Serge Lang ： 复分析

图书标准信息

• 作者 S.lang 著
• 出版社 世界图书出版公司
• 出版时间 2003-06
• 版次 1
• ISBN 9787506260060
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 485页

【内容简介】

Thepresentbookismeantasatextforacourseoncomplexanalysisattheadvancedundergraduatelevel，orfirst-yeargraduatelevel.Thefirsthalf，moreorless，canbeusedforaone-semestercourseaddressedtoundergraduates.Thesecondhalfcanbeusedforasecondsemester，ateitherlevel.Somewhatmorematerialhasbeenincludedthancanbecoveredatleisureinoneortwoterms，togiveopportunitiesfortheinstructortoexerciseindividualtaste，andtoleadthecourseinwhateverdirectionsstrikestheinstructorsfancyatthetimeaswellasextrareadingmaterialforstudentsontheirown.Alargenumberofroutineexercisesareincludedforthemorestandardportions，andafewharderexercisesofstrikingtheoreticalinterestarealsoincluded，butmaybeomittedincoursesaddressedtolessadvancedstudents.

此书为英文版！

【目录】

Foreword
Prerequisites
PARTONEBasicTheory
CHAPTERⅠComplexNumbersandFunctions
1.Definition
2.PolarForm
3.ComplexValuedFunctions
4.LimitsandCompactSets
5.ComplexDifferentiability
6.TheCauchy-RiemannEquations
7.AnglesUnderHolomorphicMaps
CHAPTERⅡPowerSeries
1.FormalPowerSeries
2.ConvergentPowerSeries
3.RelationsBetweenFormalandConvergentSeries
4.AnalyticFunctions
5.DifferentiationofPowerSeries
6.TheInverseandOpenMappingTheorems
7.TheLocalMaximumModulusPrinciple
CHAPTERⅢCauchysTheorem,FirstPart
1.HolomorphicFunctionsonConnectedSets
2.IntegralsOverPaths
3.LocalPrimitiveforaHolomorphicFunction
4.LocalPrimitiveforaHolomorphicFunction
5.TheHomotopyFormofCauchysTheorem
6.ExistenceofGlobalPrimitives.DefinitionoftheLogarithm
7.TheLocalCauchyFormula
CHAPTERⅣWindingNumbersandCauchysTheorem
CHAPTERⅤApplicationsofCauchysIntegralFormula
CHAPTERⅥCalculusofResidues
CHAPTERⅦConformalMappings
CHAPTERⅧHarmonicFunctions
PARTTWOGeometricFunctionTheory
CHAPTERⅨSchwarzReflection
CHAPTERⅩTheRiemannMappingTheorem
CHAPTERⅪAnalyticContinuationAlongCurves
PARTTHREEVariousAnalyticTopics
CHAPTERⅫApplicationsoftheMaximumModulusPrincipleandJensensFormula
CHAPTERⅩⅢEntireandMeromorphicFunctions
CHAPTERⅩⅣEllipticFunctions
CHAPTERⅩⅤTheGammaandZetaFunctions
CHAPTERⅩⅥThePrimeNumberTheorem
Appendix
Bibliography
Index