书籍简介:

隐函数定理是数学分析和几何的一个基石，是十八世纪解析函数和力学研究中出现的一部新生力量，隐函数和反函数已经发展成为偏微分方程理论、微分几何和几何分析中的蓬勃力量。隐函数有多种微分形式，包括(1)C^K函数的典型公式；（2）其它函数空间的公式；（3）非光滑函数公式；（4）退化雅克比函数公式。特别强有力的隐函数已经发展成了一些特殊的应用，比如Nash-Moser定理。上面的这些专题，还有更多别的专题都在本书中进行严格讲述。

书籍目录:

Preface

1 IntroductIon to the Implicit Function Theorem

1.1 Implicit Functions

1.2 An Informal Version ofthe Implicit Function Theorem

1.3 Thelmplicit Function Theorem Paradigm

2 History

2.1 Historicallntroduction

2.2 Newton

2.3 Lagrange

2.4 Cauchy

3 Basfcldeas

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 Smoothncss ofthc Distance Function

5 VariatIons and Genera Hzations

5.1 The Weicrstrass Preparation Theorem

5.2 ImplicU Function Theorems without Differenriability

5.3 An Inverse Function Theorcm for Continuous Mappings

5.4 Some Singular Cases of the Implicit Function Theorem

6 Advanced Impllclt Functlon Theorems

6.1 Analyticlmplicit Function Theorems

6.2 Hadamard's Globallnverse Function Thecntm

6.3 The Implicit Function Theorem via the Newton-Raphson Method

6.4 The Nash-Moscrlmplicit Function Theorem

6.4.1 Introductory Remarks

6.4.2 Enunciation of the Nash-MoserThcorem

6.4.3 First Step of the ProofofNash-Moscr

6.4.4 The Crux ofthe Matter

6.4.5 Construction ofthe Smoothing Operators

6.4.6 A UsefulCorollary

Glossary

Bibliography

Index

内容摘要:

The implicit function theorem is. along with its close cousin the inverse func- tion theorem， one of the most important， and one of the oldest， paradigms in modcrn mathemarics. One can see the germ of the idea for the implicir func tion theorem in the writings of Isaac Newton （1642-1727）， and Gottfried Leib-niz's （1646-1716） work cxplicitty contains an instance of implicit differentiation.
　　Whilc Joseph Louis Lagrange （1736-1813） found a theorcm that is essentially a version of the inverse function theorem， ic was Augustin-Louis Cauchy （1789-1857） who approached the implicit function theorem with mathematical rigor and it is he who is gencrally acknowledgcd as the discovcrer of the theorem. In Chap-ter 2， we will give details of the contributions of Newton， Lagrange， and Cauchy to the development of the implicit function theorem.

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书名	隐函数定理站内查询相似图书
	9787510048036 如需购买下载《隐函数定理》pdf扫描版电子书或查询更多相关信息，请直接复制isbn,搜索即可全网搜索该ISBN
出版地	北京	出版单位	世界图书出版公司北京公司
版次	影印本	印次	1
定价(元)	35.0	语种	英文
尺寸	23 × 15	装帧	平装
页数	180	印数

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隐函数定理是世界图书出版公司北京公司于2012.6出版的中图分类号为 O177.91 的主题关于隐函数定理－英文的书籍。