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Multivariable Analysis

  • Textbook
  • © 2011

Overview

Authors:
  1. Satish Shirali

    1. , (Mohali), Indian Inst. of Science Educ. & Research, Panchkula, India

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  2. Harkrishan Lal Vasudeva

    1. , (Mohali), Indian Inst. of Science Educ. & Research, Chandigarh, India

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    You can also search for this author in PubMed   Google Scholar

  • Contains a number of examples as well as section-by section problems, ranging from simple to complex

  • Problems illustrate the application of concepts introduced as well as further developments

  • Extensive hints and solutions are provided

  • Full chapter on extrema, including examples when the Lagrange method appears to "fail"

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-ix
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  2. Preliminaries

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 1-21

  3. Functions Between Euclidean Spaces

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 23-75

  4. Differentiation

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 77-115

  5. Inverse and Implicit Function Theorems

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 117-150

  6. Extrema

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 151-176

  7. Riemann Integration in Euclidean Space

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 177-216

  8. Transformation of Integrals

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 217-248

  9. The General Stokes Theorem

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 249-301

  10. Solutions

    • Satish Shirali, Harkrishan Lal Vasudeva
    Pages 303-386

  11. Back Matter

    Pages 387-394
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Keywords

About this book

This book provides a rigorous treatment of multivariable differential and integral calculus. Implicit function theorem and the inverse function theorem based on total derivatives is explained along with the results and the connection to solving systems of equations. 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 expounded in the last chapter. With a focus on clarity rather than brevity, this text gives clear motivation, definitions and examples with transparent proofs. Much of the material included is published for the first time in textbook form, for example Schwarz' Theorem in Chapter 2 and double sequences and sufficient conditions for constrained extrema in Chapter 4. A wide selection of problems, ranging from simple to more challenging, are included with carefully formed solutions. Ideal as a classroom text or a self study resource for students, this book will appeal to higher level undergraduates in Mathematics.

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)

Authors and Affiliations

  • , (Mohali), Indian Inst. of Science Educ. & Research, Panchkula, India

    Satish Shirali

  • , (Mohali), Indian Inst. of Science Educ. & Research, Chandigarh, India

    Harkrishan Lal Vasudeva

Bibliographic Information

  • Book Title: Multivariable Analysis

  • Authors: Satish Shirali, Harkrishan Lal Vasudeva

  • DOI: https://doi.org/10.1007/978-0-85729-192-9

  • Publisher: Springer London

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag London Limited 2011

  • Softcover ISBN: 978-0-85729-191-2Published: 20 December 2010

  • eBook ISBN: 978-0-85729-192-9Published: 13 December 2010

  • Edition Number: 1

  • Number of Pages: X, 394

  • Number of Illustrations: 18 b/w illustrations

  • Topics: Real Functions

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