Real Analysis

Series, Functions of Several Variables, and Applications

  • Miklós Laczkovich
  • Vera T. Sós

Part of the Undergraduate Texts in Mathematics book series (UTM, volume 3)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Miklós Laczkovich, Vera T. Sós
    Pages 1-65
  3. Miklós Laczkovich, Vera T. Sós
    Pages 67-94
  4. Miklós Laczkovich, Vera T. Sós
    Pages 95-121
  5. Miklós Laczkovich, Vera T. Sós
    Pages 123-153
  6. Miklós Laczkovich, Vera T. Sós
    Pages 155-192
  7. Miklós Laczkovich, Vera T. Sós
    Pages 193-228
  8. Miklós Laczkovich, Vera T. Sós
    Pages 229-301
  9. Miklós Laczkovich, Vera T. Sós
    Pages 303-360
  10. Miklós Laczkovich, Vera T. Sós
    Pages 361-381
  11. Back Matter
    Pages 383-392

About this book

Introduction

This book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable. Together, these volumes form the first English edition of the popular Hungarian original, Valós Analízis I & II, based on courses taught by the authors at Eötvös Loránd University, Hungary, for more than 30 years. Numerous exercises are included throughout, offering ample opportunities to master topics by progressing from routine to difficult problems. Hints or solutions to many of the more challenging exercises make this book ideal for independent study, or further reading.

Intended as a sequel to a course in single variable analysis, this book builds upon and expands these ideas into higher dimensions. The modular organization makes this text adaptable for either a semester or year-long introductory course. Topics include: differentiation and integration of functions of several variables; infinite numerical series; sequences and series of functions; and applications to other areas of mathematics. Many historical notes are given and there is an emphasis on conceptual understanding and context, be it within mathematics itself or more broadly in applications, such as physics. By developing the student’s intuition throughout, many definitions and results become motivated by insights from their context.

Keywords

Continuity of functions History of Fourier series History of infinite series Limit of functions Real analysis Multivariable real analysis Multivariable real analysis textbook adoption

Authors and affiliations

  • Miklós Laczkovich
    • 1
  • Vera T. Sós
    • 2
  1. 1.Department of AnalysisEötvös Loránd University—ELTEBudapestHungary
  2. 2.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-7369-9
  • Copyright Information Springer Science+Business Media LLC 2017
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-7367-5
  • Online ISBN 978-1-4939-7369-9
  • Series Print ISSN 0172-6056
  • Series Online ISSN 2197-5604
  • About this book
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