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© 2011

Multivariable Analysis

Textbook

Table of contents

  1. Front Matter
    Pages i-ix
  2. Satish Shirali, Harkrishan Lal Vasudeva
    Pages 1-21
  3. Satish Shirali, Harkrishan Lal Vasudeva
    Pages 23-75
  4. Satish Shirali, Harkrishan Lal Vasudeva
    Pages 77-115
  5. Satish Shirali, Harkrishan Lal Vasudeva
    Pages 117-150
  6. Satish Shirali, Harkrishan Lal Vasudeva
    Pages 151-176
  7. Satish Shirali, Harkrishan Lal Vasudeva
    Pages 177-216
  8. Satish Shirali, Harkrishan Lal Vasudeva
    Pages 217-248
  9. Satish Shirali, Harkrishan Lal Vasudeva
    Pages 249-301
  10. Satish Shirali, Harkrishan Lal Vasudeva
    Pages 303-386
  11. Back Matter
    Pages 387-394

About this book

Introduction

This book provides a rigorous treatment of multivariable differential and integral calculus. Inverse and implicit function theorems based on total derivatives are given and the connection with solving systems of equations is included. There is an extensive treatment of extrema, including constrained extrema and Lagrange multipliers, covering both first order necessary conditions and second order sufficient conditions. The material on Riemann integration in n dimensions, being delicate by its very nature, is discussed in detail. Differential forms and the general Stokes' Theorem are explained in the last chapter.

With a focus on clarity rather than brevity, this text gives clear motivation, definitions and examples with transparent proofs. Some of the material included is difficult to find in most texts, for example, double sequences in Chapter 2, Schwarz’ Theorem in Chapter 3 and sufficient conditions for constrained extrema in Chapter 5. A wide selection of problems, ranging from simple to challenging, is included with carefully written solutions. Ideal as a classroom text or a self study resource for students, this book will appeal to higher level undergraduates in Mathematics.

Keywords

Differential and integral Calculus in Rn Extrema Inverse and implicit function theorems Lagrange multipliers Riemann integration in Rn Transformation formula

Authors and affiliations

  1. 1., (Mohali)Indian Inst. of Science Educ. & ResearchPanchkulaIndia
  2. 2., (Mohali)Indian Inst. of Science Educ. & ResearchChandigarhIndia

Bibliographic information

  • Book Title Multivariable Analysis
  • Authors Satish Shirali
    Harkrishan Lal Vasudeva
  • DOI https://doi.org/10.1007/978-0-85729-192-9
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-0-85729-191-2
  • eBook ISBN 978-0-85729-192-9
  • Edition Number 1
  • Number of Pages X, 394
  • Number of Illustrations 18 b/w illustrations, 0 illustrations in colour
  • Topics Real Functions
  • Buy this book on publisher's site

Reviews

From the reviews:

“This is a textbook for a rigorous multivariable analysis course, intended for an undergraduate audience of juniors and seniors … . The book also includes some material not easily found in the existing literature. … also contains detailed solutions to many of its exercise; in fact, almost one-quarter of the book is devoted to solutions. … the book very attractive to people interested in self-study, as well as to instructors using different books who are looking for a source of additional problems for their classes.” (Mark Hunacek, The Mathematical Association of America, November, 2011)