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S.lang 著 / 世界图书出版公司 / 2003-06 / 平装
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复分析
Thepresentbookismeantasatextforacourseoncomplexanalysisattheadvancedundergraduatelevel,orfirst-yeargraduatelevel.Thefirsthalf,moreorless,canbeusedforaone-semestercourseaddressedtoundergraduates.Thesecondhalfcanbeusedforasecondsemester,ateitherlevel.Somewhatmorematerialhasbeenincludedthancanbecoveredatleisureinoneortwoterms,togiveopportunitiesfortheinstructortoexerciseindividualtaste,andtoleadthecourseinwhateverdirectionsstrikestheinstructorsfancyatthetimeaswellasextrareadingmaterialforstudentsontheirown.Alargenumberofroutineexercisesareincludedforthemorestandardportions,andafewharderexercisesofstrikingtheoreticalinterestarealsoincluded,butmaybeomittedincoursesaddressedtolessadvancedstudents.
此书为英文版!
ForewordPrerequisitesPARTONEBasicTheoryCHAPTERⅠComplexNumbersandFunctions1.Definition2.PolarForm3.ComplexValuedFunctions4.LimitsandCompactSets5.ComplexDifferentiability6.TheCauchy-RiemannEquations7.AnglesUnderHolomorphicMapsCHAPTERⅡPowerSeries1.FormalPowerSeries2.ConvergentPowerSeries3.RelationsBetweenFormalandConvergentSeries4.AnalyticFunctions5.DifferentiationofPowerSeries6.TheInverseandOpenMappingTheorems7.TheLocalMaximumModulusPrincipleCHAPTERⅢCauchysTheorem,FirstPart1.HolomorphicFunctionsonConnectedSets2.IntegralsOverPaths3.LocalPrimitiveforaHolomorphicFunction4.LocalPrimitiveforaHolomorphicFunction5.TheHomotopyFormofCauchysTheorem6.ExistenceofGlobalPrimitives.DefinitionoftheLogarithm7.TheLocalCauchyFormulaCHAPTERⅣWindingNumbersandCauchysTheoremCHAPTERⅤApplicationsofCauchysIntegralFormulaCHAPTERⅥCalculusofResiduesCHAPTERⅦConformalMappingsCHAPTERⅧHarmonicFunctionsPARTTWOGeometricFunctionTheoryCHAPTERⅨSchwarzReflectionCHAPTERⅩTheRiemannMappingTheoremCHAPTERⅪAnalyticContinuationAlongCurvesPARTTHREEVariousAnalyticTopicsCHAPTERⅫApplicationsoftheMaximumModulusPrincipleandJensensFormulaCHAPTERⅩⅢEntireandMeromorphicFunctionsCHAPTERⅩⅣEllipticFunctionsCHAPTERⅩⅤTheGammaandZetaFunctionsCHAPTERⅩⅥThePrimeNumberTheoremAppendixBibliographyIndex
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