TY  - BOOK
AU  - Krantz,Steven G.
AU  - Parks,Harold R.
ED  - SpringerLink (Online service)
TI  - The Implicit Function Theorem: History, Theory, and Applications 
T2  - Modern Birkhäuser Classics
SN  - 9781461459811
AV  - QA299.6-433 
U1  - 515 23
PY  - 2013///
CY  - New York, NY
PB  - Springer New York, Imprint: Birkhäuser
KW  - Mathematics
KW  - Mathematical analysis
KW  - Analysis (Mathematics)
KW  - Differential equations
KW  - Partial differential equations
KW  - Differential geometry
KW  - History
KW  - Analysis
KW  - Partial Differential Equations
KW  - Differential Geometry
KW  - History of Mathematical Sciences
KW  - Ordinary Differential Equations
N1  - Preface -- Introduction to the Implicit Function Theorem -- History -- Basic Ideas -- Applications -- Variations and Generalizations -- Advanced Implicit Function Theorems -- Glossary -- Bibliography -- Index
N2  - 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 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
UR  - http://dx.doi.org/10.1007/978-1-4614-5981-1
ER  -