复分析（英文影印版）

图书标准信息

• 作者 [美]加默兰 著
• 出版社 世界图书出版公司
• 出版时间 2008-05
• 版次 1
• ISBN 9787506292290
• 定价 66.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 478页
• 正文语种 英语

【内容简介】

Thisbookprovidesanintroductiontocomplexanalysisforstudentswithsomefamiliaritywithcomplexnumbersfromhighschool.StudentsshouldbefamiliarwiththeCartesianrepresentationofcomplexnumbersandwiththealgebraofcomplexnumbers,thatis,theyshouldknowthati2=-1.Afamiliaritywithmultivariablecalculusisalsorequired,butherethefundamentalideasarereviewed.Infact,complexanalysisprovidesagoodtraininggroundformultivariablecalculus.Itallowsstudentstoconsolidatetheirunderstandingofparametrizedcurves,tangentvectors,arclength,gradients,lineintegrals,independenceofpath,andGreenstheorem.Theideassurroundingindependenceofpathareparticularlydifficultforstudentsincalculus,andtheyarenotabsorbedbymoststudentsuntiltheyareseenagaininothercourses.

【目录】

Preface
Introduction
FIRSTPART
Chapter1TheComplexPlaneandElementaryFunctions
1.ComplexNumbers
2.PolarRepresentation
3.StereographicProjection
4.TheSquareandSquareRootFunctions
5.TheExponentialFunction
6.TheLogarithmFunction
7.PowerFunctionsandPhaseFactors
8.TrigonometricandHyperbolicFunctions

Chapter2AnalyticFunctions
1.ReviewofBasicAnalysis
2.AnalyticFunctions
3.TheCauChy-RiemannEquations
4.InverseMappingsandtheJacobian
5.HarmonicFunctions
6.ConformalMappings
7.FractionalLinearTransformations

Chapter3LineIntegralsandHarmonicFunctions
1.LineIntegralsandGreensTheorem
2.IndependenceofPath
3.HarmonicConjugates
4.TheMeanValueProperty
5.TheMaximumPrinciple
6.ApplicationstoFluidDynamics
7.OtherApplicationstoPhysics

Chapter4ComplexIntegrationandAnalyticity
1.ComplexLineIntegrals
2.FundamentalTheoremofCalculusforAnalyticFunctions
3.CauchysTheorem
4.TheCauchyIntegralFormula
5.LiouvillesTheorem
6.MorerasTheorem
7.GoursatsTheorem
8.ComplexNotationandPompeiusFormula

Chapter5PowerSeries
1.InfiniteSeries
2.SequencesandSeriesofFunctions
3.PowerSeries
4.PowerSeriesExpansionofanAnalyticFunction
5.PowerSeriesExpansionatInfinity
6.ManipulationofPowerSeries
7.TheZerosofanAnalyticFunction
8.AnalyticContinuation

Chapter6LaurentSeriesandIsolatedSingularities
1.TheLaurentDecomposition
2.IsolatedSingularitiesofanAnalyticFunction
3.IsolatedSingularityatInfinity
4.PartialFractionsDecomposition
5.PeriodicFunctions
6.FourierSeries

Chapter7TheResidueCalculus
1.TheResidueTheorem
2.IntegralsFeaturingRationalFunctions
3.IntegralsofTrigonometricFunctions
4.IntegrandswithBranchPoints
5.FractionalResidues
6.PrincipalValues
7.JordansLemma
8.ExteriorDomains

SECONDPART
Chapter8TheLogarithmicIntegral
1.TheArgumentPrinciple
2.RouchesTheorem
3.HurwitzsTheorem
4.OpenMappingandInverseFunctionTheorems
5.CriticalPoints
6.WindingNumbers
……
THIRDPART
HintsandSolutionsforSelectedExercises
References
ListofSymbols
Index