| Description |
1 online resource (xix, 279 pages) : illustrations |
| Series |
Texts and readings in mathematics ; 26 |
|
Texts and readings in mathematics ; 26.
|
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 273-274) and index |
| Notes |
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
|
digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL |
|
Print version record |
| Subject |
Normed linear spaces.
|
|
Differential calculus.
|
|
Differential calculus.
|
|
Normed linear spaces.
|
| Form |
Electronic book
|
| ISBN |
9789386279347 |
|
9386279347 |
|
