作者尼达姆(Tristan Needham) 著
出版社人民邮电出版社
出版时间2007-02
版次1
装帧平装
货号12-5
上书时间2024-07-16
商品详情
- 品相描述:九五品
图书标准信息
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作者
尼达姆(Tristan Needham) 著
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出版社
人民邮电出版社
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出版时间
2007-02
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版次
1
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ISBN
9787115155160
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定价
79.00元
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装帧
平装
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开本
16开
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纸张
胶版纸
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页数
592页
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字数
857千字
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正文语种
英语
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原版书名
Visual Complex Analysis
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丛书
图灵原版数学统计学系列
- 【内容简介】
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《复分析:可视化方法(英文版)》是复分析领域近年来较有影响的一本著作。作者用丰富的图例展示各种概念、定理和证明思路,十分便于读者理解,充分揭示了复分析的数学之美。书中讲述的内容有几何、复变函数变换、默比乌斯变换、微分、非欧几何、复积分、柯西公式、向量场、复积分、调和函数等。
- 【作者简介】
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TristanNeedham,旧金山大学教授系教授,理学院副院长。牛津大学博士,导师为RogerPenrose(与霍金齐名的英国物理学家)。因本书被美国数学会授予CarlB.Allendoerfer奖。他的研究领域包括几何、复分析、数学史、广义相对论。
- 【目录】
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1GeometryandCompleXArIthmetIc
1IntroductIon
2EulersFormula
3SomeApplIcatIons
4TransformatIonsandEuclIdeanGeometry*
5EXercIses
2CompleXFunctIonsasTransformatIons
1IntroductIon
2PolynomIals
3PowerSerIes
4TheEXponentIalFunctIon
5CosIneandSIne
6MultIfunctIons
7TheLogarIthmFunctIon
8AVeragIngoVerCIrcles*
8EXercIses
3M?bIusTransformatIonsandInVersIon
1IntroductIon
2InVersIon
3ThreeIllustrativeApplIcatIonsofInVersIon
4TheRIemannSphere
5M?bIusTransformatIons:BasIcResults
6M?bIusTransformatIonsasMatrIces*
7VisualIzatIonandClassIfIcatIon*
8DecomposItIonInto2or4ReflectIons*
8AutomorphIsmsoftheUnItDIsc*
9EXercIses
4DIfferentIatIon:TheAmplItwIstConcept
1IntroductIon
2APuzzlIngPhenomenon
3LocalDescrIptIonofMappIngsInthePlane
4TheCompleXDerivativeasAmplItwIst
5SomeSImpleEXamples
6Conformal=AnalytIc
7CrItIcalPoInts
8TheCauchy-RIemannEquatIons
8EXercIses
5FurtherGeometryofDIfferentIatIon
1Cauchy-RIemannReVealed
2AnIntImatIonofRIgIdIty
3VisualDIfferentIatIonoflog(z)
4RulesofDIfferentIatIon
5PolynomIals,PowerSerIes,andRatIonalFunc-tIons
6VisualDIfferentIatIonofthePowerFunctIon
7VisualDIfferentIatIonofeXp(z)231
8GeometrIcSolutIonofE=E
8AnApplIcatIonofHIgherDerivatives:CurVa-ture*
9CelestIalMechanIcs*
10AnalytIcContInuatIon*
11EXercIses
6Non-EuclIdeanGeometry*
2IntroductIon
2SpherIcalGeometry
3HyperbolIcGeometry
4EXercIses
7WIndIngNumbersandTopology
1WIndIngNumber
2HopfsDegreeTheorem
3PolynomIalsandtheArgumentPrIncIple
4ATopologIcalArgumentPrIncIple*
5RouchésTheorem
6MaXImaandMInIma
7TheSchwarz-PIckLemma*
8TheGeneralIzedArgumentPrIncIple
8EXercIses
8CompleXIntegratIon:CauchysTheorem
2ntroductIon
2TheRealIntegral
3TheCompleXIntegral
4CompleXInVersIon
5ConjugatIon
6PowerFunctIons
7TheEXponentIalMappIng
8TheFundamentalTheorem
8ParametrIcEValuatIon
9CauchysTheorem
10TheGeneralCauchyTheorem
11TheGeneralFormulaofContourIntegratIon
11EXercIses
9CauchysFormulaandItsApplIcatIons
1CauchysFormula
2InfInIteDIfferentIabIlItyandTaylorSerIes
3CalculusofResIdues
4AnnularLaurentSerIes
5EXercIses
10VectorFIelds:PhysIcsandTopology
1VectorFIelds
2WIndIngNumbersandVectorFIelds*
3FlowsonClosedSurfaces*
4EXercIses
11VectorFIeldsandCompleXIntegratIon
1FluXandWork
2CompleXIntegratIonInTermsofVectorFIelds
3TheCompleXPotentIal
4EXercIses
12FlowsandHarmonIcFunctIons
1HarmonIcDuals
2ConformalInVarIance
3APowerfulComputatIonalTool
4TheCompleXCurVatureReVIsIted*
5FlowAroundanObstacle
6ThePhysIcsofRIemannsMappIngTheorem
7DirichletsProblem
8ExercIses
References
IndeX
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