具體描述
《復分析》從現代數學的觀點介紹復分析的基本知識與常用工具，全書共分為8章，主要包括：復數、復函數、作為映射的解析函數、復積分、級數與乘積展開、共形映射，軟件剋雷問題、橢圓函數以及全局解析函數，此外，大部分章節後都有練習，便於學生掌握書中內容。
著者簡介
圖書目錄
Preface
Introduction
FIRST PART
Chapter 1 The Complex Plane and Elementary Functions
1.Complex Numbers
2.Polar Representation
3.Stereographic Projection
4.The Square and Square Root Functions
5.The Exponential Function
6.The Logarithm Function
7.Power Functions and Phase Factors
8.Trigonometric and Hyperbolic Functions
Chapter 2 Analytic Functions
1.Review of Basic Analysis
2.Analytic Functions
3.The CauChy-Riemann Equations
4.Inverse Mappings and the Jacobian
5.Harmonic Functions
6.Conformal Mappings
7.Fractional Linear Transformations
Chapter 3 Line Integrals and Harmonic Functions
1.Line Integrals and Greens Theorem
2.Independence of Path
3.Harmonic Conjugates
4.The Mean Value Property
5.The Maximum Principle
6.Applications to Fluid Dynamics
7.Other Applications to Physics
Chapter 4 Complex Integration and Analyticity
1.Complex Line Integrals
2.Fundamental Theorem of Calculus for Analytic Functions
3.Cauchys Theorem
4.The Cauchy Integral Formula
5.Liouvilles Theorem
6.Moreras Theorem
7.Goursats Theorem
8.Complex Notation and Pompeius Formula
Chapter 5 Power Series
1.Infinite Series
2.Sequences and Series of Functions
3.Power Series
4.Power Series Expansion of an Analytic Function
5.Power Series Expansion at Infinity
6.Manipulation of Power Series
7.The Zeros of an Analytic Function
8.Analytic Continuation
Chapter 6 Laurent Series and Isolated Singularities
1.The Laurent Decomposition
2.Isolated Singularities of an Analytic Function
3.Isolated Singularity at Infinity
4.Partial Fractions Decomposition
5.Periodic Functions
6.Fourier Series
Chapter 7 The Residue Calculus
1.The Residue Theorem
2.Integrals Featuring Rational Functions
3.Integrals of Trigonometric Functions
4.Integrands with Branch Points
5.Fractional Residues
6.Principal Values
7.Jordans Lemma
8.Exterior Domains
SECOND PART
Chapter 8 The Logarithmic Integral
1.The Argument Principle
2.Rouches Theorem
3.Hurwitzs Theorem
4.Open Mapping and Inverse Function Theorems
5.Critical Points
6.Winding Numbers
……
THIRD PART
Hints and Solutions for Selected Exercises
References
List of Symbols
Index
· · · · · · (收起)
Introduction
FIRST PART
Chapter 1 The Complex Plane and Elementary Functions
1.Complex Numbers
2.Polar Representation
3.Stereographic Projection
4.The Square and Square Root Functions
5.The Exponential Function
6.The Logarithm Function
7.Power Functions and Phase Factors
8.Trigonometric and Hyperbolic Functions
Chapter 2 Analytic Functions
1.Review of Basic Analysis
2.Analytic Functions
3.The CauChy-Riemann Equations
4.Inverse Mappings and the Jacobian
5.Harmonic Functions
6.Conformal Mappings
7.Fractional Linear Transformations
Chapter 3 Line Integrals and Harmonic Functions
1.Line Integrals and Greens Theorem
2.Independence of Path
3.Harmonic Conjugates
4.The Mean Value Property
5.The Maximum Principle
6.Applications to Fluid Dynamics
7.Other Applications to Physics
Chapter 4 Complex Integration and Analyticity
1.Complex Line Integrals
2.Fundamental Theorem of Calculus for Analytic Functions
3.Cauchys Theorem
4.The Cauchy Integral Formula
5.Liouvilles Theorem
6.Moreras Theorem
7.Goursats Theorem
8.Complex Notation and Pompeius Formula
Chapter 5 Power Series
1.Infinite Series
2.Sequences and Series of Functions
3.Power Series
4.Power Series Expansion of an Analytic Function
5.Power Series Expansion at Infinity
6.Manipulation of Power Series
7.The Zeros of an Analytic Function
8.Analytic Continuation
Chapter 6 Laurent Series and Isolated Singularities
1.The Laurent Decomposition
2.Isolated Singularities of an Analytic Function
3.Isolated Singularity at Infinity
4.Partial Fractions Decomposition
5.Periodic Functions
6.Fourier Series
Chapter 7 The Residue Calculus
1.The Residue Theorem
2.Integrals Featuring Rational Functions
3.Integrals of Trigonometric Functions
4.Integrands with Branch Points
5.Fractional Residues
6.Principal Values
7.Jordans Lemma
8.Exterior Domains
SECOND PART
Chapter 8 The Logarithmic Integral
1.The Argument Principle
2.Rouches Theorem
3.Hurwitzs Theorem
4.Open Mapping and Inverse Function Theorems
5.Critical Points
6.Winding Numbers
……
THIRD PART
Hints and Solutions for Selected Exercises
References
List of Symbols
Index
· · · · · · (收起)
讀後感
評分
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用戶評價
评分
想起來Tim說的: 哥是學過復分析的人啊...
评分教材= =
评分教材= =
评分想起來Tim說的: 哥是學過復分析的人啊...
评分教材= =
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