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复变函数及应用(英文版·第8版)


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James Ward Brown;Ruel V. Churchill
7-111-25363-1
65.00
468
2009年02月27日

数学 > 函数论 > 复变函数与积分变换

4687
英语
16开
Complex Variables and Applications Eighth Edition
教材
经典原版书库







本书初版于20世纪40年代,是经典的本科数学教材之一,对复变函数的教学影响深远,被美国加州理工学院、加州大学伯克利分校、佐治亚理工学院、普度大学、达特茅斯学院、南加州大学等众多名校采用。
  本书阐述了复变函数的理论及应用,还介绍了留数及保形映射理论在物理、流体及热传导等边值问题中的应用。
  新版对原有内容进行了重新组织,增加了更现代的示例和应用,更加方便教学。
  作者简介
  James Ward Brown 密歇根大学迪尔本分校数学系教授,美国数学学会会员。1964年于密歇根大学获得数学博士学位。他曾经主持研究美国国家自然科学基金项目,获得过密歇根大学杰出教师奖,并被列入美国名人录。
  Ruel V. Churchill 已故密歇根大学知名教授。早在60多年前,就开始编写一系列经典教材。除本书外,还与James Ward Brown合著有《Fourier Series and Boundary Value Problems》。
Preface
1 Complex Numbers
Sums and Products
Basic Algebraic Properties
Further Properties
Vectors and Moduli
Complex Conjugates
Exponential Form
Products and Powers in Exponential Form
Arguments of Products and Quotients
Roots of Complex Numbers
Examples
Regions in the Complex Plane

2 Analytic Functions
Functions of a Complex Variable
Mappings
Mappings by the Exponential Function
Limits
Theorems on Limits
Limits Involving the Point at Infinity
Continuity
Derivatives
Differentiation Formulas
Cauchy-Riemann Equations
Sufficient Conditions for Differentiability
Polar Coordinates
Analytic Functions
Examples
Harmonic Functions
Uniquely Determined Analytic Functions
Reflection Principle

3 Elementary Functions
The Exponential Function
The Logarithmic Function
Branches and Derivatives of Logarithms
Some Identities Involving Logarithms
Complex Exponents
Trigonometric Functions
Hyperbolic Functions
Inverse Trigonometric and Hyperbolic Functions

4 Integrals
Derivatives of Functions w(t)
Definite Integrals of Functions w(t)
Contours
Contour Integrals
Some Examples
Examples with Branch Cuts
Upper Bounds for Moduli of Contour Integrals
Antiderivatives
Proof of the Theorem
Cauchy-Goursat Theorem
Proof of-the Theorem
Simply Connected Domains
Multiply Connected Domains
Cauchy Integral Formula
An Extension of the Cauchy Integral Formula
Some Consequences of the Extension
Liouvilles Theorem and the Fundamental Theorem of Algebra
Maximum Modulus Principle

5 Series
Convergence of Sequences
Convergence of Series
Taylor Series
ProofofTaylors Theorem
Examples
Laurent Series
ProofofLaurents 111eorem
Examples
Absolute and Uniform Convergence of Power Series
Continuity of Sums of Power Series
Integration and Differentiation ofPower Series
Uniqueness of Series Representations
Multiplication and Division of Power Series

6 Residues and Poles
Isolated Singular Poims
Residues
Cauchys Residue Theorem
Residue at Infinity
The Three Types of Isolated Singular Points
ResiduCS at POles
Examples
Zeros of Analytic Functions
Zeros and Poles
Behavior of Functions Near Isolated Singular Points

7 Applications of Residues
Evaluation of Improper Integrals
Example
Improper Integrals from Fourier Analysis
Jordans Lemma
Indented Paths
An Indentation Around a Branch P0int
Integration Along a Branch Cut
Definite Integrals Involving Sines and Cosines
Argument Principle
Rouch6s Theorem
Inverse Laplace Transforms
Examples

8 Mapping by Elementary Functions
Linear Transformations
The TransfoITnation w=1/Z
Mappings by 1/Z
Linear Fractional Transformations
An Implicit Form
Mappings ofthe Upper HalfPlane
The Transformation w=sinZ
Mappings by z2 and Branches of z1/2
Square Roots of Polynomials
Riemann Surfaces
Surfaces forRelatedFuncfions
9 Conformal Mapping
10 Applications of Conformal Mapping
11 The Schwarz-Chrstoffer Transformation
12 Integral Formulas of the Poisson Type
Appendixes
Index
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复变函数及应用(英文版·第9版)
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