# Differential Calculus in Normed Linear Spaces: Second Edition

Share this page
*Kalyan Mukherjea*

A publication of Hindustan Book Agency

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 & Endorsements

... 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