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Several Real Variables

  • Shmuel Kantorovitz
Textbook

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Shmuel Kantorovitz
    Pages 1-57
  3. Shmuel Kantorovitz
    Pages 59-93
  4. Shmuel Kantorovitz
    Pages 95-162
  5. Shmuel Kantorovitz
    Pages 163-239
  6. Shmuel Kantorovitz
    Pages E1-E2
  7. Back Matter
    Pages 241-307

About this book

Introduction

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 line

ar algebra and analysis of one real variable.

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

Authors and affiliations

  • Shmuel Kantorovitz
    • 1
  1. 1.Department of MathematicsBar-Ilan University Ramat GanIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-27956-5
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-27955-8
  • Online ISBN 978-3-319-27956-5
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • Buy this book on publisher's site