单复变函数 第2版

图书标准信息

• 作者 John B.Conway 编
• 出版社 世界图书出版公司
• 出版时间 2004-11
• 版次 2
• ISBN 9787506271912
• 定价 45.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 316页

【内容简介】

Thisbookisintendedasatextbookforafirstcourseinthetheoryoffunctionsofonecomplexvariableforstudentswhoaremathematicallymatureenoughtounderstandandexecutearguments.Theactualpre-requisitesforreadingthisbookarequiteminimal;notmuchmorethanastiffcourseinbasiccalculusandafewfactsaboutpartialderivatives.Thetopicsfromadvancedcalculusthatareused（e.g.,Leibniz'srulefordiffer-entiatingundertheintegralsign）areprovedindetail.

【目录】

Preface
Ⅰ.TheComplexNumberSystem
1.Therealnumbers
2.Thefieldofcomplexnumbers
3.Thecomplexplane
4.Polarrepresentationandrootsofcomplexnumbers
5.Linesandhalfplanesinthecomplexplane
6.Theextendedplaneanditssphericalrepresentation

Ⅱ.MetricSpacesandtheTopologyofC
1.Definitionandexamplesofmetricspaces
2.Connectedness
3.Sequencesandcompleteness
4.Compactness
5.Continuity
6.Uniformconvergence

Ⅲ.ElementaryPropertiesandExamplesofAnalyticFunctions
1.Powerseries
2.Analyticfunctions
3.Analyticfunctionsasmappings，M6biustransformations

Ⅳ.ComplexIntegration
1.Riemann-Stieltjesintegrals
2.Powerseriesrepresentationofanalyticfunctions
3.Zerosofananalyticfunction
4.Theindexofaclosedcurve
5.Cauchy'sTheoremandIntegralFormula
6.ThehomotopicversionofCauchy'sTheroremandsimpleconnectivity
7.Countingzeros;theOpenMappingTheorem
8.Goursat'sTheorem

Ⅴ.Singularities
1.Classificationofsingularities
2.Residues
3.TheArgumentPrinciple
Ⅵ.CompactnessandConvergenceinthe
Ⅶ.Runge'sTheorem
Ⅷ.AnalyticContinuationandRiemannSurfaces
Ⅸ.HarmonicFunctions
Ⅹ.EntireFunctions
Ⅺ.TheRangeofanAnalyticFunction
AppendixA:CalculusforComplexComplexValuedFunctionsofandInterval
AppendixB:SuggestionsforFurtherStudyandBibliographicalNotes
References
Index
ListofSymbols