Modern Birkhäuser Classics

The Implicit Function Theorem

History, Theory, and Applications

Authors: Krantz, Steven G, Parks, Harold R.

  • 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
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eBook $69.99
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  • ISBN 978-1-4614-5981-1
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  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-1-4614-5980-4
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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)


Table of contents (6 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4614-5981-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-1-4614-5980-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Implicit Function Theorem
Book Subtitle
History, Theory, and Applications
Authors
Series Title
Modern Birkhäuser Classics
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-5981-1
DOI
10.1007/978-1-4614-5981-1
Softcover ISBN
978-1-4614-5980-4
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XIII, 163
Additional Information
Originally published as a softcover
Topics