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© 2015

Real Analysis

Foundations and Functions of One Variable

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-x
  2. Miklós Laczkovich, Vera T. Sós
    Pages 1-10
  3. Miklós Laczkovich, Vera T. Sós
    Pages 11-26
  4. Miklós Laczkovich, Vera T. Sós
    Pages 27-50
  5. Miklós Laczkovich, Vera T. Sós
    Pages 51-62
  6. Miklós Laczkovich, Vera T. Sós
    Pages 63-75
  7. Miklós Laczkovich, Vera T. Sós
    Pages 77-87
  8. Miklós Laczkovich, Vera T. Sós
    Pages 89-96
  9. Miklós Laczkovich, Vera T. Sós
    Pages 97-102
  10. Miklós Laczkovich, Vera T. Sós
    Pages 103-116
  11. Miklós Laczkovich, Vera T. Sós
    Pages 117-166
  12. Miklós Laczkovich, Vera T. Sós
    Pages 167-202
  13. Miklós Laczkovich, Vera T. Sós
    Pages 203-253
  14. Miklós Laczkovich, Vera T. Sós
    Pages 255-293
  15. Miklós Laczkovich, Vera T. Sós
    Pages 295-331
  16. Miklós Laczkovich, Vera T. Sós
    Pages 333-366
  17. Miklós Laczkovich, Vera T. Sós
    Pages 367-397
  18. Miklós Laczkovich, Vera T. Sós
    Pages 399-406
  19. Miklós Laczkovich, Vera T. Sós
    Pages 407-416
  20. Miklós Laczkovich, Vera T. Sós
    Pages 417-437

About this book

Introduction

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 students' mathematical intuition.


The modular organization of the book makes it adaptable for either semester or year-long introductory courses, while the wealth of material allows for it to be used at various levels of student sophistication in all programs where analysis is a part of the curriculum, including teachers' education.

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. There are frequent hints and occasional complete solutions provided for the more challenging exercises making it an ideal choice for independent study.

The book includes a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a rigorous study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous historical notes and applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of mathematical analysis.

Keywords

Fourier series Stieltjes integral continuous functions differentiation infinite sequences infinite series integration limits real analysis

Authors and affiliations

  1. 1.Department of AnalysisEötvös Loránd UniversityBudapestHungary
  2. 2.Hungarian Academy of SciencesAlfréd Rényi Institute of MathematicsBudapestHungary

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.

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
  • Series Abbreviated Title Undergraduate Texts Mathematics
  • DOI https://doi.org/10.1007/978-1-4939-2766-1
  • Copyright Information Springer New York 2015
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4939-2765-4
  • Softcover ISBN 978-1-4939-4222-0
  • eBook ISBN 978-1-4939-2766-1
  • Series ISSN 0172-6056
  • Series E-ISSN 2197-5604
  • Edition Number 1
  • Number of Pages X, 483
  • Number of Illustrations 94 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site
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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)