单复变函数 第2版
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49.64
九五品
仅1件
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
装帧平装
货号A3
上书时间2024-12-10
商品详情
- 品相描述:九五品
图书标准信息
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作者
John B.Conway 编
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出版社
世界图书出版公司
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出版时间
2004-11
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版次
2
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ISBN
9787506271912
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定价
45.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
316页
- 【内容简介】
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Thisbookisintendedasatextbookforafirstcourseinthetheoryoffunctionsofonecomplexvariableforstudentswhoaremathematicallymatureenoughtounderstandandexecutearguments.Theactualpre-requisitesforreadingthisbookarequiteminimal;notmuchmorethanastiffcourseinbasiccalculusandafewfactsaboutpartialderivatives.Thetopicsfromadvancedcalculusthatareused(e.g.,Leibniz'srulefordiffer-entiatingundertheintegralsign)areprovedindetail.
- 【目录】
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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
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