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The Implicit Function Theorem: History, Theory, and Applications

The Implicit Function Theorem: History, Theory, and Applications
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Field name Details
Dewey Class 515
Title The Implicit Function Theorem ([Ebook]) : History, Theory, and Applications / by Steven G. Krantz, Harold R. Parks.
Author Krantz, Steven George , 1951-
Added Personal Name Parks, Harold R.
Other name(s) SpringerLink (Online service)
Edition statement Reprint of the 2003 edition
Publication New York, NY : Birkhäuser , 2013
Physical Details XIII, 163 pages : online resource.
Series Modern Birkhäuser classics
ISBN 9781461459811
Summary Note 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 functions, and (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the NashâMoser 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's 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.:
Contents note Preface -- Introduction to the Implicit Function Theorem -- History -- Basic Ideas -- Applications -- Variations and Generalizations -- Advanced Implicit Function Theorems -- Glossary -- Bibliography -- Index.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site http://dx.doi.org/10.1007/978-1-4614-5981-1
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