隐函数定理

图书标准信息

• 作者 [美]克朗兹（Steven G.Krantz）、[美]Harold R.Parks 著
• 出版社 世界图书出版公司
• 出版时间 2012-09
• 版次 1
• ISBN 9787510048036
• 定价 35.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 163页
• 正文语种 英语

【内容简介】

　　Theimplicitfunctiontheoremis.alongwithitsclosecousintheinversefunc-tiontheorem，oneofthemostimportant，andoneoftheoldest，paradigmsinmodcrnmathemarics.OnecanseethegermoftheideafortheimplicirfunctiontheoreminthewritingsofIsaacNewton（1642-1727），andGottfriedLeib-niz's（1646-1716）workcxplicittycontainsaninstanceofimplicitdifferentiation.
　　WhilcJosephLouisLagrange（1736-1813）foundatheorcmthatisessentiallyaversionoftheinversefunctiontheorem，icwasAugustin-LouisCauchy（1789-1857）whoapproachedtheimplicitfunctiontheoremwithmathematicalrigoranditishewhoisgencrallyacknowledgcdasthediscovcrerofthetheorem.InChap-ter2，wewillgivedetailsofthecontributionsofNewton，Lagrange，andCauchytothedevelopmentoftheimplicitfunctiontheorem.

【目录】

Preface
1IntroductIontotheImplicitFunctionTheorem
1.1ImplicitFunctions
1.2AnInformalVersionoftheImplicitFunctionTheorem
1.3ThelmplicitFunctionTheoremParadigm

2History
2.1Historicallntroduction
2.2Newton
2.3Lagrange
2.4Cauchy

3Basfcldeas
3.1Introduction
3.2TheInductiveProofoftheImplicitFunctionTheorem
3.3TheClassicalApproachtotheImplicitFunctionTheorem
3.4TheContractionMappingFixedPointPrinciple
3.5TheRankTheoremandtheDecompositionTheorem
3.6ACounterexample

4Applications
4.1OrdinaryDifferentialEquations
4.2NumericalHomotopyMethods
4.3EquivalentDefinitionsofaSmoothSurface
4.4SmoothncssofthcDistanceFunction

5VariatIonsandGeneraHzations
5.1TheWeicrstrassPreparationTheorem
5.2ImplicUFunctionTheoremswithoutDifferenriability
5.3AnInverseFunctionTheorcmforContinuousMappings
5.4SomeSingularCasesoftheImplicitFunctionTheorem

6AdvancedImpllcltFunctlonTheorems
6.1AnalyticlmplicitFunctionTheorems
6.2Hadamard'sGloballnverseFunctionThecntm
6.3TheImplicitFunctionTheoremviatheNewton-RaphsonMethod
6.4TheNash-MoscrlmplicitFunctionTheorem
6.4.1IntroductoryRemarks
6.4.2EnunciationoftheNash-MoserThcorem
6.4.3FirstStepoftheProofofNash-Moscr
6.4.4TheCruxoftheMatter
6.4.5ConstructionoftheSmoothingOperators
6.4.6AUsefulCorollary
Glossary
Bibliography
Index