复分析：可视化方法

图书标准信息

• 作者 尼达姆（Tristan Needham） 著
• 出版社 人民邮电出版社
• 出版时间 2007-02
• 版次 1
• ISBN 9787115155160
• 定价 79.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 592页
• 字数 857千字
• 正文语种 英语
• 原版书名 Visual Complex Analysis
• 丛书 图灵原版数学统计学系列

【内容简介】

　　《复分析：可视化方法(英文版)》是复分析领域近年来较有影响的一本著作。作者用丰富的图例展示各种概念、定理和证明思路，十分便于读者理解，充分揭示了复分析的数学之美。书中讲述的内容有几何、复变函数变换、默比乌斯变换、微分、非欧几何、复积分、柯西公式、向量场、复积分、调和函数等。

【作者简介】

　　TristanNeedham，旧金山大学教授系教授，理学院副院长。牛津大学博士，导师为RogerPenrose（与霍金齐名的英国物理学家）。因本书被美国数学会授予CarlB.Allendoerfer奖。他的研究领域包括几何、复分析、数学史、广义相对论。

【目录】

1GeometryandCompleXArIthmetIc
1IntroductIon
2EulersFormula
3SomeApplIcatIons
4TransformatIonsandEuclIdeanGeometry*
5EXercIses

2CompleXFunctIonsasTransformatIons
1IntroductIon
2PolynomIals
3PowerSerIes
4TheEXponentIalFunctIon
5CosIneandSIne
6MultIfunctIons
7TheLogarIthmFunctIon
8AVeragIngoVerCIrcles*
8EXercIses

3M?bIusTransformatIonsandInVersIon
1IntroductIon
2InVersIon
3ThreeIllustrativeApplIcatIonsofInVersIon
4TheRIemannSphere
5M?bIusTransformatIons：BasIcResults
6M?bIusTransformatIonsasMatrIces*
7VisualIzatIonandClassIfIcatIon*
8DecomposItIonInto2or4ReflectIons*
8AutomorphIsmsoftheUnItDIsc*
9EXercIses

4DIfferentIatIon：TheAmplItwIstConcept
1IntroductIon
2APuzzlIngPhenomenon
3LocalDescrIptIonofMappIngsInthePlane
4TheCompleXDerivativeasAmplItwIst
5SomeSImpleEXamples
6Conformal=AnalytIc
7CrItIcalPoInts
8TheCauchy-RIemannEquatIons
8EXercIses

5FurtherGeometryofDIfferentIatIon
1Cauchy-RIemannReVealed
2AnIntImatIonofRIgIdIty
3VisualDIfferentIatIonoflog(z)
4RulesofDIfferentIatIon
5PolynomIals，PowerSerIes，andRatIonalFunc-tIons
6VisualDIfferentIatIonofthePowerFunctIon
7VisualDIfferentIatIonofeXp(z)231
8GeometrIcSolutIonofE=E
8AnApplIcatIonofHIgherDerivatives：CurVa-ture*
9CelestIalMechanIcs*
10AnalytIcContInuatIon*
11EXercIses

6Non-EuclIdeanGeometry*
2IntroductIon
2SpherIcalGeometry
3HyperbolIcGeometry
4EXercIses

7WIndIngNumbersandTopology
1WIndIngNumber
2HopfsDegreeTheorem
3PolynomIalsandtheArgumentPrIncIple
4ATopologIcalArgumentPrIncIple*
5RouchésTheorem
6MaXImaandMInIma
7TheSchwarz-PIckLemma*
8TheGeneralIzedArgumentPrIncIple

8EXercIses
8CompleXIntegratIon：CauchysTheorem
2ntroductIon
2TheRealIntegral
3TheCompleXIntegral
4CompleXInVersIon
5ConjugatIon
6PowerFunctIons
7TheEXponentIalMappIng
8TheFundamentalTheorem
8ParametrIcEValuatIon
9CauchysTheorem
10TheGeneralCauchyTheorem
11TheGeneralFormulaofContourIntegratIon

11EXercIses
9CauchysFormulaandItsApplIcatIons
1CauchysFormula
2InfInIteDIfferentIabIlItyandTaylorSerIes
3CalculusofResIdues
4AnnularLaurentSerIes
5EXercIses

10VectorFIelds：PhysIcsandTopology
1VectorFIelds
2WIndIngNumbersandVectorFIelds*
3FlowsonClosedSurfaces*
4EXercIses

11VectorFIeldsandCompleXIntegratIon
1FluXandWork
2CompleXIntegratIonInTermsofVectorFIelds
3TheCompleXPotentIal
4EXercIses

12FlowsandHarmonIcFunctIons
1HarmonIcDuals
2ConformalInVarIance
3APowerfulComputatIonalTool
4TheCompleXCurVatureReVIsIted*
5FlowAroundanObstacle
6ThePhysIcsofRIemannsMappIngTheorem
7DirichletsProblem
8ExercIses
References
IndeX