Overview
- Includes insightful historical remarks regarding real analysis
- Presents core ideas of analysis “as a way of thinking” as opposed to “a body of facts”
- Explains how and why ideas arise, then how they evolve to the mature notions of real analysis
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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About this book
Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated.
In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.
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Keywords
Table of contents (20 chapters)
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Front Matter
Reviews
“This book is written to be accessible to the competent university student. … The book is consistent in addressing the classical analysis of real functions of one real variable, and it can serve as an introduction to monographs of complex functions, functional analysis and differential equations, upon which it touches occasionally. It can also serve as an introduction to Lebesgue integration or to generalized functions, which are not mentioned.” (Luis Manuel Braga de Costa Campos, Mathematical Reviews, December, 2016)
Authors and Affiliations
About the authors
Miklós Laczkovich is Professor of Mathematics at Eötvös Loránd University and the University College London, and was awarded the Ostrowski Prize in 1993 and the Széchenyi Prize in 1998. Vera T. Sós is a Research Fellow at the Alfréd Rényi Institute of Mathematics, and was awarded the Széchenyi Prize in 1997.
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Bibliographic Information
Book Title: Real Analysis
Book Subtitle: Foundations and Functions of One Variable
Authors: Miklós Laczkovich, Vera T. Sós
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4939-2766-1
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer New York 2015
Hardcover ISBN: 978-1-4939-2765-4Published: 09 October 2015
Softcover ISBN: 978-1-4939-4222-0Published: 23 August 2016
eBook ISBN: 978-1-4939-2766-1Published: 08 October 2015
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 1
Number of Pages: X, 483
Number of Illustrations: 94 b/w illustrations
Topics: Analysis