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- 2002018234 contributor B9210749.
- 2002018234 contributor B9210750.
- 2002018234 created "c2002.".
- 2002018234 date "2002".
- 2002018234 date "c2002.".
- 2002018234 dateCopyrighted "c2002.".
- 2002018234 description "Includes bibliographical references (p. [151]-159) and index.".
- 2002018234 description "Machine generated contents note: 1 Introduction to the Implicit Function Theorem -- 1.1 Implicit Functions -- 1.2 An Informal Version of the Implicit Function Theorem -- 1.3 The Implicit Function Theorem Paradigm -- 2 History -- 2.1 Historical Introduction -- 2.2 Newton -- 2.3 Lagrange -- 2.4 Cauchy -- 3 Basic Ideas -- 3.1 Introduction -- 3.2 The Inductive Proof of the Implicit Function Theorem -- 3.3 The Classical Approach to the Implicit Function Theorem -- 3.4 The Contraction Mapping Fixed Point Principle -- 3.5 The Rank Theorem and the Decomposition Theorem -- 3.6 A Counterexample -- 4 Applications -- 4.1 Ordinary Differential Equations -- 4.2 Numerical Homotopy Methods -- 4.3 Equivalent Definitions of a Smooth Surface -- 4.4 Smoothness of the Distance Function -- 5 Variations and Generalizations -- 5.1 The Weierstrass Preparation Theorem -- 5.2 Implicit Function Theorems without Differentiability -- 5.3 An Inverse Function Theorem for Continuous Mappings -- 5.4 Some Singular Cases of the Implicit Function Theorem -- 6 Advanced Implicit Function Theorems -- 6.1 Analytic Implicit Function Theorems -- 6.2 Hadamard's Global Inverse Function Theorem -- 6.3 The Implicit Function Theorem via the Newton-Raphson Method -- 6.4 The Nash-Moser Implicit Function Theorem -- 6.4.1 Introductory Remarks -- 6.4.2 Enunciation of the Nash-Moser Theorem -- 6.4.3 First Step of the Proof of Nash-Moser -- 6.4.4 The Crux of the Matter -- 6.4.5 Construction of the Smoothing Operators -- 6.4.6 A Useful Corollary.".
- 2002018234 extent "xi, 163 p. ;".
- 2002018234 identifier "0817642854 (alk. paper)".
- 2002018234 identifier "3764342854 (alk. paper)".
- 2002018234 identifier 2002018234-d.html.
- 2002018234 identifier 2002018234.html.
- 2002018234 issued "2002".
- 2002018234 issued "c2002.".
- 2002018234 language "eng".
- 2002018234 publisher "Boston : Birkhäuser,".
- 2002018234 subject "515/.8 21".
- 2002018234 subject "Implicit functions.".
- 2002018234 subject "QA331.5 .K712 2002".
- 2002018234 tableOfContents "Machine generated contents note: 1 Introduction to the Implicit Function Theorem -- 1.1 Implicit Functions -- 1.2 An Informal Version of the Implicit Function Theorem -- 1.3 The Implicit Function Theorem Paradigm -- 2 History -- 2.1 Historical Introduction -- 2.2 Newton -- 2.3 Lagrange -- 2.4 Cauchy -- 3 Basic Ideas -- 3.1 Introduction -- 3.2 The Inductive Proof of the Implicit Function Theorem -- 3.3 The Classical Approach to the Implicit Function Theorem -- 3.4 The Contraction Mapping Fixed Point Principle -- 3.5 The Rank Theorem and the Decomposition Theorem -- 3.6 A Counterexample -- 4 Applications -- 4.1 Ordinary Differential Equations -- 4.2 Numerical Homotopy Methods -- 4.3 Equivalent Definitions of a Smooth Surface -- 4.4 Smoothness of the Distance Function -- 5 Variations and Generalizations -- 5.1 The Weierstrass Preparation Theorem -- 5.2 Implicit Function Theorems without Differentiability -- 5.3 An Inverse Function Theorem for Continuous Mappings -- 5.4 Some Singular Cases of the Implicit Function Theorem -- 6 Advanced Implicit Function Theorems -- 6.1 Analytic Implicit Function Theorems -- 6.2 Hadamard's Global Inverse Function Theorem -- 6.3 The Implicit Function Theorem via the Newton-Raphson Method -- 6.4 The Nash-Moser Implicit Function Theorem -- 6.4.1 Introductory Remarks -- 6.4.2 Enunciation of the Nash-Moser Theorem -- 6.4.3 First Step of the Proof of Nash-Moser -- 6.4.4 The Crux of the Matter -- 6.4.5 Construction of the Smoothing Operators -- 6.4.6 A Useful Corollary.".
- 2002018234 title "The implicit function theorem : history, theory, and applications / Steven G. Krantz, Harold R. Parks.".
- 2002018234 type "text".