描述
开 本: 16开纸 张: 胶版纸包 装: 平装-胶订是否套装: 否国际标准书号ISBN: 9787506271912
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 The Maximum Modulus Theorem
ⅦI.Runge’sTheorem
IX.AnalyticContinuationandRiemannSurfaces
X.HarmonicFunctions
ⅩI.EntireFunctions
ⅪI.TheRangeofanAnalyticFunction
AppendixA:CalculusforComplexComplexValuedFunctionsofandInterval
AppendixB:SuggestionsforFurtherStudyandBibliographicalNotes
References
Index
ListofSymbols
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