Overview
Contains a collection of challenging problems in elementary mathematical analysis
Uses competition-inspired problems as a platform for training typical inventive skills
Develops basic valuable techniques for solving problems in mathematical analysis on the real axis
Assumes only a basic knowledge of the topic but opens the path to competitive research in the field
Includes interesting and valuable historical accounts of ideas and methods in analysis
Presents a connection between analysis and other mathematical disciplines, such as physics and engineering
May be applied in the classroom or as a self-study
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Table of contents (11 chapters)
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Front Matter
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Qualitative Properties of Continuous and Differentiable Functions
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Front Matter
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Applications to Convex Functions and Optimization
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Front Matter
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Antiderivatives, Riemann Integrability, and Applications
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Front Matter
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Appendix
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Front Matter
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Back Matter
Keywords
About this book
Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.
Key features:
*Uses competition-inspired problems as a platform for training typical inventive skills;
*Develops basic valuable techniques for solving problems in mathematical analysis on the real axis and provides solid preparation for deeper study of real analysis;
*Includes numerous examples and interesting, valuable historical accounts of ideas and methods in analysis;
*Offers a systematic path to organizing a natural transition that bridges elementary problem-solving activity to independent exploration of new results and properties.
Authors and Affiliations
About the authors
Teodora-Liliana Radulescu received her PhD in 2005 from Babes-Bolyai University of Cluj-Napoca, Romania, with a thesis on nonlinear analysis, and she is currently a professor of mathematics at the "Fratii Buzesti" National College in Craiova, Romania. She is a member of the American Mathematical Society and the Romanian Mathematical Society. She is also a reviewer for Mathematical Reviews and Zentralblatt fur Mathematik.
Vicentiu Radulescu received both his PhD and the Habilitation at the Université Pierre et Marie Curie (Paris 6), and he is currently a professor of mathematics at the University of Craiova, Romania and a senior researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy in Bucharest, Romania. He has authored 9 books and over 100 articles.
Titu Andreescu is an associate professor of mathematics at the University of Texas at Dallas. He is also firmly involved in mathematics contests and Olympiads, being the Director of AMC (as appointed by the Mathematical Association of America), Director of MOP, Head Coach of the USA IMO Team and Chairman of the USAMO. He has also authored a large number of books on the topic of problem solving and Olympiad-style mathematics.
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Bibliographic Information
Book Title: Problems in Real Analysis
Book Subtitle: Advanced Calculus on the Real Axis
Authors: Teodora-Liliana Radulescu, Vicentiu D. Radulescu, Titu Andreescu
DOI: https://doi.org/10.1007/978-0-387-77379-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2009
Softcover ISBN: 978-0-387-77378-0Published: 29 May 2009
eBook ISBN: 978-0-387-77379-7Published: 12 June 2009
Edition Number: 1
Number of Pages: XX, 452
Number of Illustrations: 10 b/w illustrations
Topics: Analysis, Real Functions, Numerical Analysis, Ordinary Differential Equations, Applications of Mathematics