Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Undergraduate Texts in Mathematics (UTM, volume 3)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
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)
Authors and Affiliations
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.
Bibliographic Information
Book Title: Real Analysis
Book Subtitle: Series, Functions of Several Variables, and Applications
Authors: Miklós Laczkovich, Vera T. Sós
Translated by: Gergely Bálint
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4939-7369-9
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media LLC 2017
Hardcover ISBN: 978-1-4939-7367-5Published: 16 December 2017
Softcover ISBN: 978-1-4939-8464-0Published: 30 August 2018
eBook ISBN: 978-1-4939-7369-9Published: 14 December 2017
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
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: Analysis