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Texts and Readings in Mathematics

Differential Calculas in Normed Linear Spaces

Authors: Mukherjea, Kalyan

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About this book

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.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $40.00
price for USA in USD (gross)
  • ISBN 978-93-86279-34-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Differential Calculas in Normed Linear Spaces
Authors
Series Title
Texts and Readings in Mathematics
Series Volume
26
Copyright
2007
Publisher
Hindustan Book Agency
Copyright Holder
Hindustan Book Agency (India)
eBook ISBN
978-93-86279-34-7
DOI
10.1007/978-93-86279-34-7
Edition Number
2
Number of Pages
294
Topics