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Differential Calculus in Normed Linear Spaces: Second Edition
Kalyan Mukherjea, Indian Statistical Institute, Kolkata, India
A publication of Hindustan Book Agency.
cover
Hindustan Book Agency
2007; 300 pp; softcover
ISBN-10: 81-85931-76-3
ISBN-13: 978-81-85931-76-0
List Price: US$40
Member Price: US$32
Order Code: HIN/17.R
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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.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

Graduate students and research mathematicians interested in differential calculus.

Reviews

Praise for the First Edition ...

"... at this sort of level it could form the backbone for an excellent course in analysis. ... Institutional use apart, please read this remarkable, striking and original book."

-- The Mathematical Gazette

Table of Contents

  • Preliminaries
  • Linear spaces: New spaces for old
  • Normed linear spaces, metric spaces
  • Calculus
  • Existence theorems
  • Applications: stationary values
  • Appendix: Green's theorem
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