Overview
- Affordable reprint of a classic monograph
- Accessible and thorough treatment of the implicit and inverse function theorems and their applications
- Unifies disparate ideas that have played an important role in modern mathematics
Part of the book series: Modern Birkhäuser Classics (MBC)
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Table of contents (6 chapters)
Keywords
About this book
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 function, 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.​
Reviews
From the reviews:
“The book under review balances the historical analyses with presentations and discussions of the proofs of some formulations of the implicit function theorem. … The authors have taken some care to make the book self-contained, and as such a well-motivated undergraduate student can profitably read many parts of it, and the whole book is within the reach of a first-year graduate student.” (Felipe Zaldivar, MAA Reviews, March, 2013)
Authors and Affiliations
Bibliographic Information
Book Title: The Implicit Function Theorem
Book Subtitle: History, Theory, and Applications
Authors: Steven G. Krantz, Harold R. Parks
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-1-4614-5981-1
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Softcover ISBN: 978-1-4614-5980-4Published: 09 November 2012
eBook ISBN: 978-1-4614-5981-1Published: 09 November 2012
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: XIII, 163
Additional Information: Originally published as a softcover
Topics: Analysis, Partial Differential Equations, Differential Geometry, History of Mathematical Sciences, Ordinary Differential Equations