Differential Calculus in Normed Linear Spaces

  • Kalyan¬†Mukherjea

Part of the Texts and Readings in Mathematics book series (TRIM, volume 26)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Kalyan Mukherjea
    Pages 1-36
  3. Kalyan Mukherjea
    Pages 37-67
  4. Kalyan Mukherjea
    Pages 68-133
  5. Kalyan Mukherjea
    Pages 134-208
  6. Kalyan Mukherjea
    Pages 209-238
  7. Kalyan Mukherjea
    Pages 239-267
  8. Back Matter
    Pages 268-282

About this book

Introduction

This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces.The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a real variable and a little Linear Algebra should provide adequate background for understanding the book. The first two chapters cover much of the more advanced background material on Linear Algebra (like dual spaces, multilinear functions and tensor products.) Chapter 3 gives an ab initio exposition of the basic results concerning the topology of metric spaces, particularly of normed linear spaces.The last chapter deals with miscellaneous applications of the Differential Calculus including an introduction to the Calculus of Variations. As a corollary to this, there is a brief discussion of geodesics in Euclidean and hyperbolic planes and non-Euclidean geometry.

Authors and affiliations

  • Kalyan¬†Mukherjea
    • 1
  1. 1.Indian Statistical InstituteKolkataIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-93-86279-34-7
  • Copyright Information Hindustan Book Agency (India) 2007
  • Publisher Name Hindustan Book Agency, Gurgaon
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-81-85931-76-0
  • Online ISBN 978-93-86279-34-7
  • Series Print ISSN 2366-8717
  • Series Online ISSN 2366-8725
  • About this book