基本介绍

内容简介

《华章数学原版精品系列:复变函数及应用(英文版·第9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

作者：（美国）布朗（James Ward Brown） （美国）丘吉尔（Ruel V.Churchill）

图书目录

Preface Complex Numbers 1 Sums and Products 1 Basic Algebraic Properties 3 Further Algebraic Properties 5 Vectors and Moduli 8 Triangle Inequality 11 Complex Conjugates 14 Exponential Form 17 Products and Powers in Exponential Form 20 Arguments of Products and Quotients 21 Roots of Complex Numbers 25 Examples 28 Regions in the Complex Plane 32 2 Analytic Functions 37 Functions and Mappings 37 The Mapping w = z2 40 Limits 44 Theorems on Limits 47 Limits Involving the Point at Infinity 50 Continuity 52 Derivatives 55 Rules for Differentiation 59 Cauchy-Riemann Equations 62 Examples 64 Sufficient Conditions for Differentiability 65 Polar Coordinates 68 Analytic Functions 72 Further Examples 74 Harmonic Functions 77 Uniquely Determined Analytic Functions 80 Reflection Principle 82 3 Elementary Functions 87 The Exponential Function 87 The Logarithmic Function 90 Examples 92 Branches and Derivatives of Logarithms 93 Some Identities Involving Logarithms 97 The Power Function 100 Examples 101 The Trigonometric Functions sin z and cos z 103 Zeros and Singularities of Trigonometric Functions 105 Hyperbolic Functions 109 Inverse Trigonometric and Hyperbolic Functions 112 4 Integrals 115 Derivatives of Functions w (t) 115 Definite Integrals of Functions w (t) 117 Contours 120 Contour Integrals 125 …… 5 Series 6 Residues and Poles 7 Applications of Residues 8 Mapping by Elementary Functions 9 Conformal Mapping 10 Applications of Conformal Mapping 11 The Schwarz-Christoffel Transformation 12 Integral Formulas of the Poisson Type Appenclixes Index