Differential Calculus in Normed Linear Spaces (Texts and Readings in Mathematics): 26 - Softcover

Mukherjea, Kalyan

Softcover

ISBN 10: 8185931763 ISBN 13: 9788185931760

Publisher: Hindustan Book Agency, 2007

Synopsis

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.

About this title

Review

"... 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"

Edition details

• Publisher: Hindustan Book Agency
• Publication date: 2007
• Language: English
• ISBN 10: 8185931763
• ISBN 13: 9788185931760
• Binding: Paperback
• Edition number: 2
• Number of pages: 294