeremy, Britte Haugan Cheng, Nicola Hodkowski, Julie Neisler, and Lina Haldar. Evaluation of an Online Tutoring Program in Elementary Mathematics. Digital Promise, April 2020. http://dx.doi.org/10.51388/20.500.12265/94.

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Many students struggle with mathematics in late elementary school, particularly on the topic of fractions. In a best evidence syntheses of research on increasing achievement in elementary school mathematics, Pelligrini et al. (2018) highlighted tutoring as a way to help students. Online tutoring is attractive because costs may be lower and logistics easier than with face-to-face tutoring. Cignition developed an approach that combines online 1:1 tutoring with a fractions game, called FogStone Isle. The game provides students with additional learning opportunities and provides tutors with information that they can use to plan tutoring sessions. A randomized controlled trial investigated the research question: Do students who participate in online tutoring and a related mathematical game learn more about fractions than students who only have access to the game? Participants were 144 students from four schools, all serving low-income students with low prior mathematics achievement. In the Treatment condition, students received 20-25 minute tutoring sessions twice per week for an average of 18 sessions and also played the FogStone Isle game. In the Control condition, students had access to the game, but did not play it often. Control students did not receive tutoring. Students were randomly assigned to condition after being matched on pre-test scores. The same diagnostic assessment was used as a pre-test and as a post-test. The planned analysis looked for differences in gain scores ( post-test minus pre-test scores) between conditions. We conducted a t-test on the aggregate gain scores, comparing conditions; the results were statistically significant (t = 4.0545, df = 132.66, p-value < .001). To determine an effect size, we treated each site as a study in a meta-analysis. Using gain scores, the effect size was g=+.66. A more sophisticated treatment of the pooled standard deviation resulted in a corrected effect size of g=.46 with a 95% confidence interval of [+.23,+.70]. Students who received online tutoring and played the related Fog Stone Isle game learned more; our research found the approach to be efficacious. The Pelligrini et al. (2018) meta-analysis of elementary math tutoring programs found g = .26 and was based largely on face-to-face tutoring studies. Thus, this study compares favorably to prior research on face-to-face mathematics tutoring with elementary students. Limitations are discussed; in particular, this is an initial study of an intervention under development. Effects could increase or decrease as development continues and the program scales. Although this study was planned long before the current pandemic, results are particularly timely now that many students are at home under shelter-in-place orders due to COVID-19. The approach taken here is feasible for students at home, with tutors supporting them from a distance. It is also feasible in many other situations where equity could be addressed directly by supporting students via online tutors.
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Frantseva, Anastasiya. The video lectures course "Elements of Mathematical Logic" for students enrolled in the Pedagogical education direction, profile Primary education. Frantseva Anastasiya Sergeevna, April 2021. http://dx.doi.org/10.12731/frantseva.0411.14042021.

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The video lectures course is intended for full-time and part-time students enrolled in "Pedagogical education" direction, profile "Primary education" or "Primary education - Additional education". The course consists of four lectures on the section "Elements of Mathematical Logic" of the discipline "Theoretical Foundations of the Elementary Course in Mathematics" on the profile "Primary Education". The main lecture materials source is a textbook on mathematics for students of higher pedagogical educational institutions Stoilova L.P. (M.: Academy, 2014.464 p.). The content of the considered mathematics section is adapted to the professional needs of future primary school teachers. It is accompanied by examples of practice exercises from elementary school mathematics textbooks. The course assumes students productive learning activities, which they should carry out during the viewing. The logic’s studying contributes to the formation of the specified profile students of such professional skills as "the ability to carry out pedagogical activities for the implementation of primary general education programs", "the ability to develop methodological support for programs of primary general education." In addition, this section contributes to the formation of such universal and general professional skills as "the ability to perform searching, critical analysis and synthesis of information, to apply a systematic approach to solving the assigned tasks", "the ability to participate in the development of basic and additional educational programs, to design their individual components". The video lectures course was recorded at Irkutsk State University.
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Schoen, Robert, Xiaotong Yang, and Gizem Solmaz. Psychometric Report for the 2019 Knowledge for Teaching Early Elementary Mathematics (K-TEEM) Test. Florida State University Libraries, May 2021. http://dx.doi.org/10.33009/lsi.1620243057.

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The 2019 Knowledge for Teaching Early Elementary Mathematics (2019 K-TEEM) test measures teachers’ mathematical knowledge for teaching early elementary mathematics. This report presents information about a large-scale field test of the 2019 K-TEEM test with 649 practicing educators. The report contains information about the development process used for the test; a description of the sample; descriptions of the procedures used for data entry, scoring of responses, and analysis of data; recommended scoring procedures; and findings regarding the distribution of test scores, standard error of measurement, and marginal reliability. The intended use of the data from the 2019 K-TEEM test is to serve as a measure of teacher knowledge that will be used in a randomized controlled trial to investigate the impact—and variation in impact—of a teacher professional-development program for early elementary teachers.
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4

Tucker-Blackmon, Angelicque. Engagement in Engineering Pathways “E-PATH” An Initiative to Retain Non-Traditional Students in Engineering Year Three Summative External Evaluation Report. Innovative Learning Center, LLC, July 2020. http://dx.doi.org/10.52012/tyob9090.

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The summative external evaluation report described the program's impact on faculty and students participating in recitation sessions and active teaching professional development sessions over two years. Student persistence and retention in engineering courses continue to be a challenge in undergraduate education, especially for students underrepresented in engineering disciplines. The program's goal was to use peer-facilitated instruction in core engineering courses known to have high attrition rates to retain underrepresented students, especially women, in engineering to diversify and broaden engineering participation. Knowledge generated around using peer-facilitated instruction at two-year colleges can improve underrepresented students' success and participation in engineering across a broad range of institutions. Students in the program participated in peer-facilitated recitation sessions linked to fundamental engineering courses, such as engineering analysis, statics, and dynamics. These courses have the highest failure rate among women and underrepresented minority students. As a mixed-methods evaluation study, student engagement was measured as students' comfort with asking questions, collaboration with peers, and applying mathematics concepts. SPSS was used to analyze pre-and post-surveys for statistical significance. Qualitative data were collected through classroom observations and focus group sessions with recitation leaders. Semi-structured interviews were conducted with faculty members and students to understand their experiences in the program. Findings revealed that women students had marginalization and intimidation perceptions primarily from courses with significantly more men than women. However, they shared numerous strategies that could support them towards success through the engineering pathway. Women and underrepresented students perceived that they did not have a network of peers and faculty as role models to identify within engineering disciplines. The recitation sessions had a positive social impact on Hispanic women. As opportunities to collaborate increased, Hispanic womens' social engagement was expected to increase. This social engagement level has already been predicted to increase women students' persistence and retention in engineering and result in them not leaving the engineering pathway. An analysis of quantitative survey data from students in the three engineering courses revealed a significant effect of race and ethnicity for comfort in asking questions in class, collaborating with peers outside the classroom, and applying mathematical concepts. Further examination of this effect for comfort with asking questions in class revealed that comfort asking questions was driven by one or two extreme post-test scores of Asian students. A follow-up ANOVA for this item revealed that Asian women reported feeling excluded in the classroom. However, it was difficult to determine whether these differences are stable given the small sample size for students identifying as Asian. Furthermore, gender differences were significant for comfort in communicating with professors and peers. Overall, women reported less comfort communicating with their professors than men. Results from student metrics will inform faculty professional development efforts to increase faculty support and maximize student engagement, persistence, and retention in engineering courses at community colleges. Summative results from this project could inform the national STEM community about recitation support to further improve undergraduate engineering learning and educational research.
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