复变函数及应用（英文版·第9版） pdf 网盘 高速 下载地址大全 免费

《华章数学原版精品系列：复变函数及应用（英文版·第9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。这本经典的教材对复变函数的教学影响深远，被美国斯坦福大学、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。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。

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

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