The Implicit Function Theorem
Subtitle: History, Theory, and Applications
By: by Steven G. Krantz, Harold R. Parks
Contributors: Parks, Harold R.; SpringerLink (Online service)
Series: Modern Birkhäuser Classics
Publisher: Springer New York; Imprint: Birkhäuser
Published: 2013
Place of publication: New York, NY
Language: eng
Format: [electronic resource] :
Number of pages: 163
ISBN-13: 9781461459811
Subjects: Differential equations; History of Mathematical Sciences; Ordinary Differential Equations; Global analysis (Mathematics); Analysis; Partial Differential equations; Differential Geometry; Mathematics; Global differential geometry
Description: <p>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.  </p><p><p>There are many different forms of the implicit function theorem, including (i) the classical formulation for <i>C<sup>k</sup></i> 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.</p><p><p>Originally published in 2002, <i>The Implicit Function Theorem</i> 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.</p>
Table of contents: title: ​Preface; title: Introduction to the Implicit Function Theorem; title: History; title: Basic Ideas; title: Applications; title: Variations and Generalizations; title: Advanced Implicit Function Theorems; title: Glossary; title: Bibliography; title: Index.