The implicit function theorem : history, theory, and applications / Steven G. Krantz, Harold R. Parks.

Format:

Book

Author/Creator:

Krantz, Steven G. (Steven George), 1951-

Contributor:

Parks, Harold R., 1949-

Anne and Joseph Trachtman Memorial Book Fund.

Language:

English

Subjects (All):

Implicit functions.

Physical Description:

xi, 163 pages ; 24 cm

Place of Publication:

Boston : Birkhäuser, [2002]

Summary:

The implicit function theorem, part of the bedrock of mathematical analysis and geometry, has important implications in the theories of partial differential equations, differential geometry, and geometric analysis. Its history is lively and complex, and is intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples, is recounted for the first time here.

Contents:

Implicit functions

An informal version of the implicit function theorem

The implicit function theorem paradigm

Historical introduction

Newton

Lagrange

Cauchy

The inductive proof of the implicit function theorem

The classical approach to the implicit function theorem

The contraction mapping fixed point principle

The rank theorem and the decomposition theorem

A counterexample

Ordinary differential equations

Numerical homotopy methods

Equivalent definitions of a smooth surface

Smoothness of the distance function

The Weierstrass preparation theorem

Implicit function theorems without differentiability

An inverse function theorem for continuous mappings

Some singular cases of the implicit function theorem

Analytic implicit function theorems

Hadamard's global inverse function theorem

The implicit function theorem via the Newton-Raphson method

the Nash-Moser implicit function theorem.

Notes:

Includes bibliographical references (pages [151]-159) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Anne and Joseph Trachtman Memorial Book Fund.

ISBN:

0817642854

9780817642853

3764342854

9783764342852

OCLC:

48958382

Publisher Number:

99934671049