| （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。 |
| 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 11 MultipleIntegrals 11.1 TheRiemannIntegraloverann-DimensionalInterval 11.2 TheIntegraloveraSet 11.3 GeneralPropertiesoftheIntegral 11.4 ReductionofaMultipleIntegraltoanIteratedIntegral 11.5 ChangeofVariableinaMultipleIntegral 11.6 ImproperMultipleIntegrals 12 SurfacesandDifferentialFormsinRn 12.1 SurfacesinRn 12.2 OrientationofaSurface 12.3 TheBoundaryofaSurfaceanditsOrientation 12.4 TheAreaofaSurfaceinEuclideanSpace 12.5 ElementaryFactsaboutDifferentialForms 13 LineandSurfaceIntegrals 13.1 TheIntegralofaDifferentialForm 13.2 TheVolumeElement.IntegralsofFirstandSecondKind.. 13.3 TheFundamentalIntegralFormulasofAnalysis 14 ElementsofVectorAnalysisandFieldTheory 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 16 UniformConvergenceandBasicOperationsofAnalysis 16.1 PointwiseandUniformConvergence 16.2 UniformConvergenceofSeriesofFunctions 16.3 FunctionalPropertiesofaLimitFunction 16.4 *SubsetsoftheSpaceofContinuousFunctions 17 IntegralsDependingonaParameter 17.1 ProperIntegralsDependingonaParameter 17.2 ImproperIntegralsDependingonaParameter 17.3 TheEulerianIntegrals 17.4 ConvolutionandGeneralizedFunctions 17.5 MultipleIntegralsDependingonaParameter 18 FourierSeriesandtheFourierTransform 18.1 BasicGeneralConceptsConnectedwithFourierSeries 18.2 TrigonometricFourierSeries 18.3 TheFourierTransform 19 AsymptoticExpansions 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 |
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