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Real Analysis

Foundations and Functions of One Variable

  • Miklós Laczkovich
  • Vera T. Sós

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
  21. Miklós Laczkovich, Vera T. Sós
    Pages E1-E1
  22. Back Matter
    Pages 439-483

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

  • Miklós Laczkovich
    • 1
  • Vera T. Sós
    • 2
  1. 1.Department of AnalysisEötvös Loránd UniversityBudapestHungary
  2. 2.Hungarian Academy of SciencesAlfréd Rényi Institute of MathematicsBudapestHungary

Bibliographic information

  • 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
  • Print ISBN 978-1-4939-2765-4
  • Online ISBN 978-1-4939-2766-1
  • Series Print ISSN 0172-6056
  • Series Online ISSN 2197-5604
  • Buy this book on publisher's site
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