作者[荷兰]杜斯特马特 著
出版社世界图书出版公司
出版时间2009-08
版次1
装帧平装
上书时间2024-08-20
商品详情
- 品相描述:全新
图书标准信息
-
作者
[荷兰]杜斯特马特 著
-
出版社
世界图书出版公司
-
出版时间
2009-08
-
版次
1
-
ISBN
9787510004520
-
定价
49.00元
-
装帧
平装
-
开本
24开
-
纸张
胶版纸
-
页数
422页
-
正文语种
英语
- 【内容简介】
-
Thisbook,whichisintwoparts,providesanintroductiontothetheoryofvector-valuedfunctionsonEuclideanspace.Wefocusonfourmainobjectsofstudyandinadditionconsidertheinteractionsbetweenthese.VolumeIisdevotedtodifferentiation.DifferentiablefunctionsonRncomefirst,inChapters1through3.Next,differentiablemanifoldsembeddedinRarediscussed,inChapters4and5.InVolume11wetakeupintegration.Chapter6dealswiththetheoryofn-dimensionalintegrationoverR.Finally,inChapters7and8lower-dimensionalintegrationoversubmanifoldsofRnisdeveloped;particularattentionispaidtovectoranalysisandthetheoryofdifferentialforms,whicharetreatedindependentlyfromeachother.Generallyspeaking,theemphasisisongeometricaspectsofanalysisratherthanonmattersbelongingtofunctionalanalysis.
- 【目录】
-
VolumeⅠ
Preface
Acknowledgments
Introduction
1Continuity
1.1Innerproductandnorm
1.2Openandclosedsets
1.3Limitsandcontinuousmappings
1.4Compositionofmappings
1.5Homeomorphisms
1.6Completeness
1.7Contractions
1.8Compactnessanduniformcontinuity
1.9Connectedness
2Differentiation
2.1Linearmappings
2.2Differentiablemappings
2.3Directionalandpartialderivatives
2.4Chainrule
2.5MeanValueTheorem
2.6Gradient
2.7Higher-orderderivatives
2.8Taylor'sformula
2.9Criticalpoints
2.10Commutinglimitoperations
3InverseFunctionandImplicitFunctionTheorems
3.1Diffeomorphisms
3.2InverseFunctionTheorems
3.3ApplicationsoflnverseFunctionTheorems
3.4Implicitlydefinedmappings
3.5ImplicitFunctionTheorem
3.6ApplicationsoftheImplicitFunctionTheorem
3.7ImplicitandInverseFunctionTheoremsonC
4Manifolds
4.1Introductoryremarks
4.2Manifolds
4.3ImmersionTheorem
4.4Examplesofimmersions
4.5SubmersionTheorem
4.6Examplesofsubmersions
4.7Equivalentdefinitionsofmanifold
4.8Morse'sLemma
5TangentSpaces
5.1Definitionoftangentspace
5.2Tangentmapping
5.3Examplesoftangentspaces
5.4MethodofLagrangemultipliers
5.5Applicationsofthemethodofmultipliers
5.6Closerinvestigationofcriticalpoints
5.7Gaussiancurvatureofsurface
5.8CurvatureandtorsionofcurveinR3
5.9One-parametergroupsandinfinitesimalgenerators
5.10LinearLiegroupsandtheirLiealgebras
5.11Transversality
Exercises
ReviewExercises
ExercisesforChapter1
ExercisesforChapter2
ExercisesforChapter3
ExercisesforChapter4
ExercisesforChapter5
Notation
Index
VolumeⅡ
Preface
Acknowledgments
Introduction
6Integration
6.1Rectangles
6.2Riemannintegrability
6.3Jordanmeasurability
6.4Successiveintegration
6.5Examplesofsuccessiveintegration
6.6ChangeofVariablesTheorem:formulationandexamples
6.7Partitionsofunity
6.8ApproximationofRiemannintegrablefunctions
6.9ProofofChangeofVariablesTheorem
6.10AbsoluteRiemannintegrability
6.11Applicationofintegration:Fouriertransformation
6.12Dominatedconvergence
6.13Appendix:twootherproofsofChangeofVariablesTheorem
7IntegrationoverSubmanifolds
7.1Densitiesandintegrationwithrespecttodensity
7.2AbsoluteRiemannintegrabilitywithrespecttodensity
7.3Euclideand-dimensionaldensity
7.4ExamplesofEuclideandensities
7.5Opensetsatonesideoftheirboundary
7.6Integrationofatotalderivative
7.7Generalizationsoftheprecedingtheorem
7.8Gauss'DivergenceTheorem
7.9ApplicationsofGauss'DivergenceTheorem
8OrientedIntegration
8.1Lineintegralsandpropertiesofvectorfields
8.2Antidifferentiation
8.3Green'sandCauchy'sIntegralTheorems
8.4Stokes'IntegralTheorem
8.5ApplicationsofStokes'IntegralTheorem
8.6Apotheosis:differentialformsandStokes'Theorem.
8.7Propertiesofdifferentialforms
8.8Applicationsofdifferentialforms
8.9HomotopyLemma
8.10Poincare'sLemma
8.11Degreeofmapping
Exercises
ExercisesforChapter6
ExercisesforChapter7
ExercisesforChapter8
Notation
Index
点击展开
点击收起
— 没有更多了 —
以下为对购买帮助不大的评价