《复变函数及应用（英文版）（第8版）》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。
《复变函数及应用（英文版）（第8版）》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。
目录
- 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
