Multivariable Analysis

  • Satish Shirali
  • Harkrishan Lal Vasudeva

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

  • Satish Shirali
    • 1
  • Harkrishan Lal Vasudeva
    • 2
  1. 1., (Mohali)Indian Inst. of Science Educ. & ResearchPanchkulaIndia
  2. 2., (Mohali)Indian Inst. of Science Educ. & ResearchChandigarhIndia

Bibliographic information

  • 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
  • Print ISBN 978-0-85729-191-2
  • Online ISBN 978-0-85729-192-9
  • About this book