《複分析》是人民郵電出版社出版的圖書，作者是（美）尼達姆著
基本介紹
- 中文名：複分析
- 作者：尼達姆
- 出版社：人民郵電出版社
- ISBN：9787115155160
- 定價：377 元
內容簡介,圖書目錄,
內容簡介
《複分析：可視化方法(英文版)》是複分析領域近年來較有影響的一本著作。作者用豐富的圖例展示各種概念、定理和證明思路，十分便於讀者理解，充分揭示了複分析的數學之美。書中講述的內容有幾何、複變函數變換、默比烏斯變換、微分、非歐幾何、復積分、柯西公式、向量場、復積分、調和函式等。
圖書目錄
1 Geometry and CompleX ArIthmetIc
1 IntroductIon
2 Eulers Formula
3 Some ApplIcatIons
4 TransformatIons and EuclIdean Geometry*
5 EXercIses
2 CompleX FunctIons as TransformatIons
1 IntroductIon
2 PolynomIals
3 Power SerIes
4 The EXponentIal FunctIon
5 CosIne and SIne
6 MultIfunctIons
7 The LogarIthm FunctIon
8 AVeragIng oVer CIrcles*
8 EXercIses
3 M?bIus TransformatIons and InVersIon
1 IntroductIon
2 InVersIon
3 Three Illustrative ApplIcatIons of InVersIon
4 The RIemann Sphere
5 M?bIus TransformatIons： BasIc Results
6 M?bIus TransformatIons as MatrIces*
7 VisualIzatIon and ClassIfIcatIon*
8 DecomposItIon Into 2 or 4 ReflectIons*
8 AutomorphIsms of the UnIt DIsc*
9 EXercIses
4 DIfferentIatIon： The AmplItwIst Concept
1 IntroductIon
2 A PuzzlIng Phenomenon
3 Local DescrIptIon of MappIngs In the Plane
4 The CompleX Derivative as AmplItwIst
5 Some SImple EXamples
6 Conformal = AnalytIc
7 CrItIcal PoInts
8 The Cauchy-RIemann EquatIons
8 EXercIses
5 Further Geometry of DIfferentIatIon
1 Cauchy-RIemann ReVealed
2 An IntImatIon of RIgIdIty
3 Visual DIfferentIatIon of log(z)
4 Rules of DIfferentIatIon
5 PolynomIals， Power SerIes， and RatIonal Func-tIons
6 Visual DIfferentIatIon of the Power FunctIon
7 Visual DIfferentIatIon of eXp(z) 231
8 GeometrIc SolutIon of E= E
8 An ApplIcatIon of HIgher Derivatives： CurVa-ture*
9 CelestIal MechanIcs*
10 AnalytIc ContInuatIon*
11 EXercIses
6 Non-EuclIdean Geometry*
2 IntroductIon
2 SpherIcal Geometry
3 HyperbolIc Geometry
4 EXercIses
7 WIndIng Numbers and Topology
1 WIndIng Number
2 Hopfs Degree Theorem
3 PolynomIals and the Argument PrIncIple
4 A TopologIcal Argument PrIncIple*
5 Rouchés Theorem
6 MaXIma and MInIma
7 The Schwarz-PIck Lemma*
8 The GeneralIzed Argument PrIncIple
8 EXercIses
8 CompleX IntegratIon： Cauchys Theorem
2ntroductIon
2 The Real Integral
3 The CompleX Integral
4 CompleX InVersIon
5 ConjugatIon
6 Power FunctIons
7 The EXponentIal MappIng
8 The Fundamental Theorem
8 ParametrIc EValuatIon
9 Cauchys Theorem
10 The General Cauchy Theorem
11 The General Formula of Contour IntegratIon
11 EXercIses
9 Cauchys Formula and Its ApplIcatIons
1 Cauchys Formula
2 InfInIte DIfferentIabIlIty and Taylor SerIes
3 Calculus of ResIdues
4 Annular Laurent SerIes
5 EXercIses
10 Vector FIelds： PhysIcs and Topology
1 Vector FIelds
2 WIndIng Numbers and Vector FIelds*
3 Flows on Closed Surfaces*
4 EXercIses
11 Vector FIelds and CompleX IntegratIon
1 FluX and Work
2 CompleX IntegratIon In Terms of Vector FIelds
3 The CompleX PotentIal
4 EXercIses
12 Flows and HarmonIc FunctIons
1 HarmonIc Duals
2 Conformal I nVarIance
3 A Powerful ComputatIonal Tool
4 The CompleX CurVature ReVIsIted*
5 Flow Around an Obstacle
6 The PhysIcs of RIemanns MappIng Theorem
7 Dirichlets Problem
8 ExercIses
References
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