The Implicit Function Theorem: History, Theory, and Applications / Edition 1

The Implicit Function Theorem: History, Theory, and Applications / Edition 1

by Steven G. Krantz, Harold R. Parks
     
 

ISBN-10: 0817642854

ISBN-13: 9780817642853

Pub. Date: 04/01/2002

Publisher: Birkhauser Verlag

The implicit function theorem is part of the bedrock of mathematics 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

Overview

The implicit function theorem is part of the bedrock of mathematics 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 function, (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 volume.

The history of the implicit function theorem is a lively and complex store, and intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples and proofs, is recounted for the first time here. It is an exciting tale, and it continues to evolve.

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 stunts, 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.

Product Details

ISBN-13:
9780817642853
Publisher:
Birkhauser Verlag
Publication date:
04/01/2002
Pages:
174
Product dimensions:
6.40(w) x 9.30(h) x 0.70(d)

Table of Contents

Preface
• Introduction to the Implicit Function Theorem
• History
• Basic Ideas
• Applications
• Variations and Generalizations
• Advanced Implicit Function Theorems
• Glossary
• Bibliography
• Index

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >