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尼达姆 (Tristan Needham) 著 / 人民邮电出版社 / 2007-02 / 平装
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复分析:可视化方法
《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。
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。
1GeometryandCompleXArIthmetIc1IntroductIon2EulersFormula3SomeApplIcatIons4TransformatIonsandEuclIdeanGeometry*5EXercIses2CompleXFunctIonsasTransformatIons1IntroductIon2PolynomIals3PowerSerIes4TheEXponentIalFunctIon5CosIneandSIne6MultIfunctIons7TheLogarIthmFunctIon8AVeragIngoVerCIrcles*8EXercIses3M?bIusTransformatIonsandInVersIon1IntroductIon2InVersIon3ThreeIllustrativeApplIcatIonsofInVersIon4TheRIemannSphere5M?bIusTransformatIons:BasIcResults6M?bIusTransformatIonsasMatrIces*7VisualIzatIonandClassIfIcatIon*8DecomposItIonInto2or4ReflectIons*8AutomorphIsmsoftheUnItDIsc*9EXercIses4DIfferentIatIon:TheAmplItwIstConcept1IntroductIon2APuzzlIngPhenomenon3LocalDescrIptIonofMappIngsInthePlane4TheCompleXDerivativeasAmplItwIst5SomeSImpleEXamples6Conformal=AnalytIc7CrItIcalPoInts8TheCauchy-RIemannEquatIons8EXercIses5FurtherGeometryofDIfferentIatIon1Cauchy-RIemannReVealed2AnIntImatIonofRIgIdIty3VisualDIfferentIatIonoflog(z)4RulesofDIfferentIatIon5PolynomIals,PowerSerIes,andRatIonalFunc-tIons6VisualDIfferentIatIonofthePowerFunctIon7VisualDIfferentIatIonofeXp(z)2318GeometrIcSolutIonofE=E8AnApplIcatIonofHIgherDerivatives:CurVa-ture*9CelestIalMechanIcs*10AnalytIcContInuatIon*11EXercIses6Non-EuclIdeanGeometry*2IntroductIon2SpherIcalGeometry3HyperbolIcGeometry4EXercIses7WIndIngNumbersandTopology1WIndIngNumber2HopfsDegreeTheorem3PolynomIalsandtheArgumentPrIncIple4ATopologIcalArgumentPrIncIple*5RouchésTheorem6MaXImaandMInIma7TheSchwarz-PIckLemma*8TheGeneralIzedArgumentPrIncIple8EXercIses8CompleXIntegratIon:CauchysTheorem2ntroductIon2TheRealIntegral3TheCompleXIntegral4CompleXInVersIon5ConjugatIon6PowerFunctIons7TheEXponentIalMappIng8TheFundamentalTheorem8ParametrIcEValuatIon9CauchysTheorem10TheGeneralCauchyTheorem11TheGeneralFormulaofContourIntegratIon11EXercIses9CauchysFormulaandItsApplIcatIons1CauchysFormula2InfInIteDIfferentIabIlItyandTaylorSerIes3CalculusofResIdues4AnnularLaurentSerIes5EXercIses10VectorFIelds:PhysIcsandTopology1VectorFIelds2WIndIngNumbersandVectorFIelds*3FlowsonClosedSurfaces*4EXercIses11VectorFIeldsandCompleXIntegratIon1FluXandWork2CompleXIntegratIonInTermsofVectorFIelds3TheCompleXPotentIal4EXercIses12FlowsandHarmonIcFunctIons1HarmonIcDuals2ConformalInVarIance3APowerfulComputatIonalTool4TheCompleXCurVatureReVIsIted*5FlowAroundanObstacle6ThePhysIcsofRIemannsMappIngTheorem7DirichletsProblem8ExercIsesReferencesIndeX
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