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Springer Undergraduate Mathematics Series

Several Real Variables

Authors: Kantorovitz, Shmuel

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  • A modern, self-contained exposition of the basic analysis of functions of several real variables 
  • An easy-to-read introduction to first-order logic and model theory
  • Presents the essential aspects of model theory needed to understand model theoretic algebra
  • Includes interesting and profound applications of model theory to algebra 
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eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-319-27956-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $44.99
price for USA in USD
  • ISBN 978-3-319-27955-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This undergraduate textbook is based on lectures given by the author on the differential and integral calculus of functions of several real variables. The book has a modern approach and includes topics such as:

•The p-norms on vector space and their equivalence

•The Weierstrass and Stone-Weierstrass approximation theorems

•The differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables

•The Implicit Function Theorem for a system of equations, proved via Banach’s Fixed Point Theorem

•Applications to Ordinary Differential Equations

•Line integrals and an introduction to surface integrals

This book features numerous examples, detailed proofs, as well as exercises at the end of sections. Many of the exercises have detailed solutions, making the book suitable for self-study.

Several Real Variables will be useful for undergraduate students in mathematics who have completed first courses in linear algebra and analysis of one real variable.

About the authors

The author is an expert in Spectral Theory and semigroups of operators, researching in this area for 50 years, publishing numerous papers and three monographs.  

Reviews

“This textbook is excellent for self-study as it contains a lot of well-chosen examples and complete proofs. Each topic is followed by a set of suitable exercises, accompanied with detailed solutions, which complement the presented material significantly. … The reader can obtain a very deep insight into analysis and related theories as the book provides deep understanding of principles.” (Roza Aceska, zbMATH 1405.26003, 2019)​

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-319-27956-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $44.99
price for USA in USD
  • ISBN 978-3-319-27955-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Several Real Variables
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-27956-5
DOI
10.1007/978-3-319-27956-5
Softcover ISBN
978-3-319-27955-8
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XII, 307
Number of Illustrations
16 b/w illustrations
Topics