Table of contents

  1. Front Matter
    Pages 1-9
  2. Asen L. Dontchev, R. Tyrrell Rockafellar
    Pages 1-59
  3. Asen L. Dontchev, R. Tyrrell Rockafellar
    Pages 61-130
  4. Asen L. Dontchev, R. Tyrrell Rockafellar
    Pages 131-195
  5. Asen L. Dontchev, R. Tyrrell Rockafellar
    Pages 197-250
  6. Asen L. Dontchev, R. Tyrrell Rockafellar
    Pages 251-310
  7. Asen L. Dontchev, R. Tyrrell Rockafellar
    Pages 311-362
  8. Back Matter
    Pages 1-12

About this book


The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This book treats the implicit function paradigm in the classical framework and beyond, focusing largely on properties of solution mappings of variational problems.

The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. The first chapter of the book treats the classical implicit function theorem in a way that will be useful for students and teachers of undergraduate calculus. The remaining part becomes gradually more advanced, and considers implicit mappings defined by relations other than equations, e.g., variational problems. Applications to numerical analysis and optimization are also provided.

This valuable book is a major achievement and is sure to become a standard reference on the topic.


Derivative Implicit function calculus differential equation optimization partial differential equation

Authors and affiliations

  • Asen L. Dontchev
    • 1
  • R. Tyrrell Rockafellar
    • 2
  1. 1.Dept. MathematicsUniversity of MichiganAnn Arbor U.S.A.
  2. 2.Dept. MathematicsUniversity of WashingtonSeattleU.S.A.

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-87820-1
  • Online ISBN 978-0-387-87821-8
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site
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