分析Ⅱ（影印版）

图书标准信息

• 作者 [法]戈德门特（Godement R.） 著
• 出版社 高等教育出版社
• 出版时间 2009-12
• 版次 1
• ISBN 9787040279542
• 定价 35.60元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 443页
• 字数 480千字
• 正文语种 英语
• 丛书 天元基金影印数学丛书

【内容简介】

　　《天元基金影印数学丛书：分析2（影印版）》是作者在巴黎第七大学讲授分析课程数十年的结晶，其目的是阐明分析是什么，它是如何发展的。本书非常巧妙地将严格的数学与教学实际、历史背景结合在一起，对主要结论常常给出各种可能的探索途径，以使读者理解基本概念、方法和推演过程了作者在本书中较早地引入了一些较深的内容，如在第一卷中介绍了拓扑空间的概念，在第二卷中介绍了Lebesgue理论的基本定理和Weierstrass椭圆函数的构造。

　　《天元基金影印数学丛书：分析2（影印版）》第一卷的内容包括集合与函数、离散变量的收敛性、连续变量的收敛性、幂函数、指数函数与三角函数；第二卷的内容包括Fourier级数和Fourier积分以及可以通过Fourier级数解释的Weierstrass的解析函数理论。

【目录】

V-DifferentialandIntegralCalculus

1.TheRiemannIntegral

1-Upperandlowerintegralsofaboundedfunction

2-Elementarypropertiesofintegrals

3-Riemannsums.Theintegralnotation

4-Uniformlimitsofintegrablefunctions

5-ApplicationtoFourierseriesandtopowerseries

2.IntegrabilityConditions

6-TheBorel-LebesgueTheorem

7-Integrabilityofregulatedorcontinuousfunctions

8-Uniformcontinuityanditsconsequences

9-Differentiationandintegrationunderthefsign

10-Semicontinuousfunctions

11-Integrationofsemicontinuousfunctions

3.The"FundamentalTheorem"（FT）

12-Thefundamentaltheoremofthedifferentialandintegralcalculus

13-Extensionofthefundamentaltheoremtoregulatedfunctions

14-Convexfunctions;HolderandMinkowskiinequalities

4.Integrationbyparts

15-Integrationbyparts

16-ThesquarewaveFourierseries

17-Wallisformula

5.TaylorsFormula

18-TaylorsFormula

6.Thechangeofvariableformula

19-Changeofvariableinanintegral

20-Integrationofrationalfractions

7.GeneralisedRiemannintegrals

21-Convergentintegrals：examplesanddefinitions

22-Absolutelyconvergentintegrals

23-Passagetothelimitunderthefsign

24-Seriesandintegrals

25-Differentiationunderthefsign

26-Integrationunderthefsign

8.ApproximationTheorems

27-HowtomakeCafunctionwhichisnot

28-Approximationbypolynomials

29-Functionshavinggivenderivativesatapoint

9.RadonmeasuresinRorC

30-Radonmeasuresonacompactset

31-Measuresonalocallycompactset

32-TheStieltjesconstruction

33-Applicationtodoubleintegrals

10.Schwartzdistributions

34-Definitionandexamples

35-Derivativesofadistribution

AppendixtoChapterV-IntroductiontotheLebesgueTheory

VI-AsymptoticAnalysis

1.Truncatedexpansions

1-Comparisonrelations

2-Rulesofcalculation

3-Truncatedexpansions

4-Truncatedexpansionofaquotient

5-Gaussconvergencecriterion

6-Thehypergeometricseries

7-Asymptoticstudyoftheequationxex=t

8-Asymptoticsoftherootsofsinxlogx=1

9-Keplersequation

10-AsymptoticsoftheBesselfunctions

2.Summationformulae

11-Cavalieriandthesums1k+2k+...+nk

12-JakobBernoulli

13-Thepowerseriesforcotz

14-Eulerandthepowerseriesforarctanx

15-Euler，Maclaurinandtheirsummationformula

16-TheEuler-Maclaurinformulawithremainder

17-Calculatinganintegralbythetrapezoidalrule

18-Thesum1+1/2...+l/n，theinfiniteproductfortheFfunction，andStirlingsformula

19-Analyticcontinuationofthezetafunction

VII-HarmonicAnalysisandHolomcrphicFunctions

1-Cauchysintegralformulaforacircle

1.Analysisontheunitcircle

2-Functionsandmeasuresontheunitcircle

3-Fouriercoefficients

4-Convolutionproducton

5-DiracsequencesinT

2.ElementarytheoremsonFourierseries

6-AbsolutelyconvergentFourierseries

7-Hilbertiancalculations

8-TheParseval-Besselequality

9-Fourierseriesofdifferentiablefunctions

10-Distributionson

3.Dirichletsmethod

11-Dirichletstheorem

12-Fejerstheorem

13-UniformlyconvergentFourierseries

4.Analyticandholomorphicfunctions

14-Analyticityoftheholomorphicfunctions

15-Themaximumprinciple

16-Functionsanalyticinanannulus.Singularpoints.Meromorphicfunctions

17-Periodicholomorphicfunctions

18-ThetheoremsofLiouvilleanddAlembert-Gauss

19-Limitsofholomorphicfunctions

20-Infiniteproductsofholomorphicfunctions

5.HarmonicfunctionsandFourierseries

21-AnalyticfunctionsdefinedbyaCauchyintegral

22-Poissonsfunction

23-ApplicationstoFourierseries

24-Harmonicfunctions

25-Limitsofharmonicfunctions

26-TheDirichletproblemforadisc

6.FromFourierseriestointegrals

27-ThePoissonsummationformula

28-Jacobisthetafunction

29-FundamentalformulaefortheFouriertransform

30-Extensionsoftheinversionformula

31-TheFouriertransformanddifferentiation

32-Tempereddistributions

Postface.Science，technology，arms

Index

TableofContentsofVolumeI