Problems in Real Analysis: Advanced Calculus on the Real Axis

Paperback | May 29, 2009

byTeodora-Liliana Radulescu

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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.

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From the Publisher

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...

From the Jacket

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...

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 So...
Format:PaperbackDimensions:472 pages, 9.25 × 6.1 × 0.04 inPublished:May 29, 2009Publisher:SpringerLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387773789

ISBN - 13:9780387773780

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Table of Contents

Part I: Sequences, Series, and Limits of Functions.- Sequences.- Series.- Limits of Functions.- Part II: Qualitative Properties of Continuous and Differentiable Functions.- Continuity.- Differentiability.- Part III: Applications to Convex Functions and Optimizatin.- Convex Functions.- Inequalities and Extremum Problems.- Part IV: Antiderivatives, Riemann Integrability, and Applications.- Antiderivatives.- Riemann Integrability.- Applications of the Integral Calculus.- Appendix A: Basic Elements of Set Theory.- Appendix B: Topology of the Real Line.- Glossary.- References.- Index.

Editorial Reviews

From the reviews:"The book . is a problem book in real analysis, chosen mostly from mathematical Olympiads and from problem journals. . The book focuses on analysis on the real line, which is also known as advanced real calculus. . the book under review is a collection of interesting and fresh problems with detailed solutions. The target audience seems to be students preparing for Olympiads and other competitions, but undergraduate students, mathematics teachers and professors of Mathematical Analysis and Calculus courses may also find interesting things here." (Mehdi Hassani, The Mathematical Association of America, August, 2009)"In this book, the authors intend 'to build a bridge between ordinary high-school or undergraduate exercises and more difficult and abstract concepts or problems' in mathematical analysis. . The book may readily be used as a self-study text or . as a classroom text. The introductory material in each section is reasonably self-contained and includes interesting examples and applications. . the collection is a very worth-while contribution and should be included in every high school, college, and university mathematics library collection." (F. J. Papp, Zentralblatt MATH, Vol. 1209, 2011)