Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
Keywords
- complete metric space
- compact set
- continuous function
- Weierstrass Approximation Theorem
- Stone-Weierstrass Theorem
- differential
- Jacobian
- Banach Fixed Point Theorem
- Implicit Function Theorem
- extrema with constraints
- line integrals
- conservative fields
- Green's theorem
- integration on domains
- surface integrals
About this book
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.
Reviews
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Several Real Variables
Authors: Shmuel Kantorovitz
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-319-27956-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-27955-8Published: 19 February 2016
eBook ISBN: 978-3-319-27956-5Published: 09 February 2016
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XII, 307
Number of Illustrations: 16 b/w illustrations
Topics: Real Functions