复分析

作者简介

《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。

书籍目录

1  Geometry and CompleX ArIthmetIc　Ⅰ  IntroductIon　　Ⅱ  Euler's Formula　　Ⅲ  Some ApplIcatIons　　Ⅳ  TransformatIons and EuclIdean Geometry*　　Ⅴ  EXercIses　2　CompleX FunctIons as TransformatIons　  Ⅰ  IntroductIon　　Ⅱ  PolynomIals　　Ⅲ  Power SerIes　　Ⅳ  The EXponentIal FunctIon　　Ⅴ  CosIne and SIne　　Ⅵ  MultIfunctIons　　Ⅶ　The LogarIthm FunctIon　　Ⅷ　AVeragIng oVer CIrcles*　　Ⅸ  EXercIses　3 M?bIus TransformatIons and InVersIon　　Ⅰ  IntroductIon　　Ⅱ  InVersIon　　Ⅲ  Three Illustrative ApplIcatIons of InVersIon　　Ⅳ  The RIemann Sphere　　Ⅴ  M?bIus TransformatIons: BasIc Results　　Ⅵ  M?bIus TransformatIons as MatrIces*　　Ⅶ　VisualIzatIon and ClassIfIcatIon*　Ⅷ　DecomposItIon Into 2 or 4 ReflectIons*　　Ⅸ  AutomorphIsms of the UnIt DIsc*　　Ⅹ  EXercIses　4　DIfferentIatIon: The AmplItwIst Concept　　Ⅰ  IntroductIon　　Ⅱ  A PuzzlIng Phenomenon　　Ⅲ  Local DescrIptIon of MappIngs In the Plane　　Ⅳ  The CompleX Derivative as AmplItwIst　　Ⅴ  Some SImple EXamples　　Ⅵ  Conformal = AnalytIc　　Ⅶ　CrItIcal PoInts　　Ⅷ　The Cauchy-RIemann EquatIons　　Ⅸ  EXercIses　5　Further Geometry of DIfferentIatIon　Ⅰ  Cauchy-RIemann ReVealed　　Ⅱ  An IntImatIon of RIgIdIty　　Ⅲ  Visual DIfferentIatIon of log(z)　　Ⅳ  Rules of DIfferentIatIon　　Ⅴ  PolynomIals, Power SerIes, and RatIonal Func-tIons　　Ⅵ  Visual DIfferentIatIon of the Power FunctIon　　Ⅶ　Visual DIfferentIatIon of eXp(z)　231　Ⅷ　GeometrIc SolutIon of E'= E　　　Ⅸ  An ApplIcatIon of HIgher Derivatives: CurVa-ture*　　Ⅹ  CelestIal MechanIcs*　　Ⅺ  AnalytIc ContInuatIon*　　Ⅻ　EXercIses　6　Non-EuclIdean Geometry*　　Ⅱ  IntroductIon　　Ⅱ  SpherIcal Geometry　　Ⅲ  HyperbolIc Geometry　　Ⅳ  EXercIses　7　WIndIng Numbers and Topology　Ⅰ　WIndIng Number　Ⅱ  Hopf's Degree Theorem　　Ⅲ  PolynomIals and the Argument PrIncIple　　Ⅳ  A TopologIcal Argument PrIncIple*　　Ⅴ  Rouché's Theorem　　Ⅵ  MaXIma and MInIma　　Ⅶ　The Schwarz-PIck Lemma*　　Ⅷ　The GeneralIzed Argument PrIncIple　　Ⅸ  EXercIses　8　CompleX IntegratIon: Cauchy's Theorem　　ⅡntroductIon　　Ⅱ  The Real Integral　　Ⅲ  The CompleX Integral　　Ⅳ  CompleX InVersIon　　Ⅴ  ConjugatIon　　Ⅵ  Power FunctIons　　Ⅶ　The EXponentIal MappIng　　Ⅷ　The Fundamental Theorem　　Ⅸ  ParametrIc EValuatIon　　Ⅹ  Cauchy's Theorem　　Ⅺ  The General Cauchy Theorem　　Ⅻ　The General Formula of Contour IntegratIon  　Ⅻ　EXercIses　9　Cauchy's Formula and Its ApplIcatIons　　Ⅰ  Cauchy's Formula　　Ⅱ  InfInIte DIfferentIabIlIty and Taylor SerIes　　Ⅲ  Calculus of ResIdues　　Ⅳ  Annular Laurent SerIes　　Ⅴ  EXercIses　10　Vector FIelds: PhysIcs and Topology　　Ⅰ  Vector FIelds　　Ⅱ  WIndIng Numbers and Vector FIelds*　　Ⅲ  Flows on Closed Surfaces*　　Ⅳ  EXercIses　11　Vector FIelds and CompleX IntegratIon　　Ⅰ  FluX and Work　　Ⅱ  CompleX IntegratIon In Terms of Vector FIelds  　Ⅲ  The CompleX PotentIal　　Ⅳ  EXercIses　12　Flows and HarmonIc FunctIons　　Ⅰ  HarmonIc Duals　　Ⅱ  Conformal I nVarIance　　Ⅲ  A Powerful ComputatIonal Tool　　Ⅳ  The CompleX CurVature ReVIsIted*　　Ⅴ  Flow Around an Obstacle　　Ⅵ  The PhysIcs of RIemann's MappIng Theorem  　Ⅶ  Dirichlet's Problem　　Ⅷ　ExercIses　References　IndeX

编辑推荐

　　《复分析：可视化方法(英文版)》可作为大学本科、研究生的复分析课程教材或参考书。

内容概要

Tristan Needham，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Roger Penrose（与霍金齐名的英国物理学家）。因本书被美国数学会授予Carl B.Allendoerfer奖。他的研究领域包括几何、复分析、数学史、广义相对论。

图书封面

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