James Ward Brown，密歇根大学迪尔伯恩分校数学系荣休教授，美国数学会会士，入编《美国名人录》和《世界名人录》。1964年于密歇根大学获得博士学位，1971年至2011年任密歇根大学教授，并于 1976年获得密歇根大学杰出教学奖。
Ruel V. Churchill(1899—1987 )生前是密歇根大学知名教授，于芝加哥大学取得理学学士学位，于密歇根大学取得物理学硕士及数学博士学位，自1922年起在密歇根大学执教。他从20世纪40年代开始 编写一系列经典教材，除本书外，还与James Ward Rrown合著有《Fourier Series and Boundary Value Problems》。
目录
Preface 1 Complex Numbers Sums and Products Basic Algebraic Properties Further Algebraic Properties Vectors and Moduli Triangle Inequality 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 and Mappings The Mapping w = zz Limits Theorems on Limits Limits Involving the Point at Infinity Continuity Derivatives Rules for Differentiation Cauchy-Riemann Equations Examples Sufficient Conditions for Differentiability Polar Coordinates Analytic Functions Further Examples Harmonic Functions Uniquely Determined Analytic Functions Reflection Principle 3 Elementary Functions The Exponential Function The Logarithmic Function Examples Branches and Derivatives of Logarithms Some Identities Involving Logarithms The Power Function Examples The Trigonometric Functions sin z and cos z Zeros and Singularities of 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 Involving 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 Verification of the Extension Some Consequences of the Extension Liouville's Theorem and the Fundamental Theorem of Algebra Maximum Modulus Principle 5 Series Convergence of Sequences Convergence of Series Taylor Series Proof of Taylor's Theorem Examples Negative Powers of (z - z0) Laurent Series Proof of Laurent's Theorem Examples Absolute and Uniform Convergence of Power Series Continuity of Sums of Power Series Integration and Differentiation of Power Series Uniqueness of Series Representations Multiplication and Division of Power Series 6 Residues and Poles Isolated Singular Points Residues Cauchy's Residue Theorem Residue at Infinity The Three Types of Isolated Singular Points Examples Residues 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 Jordan's Lemma An Indented Path An Indentation Around a Branch Point Integration Along a Branch Cut Definite Integrals Involving Sines and Cosines Argument Principle Rouche's Theorem Inverse Laplace Transforms Mapping by Elementary Functions Linear Transformations The Transformation w = 1/z Mappings by 1/z Linear Fractional Transformations An Implicit Form Mappings of the Upper Half Plane Examples Mappings by the Exponential Function Mapping Vertical Line Segments by w=sin z Mapping Horizontal Line Segments by w=sin z Some Related Mappings Mappings by z2 Mappings by Branches of z1/2 Square Roots of Polynomials Riemann Surfaces Surfaces for Related Functions 9 Conformal Mapping Preservation of Angles and Scale Factors Further Examples Local Inverses Harmonic Conjugates Transformations of Harmonic Functions Transformations of Boundary Conditions 10 Applications of Conformal Mapping Steady Temperatures Steady Temperatures in a Half Plane A Related Problem Temperatures in a Quadrant Electrostatic Potential Examples Two-Dimensional Fluid Flow The Stream Function Flows Around a Comer and Around a Cylinder 11 The Schwarz-Christoffel Transformation Mapping the Real Axis onto a Polygon Schwarz-Christoffel Transformation Triangles and Rectangles Degenerate Polygons Fluid Flow in a Channel through a Slit Flow in a Channel with an Offset Electrostatic Potential about an Edge of a Conducting Plate 12 Integral Formulas of the Poisson Type Poisson Integral Formula Dirichlet Problem for a Disk Examples Related Boundary Value Problems Schwarz Integral Formula Dirichlet Problem for a Half Plane Neumann Problems Appendixes Bibliography Table of Transformations of Regions Index
