数学分析-(第2卷)

内容简介

[

本书内容涉及从实数到流形上的微分形式，其中包括渐近方法、傅立叶分析、拉普拉斯变换、勒让德变换、椭圆函数以及频率分布。

]

目录

9 *ContinuousMappings(GeneralTheory). 9.1 MetricSpaces 9.2 TopologicalSpaces 9.3 CompactSets 9.4 ConnectedTopologicalSpaces 9.5 CompleteMetricSpaces 9.6 ContinuousMappingsofTopologicalSpaces 9.7 TheContractionMappingPrinciple10 *DifferentialCalculusfromaGeneralViewpoint 10.1 Normed Vector SPaces 10.2 LinearandMultilinearTransformations 10.3 TheDifferentialofaMapping 10.4 TheFinite-increment(Mean-value)Theorem 10.5 Higher-orderDerivatives 10.6 Taylor’sFormulaandtheStudyofExtrema 10.7 TheGeneralImplicitFunctionTheorem11 MultipleIntegrals 11.1 TheRiemannIntegraloverann-DimensionalInterval 11.2 TheIntegraloveraSet 11.3 GeneralPropertiesoftheIntegral 11.4 ReductionofaMultipleIntegraltoanIteratedIntegral 11.5 ChangeofVariableinaMultipleIntegral 11.6 ImproperMultipleIntegrals12 SurfacesandDifferentialFormsinRn 12.1 SurfacesinRn 12.2 OrientationofaSurface 12.3 TheBoundaryofaSurfaceanditsOrientation 12.4 TheAreaofaSurfaceinEuclideanSpace 12.5 ElementaryFactsaboutDifferentialForms13 LineandSurfaceIntegrals 13.1 TheIntegralofaDifferentialForm 13.2 TheVolumeElement.IntegralsofFirstandSecondKind.. 13.3 TheFundamentalIntegralFormulasofAnalysis14 ElementsofVectorAnalysisandFieldTheory 14.1 TheDifferentialOperationsofVectorAnalysis 14.2 TheIntegralFormulasofFieldTheory 14.3 PotentialFields 14.4 ExamplesofApplications15 *IntegrationofDifferentialFormsonManifolds 15.1 ABriefReviewofLinearAlgebra 15.2 Manifolds 15.3 DifferentialFormsandIntegrationonManifolds 15.4 ClosedandExactFormsonManifolds16 UniformConvergenceandBasicOperationsofAnalysis 16.1 PointwiseandUniformConvergence 16.2 UniformConvergenceofSeriesofFunctions 16.3 FunctionalPropertiesofaLimitFunction 16.4 *SubsetsoftheSpaceofContinuousFunctions17 IntegralsDependingonaParameter 17.1 ProperIntegralsDependingonaParameter 17.2 ImproperIntegralsDependingonaParameter 17.3 TheEulerianIntegrals 17.4 ConvolutionandGeneralizedFunctions 17.5 MultipleIntegralsDependingonaParameter18 FourierSeriesandtheFourierTransform 18.1 BasicGeneralConceptsConnectedwithFourierSeries 18.2 TrigonometricFourierSeries 18.3 TheFourierTransform19 AsymptoticExpansions 19.1 AsymptoticFormulasandAsymptoticSeries 19.2 TheAsymptoticsofIntegrals(Laplace’sMethod)TopicsandQuestionsforMidtermExaminations 1.SeriesandIntegralsDependingonaParameter 2.ProblemsRecommendedasMidtermQuestions 3.IntegralCalculus(SeveralVariables) 4.ProblemsRecommendedforStudyingtheMidtermTopicsExaminationTopics 1.SeriesandIntegralsDependingonaParameter 2.IntegralCalculus(SeveralVariables)References 1.ClassicWorks 2.Textbooks 3.ClassroomMaterials 4.FurtherReadingIndexofBasicNotationSubjectIndexNameIndex

封面

书名:数学分析-(第2卷)

作者:佐里奇

页数:681

定价:¥69.0

出版社:世界图书出版公司

出版日期:2006-01-01

ISBN:9787506282239

PDF电子书大小:48MB 高清扫描完整版