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1、COMPLEXANALYSISAnIntroductiontotheTheoryofAnalyticFunctionsofOneComplexVariableThirdEditionLarsV.AhlforsProfessorofMathematics,EmeritusHarvardUniversityMcGraw-Hill,Inc.NewYorkSt.LouisSanFranciscoAucklandBogotaCaracasLisbonLondonMadridMexicoCityMilanMontrea
2、lNewDelhiSanJuanSingaporeSydneyTokyoTorontoCOMPLEXANALYSISCopyright©1979,1966byMcGraw-Hili,Inc.Allrightsreserved.Copyright1953byMcGraw-Hill,Inc.Allrightsreserved..PrintedintheUnitedStatesofAmerica.Nopartofthispublicationmaybereproduced,storedinaretrievalsy
3、stem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorwrittenpermissionofthepublisher.2223BRBBRB9876543ThisbookwassetinModern8AbyMonotypeCompositionCompany,Inc.TheeditorswereCarolNapierandStephenWa
4、gley;theproductionsupervisorwasJoeCampanella.LibraryofCongretlllCataloginginPublicationDataAhlfors,LarsValerian,dateComplexanalysis.(Internationalseriesinpureandappliedmathematics)Includesindex.1.Analyticfunctions.I.Title.QA331.A451979515'.9378-17078ISBNM7
5、-000657-1ToErnaContentsPrefacexiiiCHAPTER1COMPLEXNUMBERS11TheAlgebraofComplexNumbers11.1ArithmeticOperations11.2SquareRoots31.3Justification41.4Conjugation,AbsoluteValue61.5Inequalities92TheGeometricRepresentationofComplexNumbers122.1GeometricAdditionandMu
6、ltiplication122.2TheBinomialEquation152.3AnalyticGeometry172.4TheSphericalRepresentation18CHAPTER2COMPLEXFUNCTIONS211IntroductiontotheConceptofAnalyticFunction211.1LimitsandContinuity221.2AnalyticFunctions241.3Polynomials281.4RationalFunctions302Elementary
7、TheoryofPowerSeries332.1Sequences332.2Series35viivIIICONTENTS2.3UniformConvergence352.4PowerSeries382.5Abel'sLimitTheorem413TheExponentialandTrigonometricFunctions423.1TheExponential423.2TheTrigonometricFunctions433.3ThePeriodicity,443.4TheLogarithm46CHAPT
8、ER3ANALYTICFUNCTIONSASMAPPINGS491ElementaryPointSetTopology501.1SetsandElements501.2MetricSpaces511.3Connectedness541.4Compactness591.5ContinuousFunctions631.6TopologicalSpaces662Conformality672.1ArcsandClose
