在数学中，隐函数定理是一个描述关系以隐函数表示的某些变量之间是否存在显式关系的定理。

克朗兹编著的《隐函数定理》介绍了隐函数定理的基本知识，是全英文版。

Preface

1 Introduction to the Implicit Function Theorem

 1.l 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

Glossary

Bibliography

Index