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-

Series:

Modern Birkhäuser classics

Language:

English

Subjects (All):

Implicit functions.

Physical Description:

1 online resource

Place of Publication:

New York Birkhäuser ©2013

Language Note:

English

System Details:

text file

PDF

Summary:

The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth functions, and (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash-Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present uncorrected reprint of this classic monograph. Originally published in 2002, The Implicit Function Theorem is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas

Contents:

Introduction to the implicit function theorem History Basic ideas Applications Variations and generalizations Advanced implicit function theorems

Notes:

"Reprint of the 2003 Edition"

Includes bibliographical references and index

Online resource; title from digital title page (viewed on June 11, 2021)

Other Format:

Print version Krantz, Steven G. Implicit function theorem

ISBN:

9781461459811

1461459818

146145980X

9781461459804

1283908867

9781283908863

OCLC:

820204665

Access Restriction:

Restricted for use by site license