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數學分析-(第2卷) 版權信息
- ISBN：7506282232
- 條形碼：9787506282239 ; 978-7-5062-8223-9
- 裝幀：簡裝本
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
數學分析-(第2卷) 本書特色
這是一套完整介紹數學分析的教材，內容涉及從實數到流形上的微分形式，其中包括漸近方法、傅立葉分析，拉普拉斯變換、勒讓德變換，橢圓函數以及頻率分布。《數學分析》(第2卷)語言通俗，表達清晰，各章有大量的練習、思考題以及*新應用實例。
數學分析-(第2卷) 內容簡介
本書內容涉及從實數到流形上的微分形式，其中包括漸近方法、傅立葉分析、拉普拉斯變換、勒讓德變換、橢圓函數以及頻率分布。
數學分析-(第2卷) 目錄
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
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
展開全部
數學分析-(第2卷) 作者簡介
（俄羅斯）佐里奇，本書作者（VladimirA.Zorich)是莫斯科國立大學教授。主要從事分析、保角幾何、擬共形映照方面的研究工作。近期從事熱力學中的數學問題的研究。他解決了空間擬共形照下的球面同胚問題，并因該研究成果獲了“青年數學家國家獎”（National Prize for Young Mathematicians)同時還擁有一項技術專利。 作為莫斯科國立大學數學力學系高級實驗課程的組織者之一，他在一些大學中開設并教授現代分析學課程，并發表了大量的數學研究成果。
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