- 复分析(第4版影印版)
- - 作者：(美)S.朗|责编:高蓉//李黎
  - 出版社：世界图书出版公司
  - ISBN：9787506260060
  - 出版日期：2003/12/01
  - 页数：485
- 售价：47.6

内容大纲
本书共十六章，书中全面论述了复分析的基本理论和许多论题,如黎曼映射定理、γ函数、解析开拓。本书前半部分内容适用于数学系本科生复分析一学期课程。后半部分适用于研究生专题课程。与第2版相比，本版内容做了较大改动，页数增加了120页。
作者介绍
目录
Foreword
Prerequisites
PART ONE  Basic Theory
  CHAPTER Ⅰ  Complex Numbers and Functions
    1.Definition
    2.Polar Form
    3.Complex Valued Functions
    4.Limits and Compact Sets Compact Sets
    5.Complex Differentiability
    6.The Cauchy-Riemann Equations
    7.Angles Under Holomorphic Maps
  CHAPTER Ⅱ  Power Series
    1.Formal Power Series
    2.Convergent Power Series
    3.Relations Between Formal and Convergent Series
      Sums and Products
      Quotients
      Composition of Series
    4.Analytic Functions
    5.Differentiation of Power Series
    6.The Invelse and Open Mapping Theorems
    7.The Local Maximum Modulus Principle
  CHAPTER Ⅲ  Cauchy's Theorem, First Part
    1.Holomorphic Functions on Connected Sets  Appendix: Connectedness
    2.Integrals Oer Paths
    3.Local Primitive for a Holomorphic Function
    4.Ancther Description of 1he Integral Along a Path
    5.The Homotopy Form of Cauchy's Theorem
    6.Existence of Global Primitives.Definition of the Logarithm
    7.The Local Cauchy Formula
  CHAPTER Ⅳ  Winding Numbers and Cauchy's Theorem
    1.The Winding Number
    2.The Global Catchy Theorem Dixon's PIocf of Theorem 2.5 (Cauchy's Formula)
    3.Artin's Proof
  CHAPTER Ⅴ  Applications 1 Cauchy's Integral Formula
    1.Uniform Limits of Analytic Functions
    2.Lament Series
    3.Isolated Singularities
      Removable Singularities
      Poles
      E sential Singularities
  CHAPTER Ⅵ  Calculus ot Residues
    1.The Residue Formula
      Residues of Differentials
    2.Evaluation of Definite Integrals
      Fourier Transforms
      Trigonometric Integrals
      Mellin Transforms
  CHAPTER Ⅶ  Conlormsl Mappings
    1.Schwarz Lemma

    2.Analytic Automorphisms of the Dic
    3.The Upper Half Plane
    4.Olher Examples
    5.Fractional Linear Transformations
  CHAPTER Ⅷ  Harmonic Functions
    1.Definition
      Application: Perpendicularity
      Application: Flow Lines
    2.Examples
    3.Basic Properties of Harmonic Functions
    4.The Poisson Formula
      The Poisson Integral as a Convolution
    5.Construction of Harmonic Furctions
    6.Appendix. Differentiating Under the Integral Sign
PART TWO  Geometric Function Theory
  CHAPTER Ⅸ  Schwarz Reflection
    1.Schwarz Reflection (by Complex Conjugation)
    2.Reflection Across Analytic Arcs
    3.Application cf Schwatz Reflection
  CHAPTER Ⅹ  The Riemann Mapping Theorem
    1.Statement of the Theorem
    2.Compact Sets in Function Spces
    3.Proof cf the Riemann Mapping Theorem
    4.Behavior at the Boundary
  CHAPTER Ⅺ  Analytic Continuation Along Curves
    1.Continuation Along a Curve
    2.The Dilogarithm
    3.Application lo Picard's Theorem
PART THREE  Various Analytic Topics
  CHAPTER Ⅻ  Applications of the Maximum Modulus Principle and Jensen's Formula
    1.Jensen's Formula
    2.The Picard-Borel Theorem
    3.Bounds by the Real Part, Borel-Carathrodory Theorem
    4.The Use cf Three Circles and the Effect of Small Derivatives
      Hermite Interpolation Formula
    5.Entire Functions with Rational Valves
    6.The Phragmen-Lindelrf and Hadamard Theorems
  CHAPTER ⅩⅢ  Entire and Meromorphic Functions
    1.Infinite Products
    2.Weierstrass Products
    3.Functions of Finite Order
    4.Meromorphic Functions, Mittag-Leffler Theorem
  CHAPTER XIV  Elliptic Functions
    1.The Liouville Theorems
    2.The Weierstrass Function
    3.The Addition Theorem
    4.The Sigma and Zeta Functions
  CHAPTER ⅩⅤ  The Gamma and Zeta Functions
    1.The Differentiation Lemma
    2.The Gamma Function

      Weierstrass Product
      The Gauss Multiplication Formula (Distribution Relation)
      The (Other) Gauss Formula
      The Mellin Transform
      The Starling Formula
      Proof of Starling's Formula
    3.The Lerch Formula
    4.Zeta Functions
  CHAPTER ⅩⅥ  The Prime Number Theorem
    1.Basic Analytic Properties of the Zeta Function
    2.The Main Lemma and its Application
    3.Proof of the Main Lemma
Appenflix
  1.Summation by Parts and Non-Absolute Convergence
  2.Difference Equations
  3.Analytic Differential Equations
  4.Fixed Points of a Fractional Linear Transformation
  5.Cauchy's Formula for C Functions
  6.Cauchy's Theorem for Locally Integrable Vector Fields
Bibliography
Index

内容大纲

作者介绍

目录

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