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。

数学分析-(第2卷) 本书特色

这是一套完整介绍数学分析的教材，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。《数学分析》(第2卷)语言通俗，表达清晰，各章有大量的练习、思考题以及*新应用实例。

数学分析-(第2卷) 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 TheContractionMappingPrinciple
10*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 TheGeneralImplicitFunctionTheorem
11MultipleIntegrals
11.1 TheRiemannIntegraloverann-DimensionalInterval
11.2 TheIntegraloveraSet
11.3 GeneralPropertiesoftheIntegral
11.4 ReductionofaMultipleIntegraltoanIteratedIntegral
11.5 ChangeofVariableinaMultipleIntegral
11.6 ImproperMultipleIntegrals
12SurfacesandDifferentialFormsinRn
12.1 SurfacesinRn
12.2 OrientationofaSurface
12.3 TheBoundaryofaSurfaceanditsOrientation
12.4 TheAreaofaSurfaceinEuclideanSpace
12.5 ElementaryFactsaboutDifferentialForms
13LineandSurfaceIntegrals
13.1 TheIntegralofaDifferentialForm
13.2 TheVolumeElement.IntegralsofFirstandSecondKind..
13.3 TheFundamentalIntegralFormulasofAnalysis
14ElementsofVectorAnalysisandFieldTheory
14.1 TheDifferentialOperationsofVectorAnalysis
14.2 TheIntegralFormulasofFieldTheory
14.3 PotentialFields
14.4 ExamplesofApplications
15*IntegrationofDifferentialFormsonManifolds
15.1 ABriefReviewofLinearAlgebra
15.2 Manifolds
15.3 DifferentialFormsandIntegrationonManifolds
15.4 ClosedandExactFormsonManifolds
16UniformConvergenceandBasicOperationsofAnalysis
16.1 PointwiseandUniformConvergence
16.2 UniformConvergenceofSeriesofFunctions
16.3 FunctionalPropertiesofaLimitFunction
16.4 *SubsetsoftheSpaceofContinuousFunctions
17IntegralsDependingonaParameter
17.1 ProperIntegralsDependingonaParameter
17.2 ImproperIntegralsDependingonaParameter
17.3 TheEulerianIntegrals
17.4 ConvolutionandGeneralizedFunctions
17.5 MultipleIntegralsDependingonaParameter
18FourierSeriesandtheFourierTransform
18.1 BasicGeneralConceptsConnectedwithFourierSeries
18.2 TrigonometricFourierSeries
18.3 TheFourierTransform
19AsymptoticExpansions
19.1 AsymptoticFormulasandAsymptoticSeries
19.2 TheAsymptoticsofIntegrals(Laplace'sMethod)
TopicsandQuestionsforMidtermExaminations
1.SeriesandIntegralsDependingonaParameter
2.ProblemsRecommendedasMidtermQuestions
3.IntegralCalculus(SeveralVariables)
4.ProblemsRecommendedforStudyingtheMidtermTopics
ExaminationTopics
1.SeriesandIntegralsDependingonaParameter
2.IntegralCalculus(SeveralVariables)
References
1.ClassicWorks
2.Textbooks
3.ClassroomMaterials
4.FurtherReading
IndexofBasicNotation
SubjectIndex
NameIndex

数学分析-(第2卷) 作者简介

（俄罗斯）佐里奇，本书作者（VladimirA.Zorich)是莫斯科国立大学教授。主要从事分析、保角几何、拟共形映照方面的研究工作。近期从事热力学中的数学问题的研究。他解决了空间拟共形照下的球面同胚问题，并因该研究成果获了“青年数学家国家奖”（National Prize for Young Mathematicians)同时还拥有一项技术专利。作为莫斯科国立大学数学力学系高级实验课程的组织者之一，他在一些大学中开设并教授现代分析学课程，并发表了大量的数学研究成果。