Undergraduate Texts in Mathematics

Real Analysis

Series, Functions of Several Variables, and Applications

Authors: Laczkovich, Miklós, T. Sós, Vera

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  • Corresponds to a second course in real analysis to follow the authors' book Real Analysis: Foundations and Functions of One Variable
  • Motivates ideas and results in analysis by exploring concepts and applications
  • Showcases a comprehensive collection of exercises, allowing students to develop proficiency over a broad range of problems
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eBook $19.99
$47.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-1-4939-7369-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $34.99
$69.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-1-4939-7367-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $34.99
$69.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-1-4939-8464-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this Textbook

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.

About the authors

Miklós Laczkovich is a member of the Hungarian Academy of Sciences and professor emeritus at Eötvös Loránd University Budapest and University College London. He was awarded the Ostrowski Prize in 1993 and the Széchenyi Prize in 1998.

Vera T. Sós is a member of the Hungarian Academy of Sciences and professor emeritus at Eötvös Loránd Univesity Budapest and the Alfred Renyi Mathematical Institute of the Hungarian Academy of Sciences. She was awarded the Széchenyi Prize in 1997.

Reviews

“This book develops a thorough treatment of multivariate derivatives, viewing them both as linear transformations and as partial derivatives. … The book is consistent in addressing the classical analysis of real functions of several variables. This volume will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis.” (Teodora-Liliana Rădulescu, zbMATH 1407.26001, 2019)


“The explicit intent of the authors is to present material gradually, and to develop precision based on intuition with the help of well-designed examples. The book contains 600 exercises. In my opinion this interesting book represents an alternative viewpoint in real analysis.” (Zbigniew Grande, Mathematical Reviews, August, 2018)​

Table of contents (9 chapters)

Table of contents (9 chapters)
  • $${\mathbb {R}^{p}}\rightarrow \mathbb {R}$$ functions

    Pages 1-65

    Laczkovich, Miklós (et al.)

  • Functions from $$\mathbb {R}^{p}$$ to $$\mathbb {R}^{q}$$

    Pages 67-94

    Laczkovich, Miklós (et al.)

  • The Jordan Measure

    Pages 95-121

    Laczkovich, Miklós (et al.)

  • Integrals of Multivariable Functions I

    Pages 123-153

    Laczkovich, Miklós (et al.)

  • Integrals of Multivariable Functions II

    Pages 155-192

    Laczkovich, Miklós (et al.)

Buy this book

eBook $19.99
$47.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-1-4939-7369-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $34.99
$69.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-1-4939-7367-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $34.99
$69.99 (listprice)
price for USA in USD
valid through June 30, 2021
  • ISBN 978-1-4939-8464-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Real Analysis
Book Subtitle
Series, Functions of Several Variables, and Applications
Authors
Translated by
Bálint, G.
Series Title
Undergraduate Texts in Mathematics
Copyright
2017
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media LLC
eBook ISBN
978-1-4939-7369-9
DOI
10.1007/978-1-4939-7369-9
Hardcover ISBN
978-1-4939-7367-5
Softcover ISBN
978-1-4939-8464-0
Series ISSN
0172-6056
Edition Number
1
Number of Pages
IX, 392
Number of Illustrations
44 b/w illustrations
Additional Information
First English Edition, translated from 2nd Hungarian edition by Gergely Bálint
Topics