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复分析基础及工程应用（英文版）
作者：（美）E.B.Saff，（美）A.D.Snider等著
出版社：机械工业出版社
出版时间：2004-10-01
ISBN：9787111152170
定价：¥59.00
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内容简介
《复分析基础及工程应用（英文版）（第3版）》全面介绍复变理论及其在当今工程问题上的应用，理论与实际应用密切结合 ，对工程类学科的学生来说，这种方式使数学方法更具生动性。本书的主要特点：●结合使用MATLAB工具箱：使复杂算术运算及保形映射更加可视化。●对复函数在线性分析中的用途的最新阐述：为学生提供了交流电路、运动学及信号处理等应用的另一种视角。●茹利亚集：使学生熟悉复分析研究的最新论题。●以两种可选的方式给出了柯西定理：提供了更易子可视化、更易子应用到特定情况的方法。●对数值保形映射的高可读性阐述：这对现代技术领域中的应用非常重要，与其他数学领域也密切相关。●在实际工程问题中的应用：吸引并帮助学生灵活应用数学方法。
作者简介
E.B.Saff1964年子佐治亚理工学院获得学士学位，1968年子马里兰大学获得博士学位，现为范德比尔特大学数学系教授，构造逼近中心教授、主任他主要从事逼近论、位势论、复分析和数值分析等领域的研究。A.D.1Snider1962年于麻省理工学院获得数学学士学位，21966年子波士顿大学获得物理学硕士学位，21971年子纽约大学数学系获得博士学位，现为南佛罗里达大学电子工程系教授。他主要从事光谱分析。最优化、电子学与电磁学的数学建模及通信理论等方面的研究。相关图书软件过程改进（英文版）80X86汇编语言与计算机体系结构计算机体系结构：量化研究方法：第3版计算机科学概论（英文版·第2版）分布式系统概念设计调和分析导论（英文第三版）人工智能：智能系统指南（英文版）第二版电力系统分析（英文版·第2版）面向计算机科学的数理逻辑：系统建模与推理（英文版·第2版）数学规划导论英文版抽样理论与方法（英文版）Java2专家导引（英文版·第3版）机器视觉教程（英文版）（含盘）支持向量机导论（英文版）电子设计自动化基础（英文版）Java程序设计导论（英文版·第5版）数据挖掘：实用机器学习技术（英文版·第2版）UML参考手册（第2版）Java教程（英文版·第2版）软件需求管理：用例方法（英文版·第2版）数字通信导论离散事件系统仿真（英文版·第4版）复杂SoC设计（英文版）基于FPGA的系统设计（英文版）UML参考手册（英文版·第2版）计算理论导引实用软件工程（英文版）计算机取证（英文版）EffectiveC#（英文版）基于用例的面向方面软件开发（英文版）UNIX教程（英文版·第2版）软件测试（英文版第2版）设计模式精解（英文版第2版）Linux内核编程必读-经典原版书库实分析和概率论-经典原版书库（英文版.第2版）
目录
Preface
1 Complex Numbers
1.1 The Algebra of Complex Numbers
1.2 Point Representation of Complex Numbers
1.3 Vectors and Polar Forms
1.4 The Complex Exponential
1.5 Powers and Roots
1.6 Planar Sets
1.7 The Riemann Sphere and Stereographic Projection
Summary
2 Analytic Functions
2.1 Functions of a Complex Variable
2.2 Limits and Continuity
2.3 Analyticity
2.4 The Cauchy-Riemann Equations
2.5 Harmonic Functions
2.6 *Steady-State Temperature as a Harmonic Function
2.7 *Iterated Maps:Julia and Mandelbrot Sets
Summary
3 Elementary Eunctions
3.1 Polynomials and Rational Functions
3.2 The Exponential,Trigonometric,and Hyperbolic Functions
3.3 The Logarithmic Function
3.4 Washers,Wedges,and Walls
3.5 Complex Powers and Inverse Trigonometric Functions
3.6 *Application to Oscillating Systems
Summary
4 Complex Integration
4.1 Contours
4.2 Contour Integrals
4.3 Independence of Path
4.4 Cauchy's Integral Theorem
4.4a Deformation of Contours Approach
4.4b Vector Analysis Approach
4.5 Cauchy's Intergral Formula and Its Consequences
4.6 Bounds for Analytic Functions
4.7 *Applications to Harmonic Functions
Summary
5 Series Representations for Analytic Functions
5.1 Sequences and Series
5.2 Taylor Series
5.3 Power Series
5.4 *Mathematical Theory of Convergence
5.5 Laurent Series
5.6 Zeros and Singularities
5.7 The Point at Infinity
5.8 *Analytic Continuation
Summary
6 Residue Theory
6.1 The Residue Theorem
6.2 Trigonometric Integrals over[0,2π]
6.3 Improper Integrals of Certain Functions over
6.4 Improper Integrals Involving Trigonometric Functions
6.5 Indented Contours
6.6 Integrals Involving Multiple-Valued Functions
6.7 The Argument Principle and Rouche's Theorem
Summary
7 Conformal Mapping
7.1 Invariance of Laplace's Equation
7.2 Geometric Considerations
7.3 Mobius Transformations
7.4 Mobius Transformations,Continued
7.5 The Schwarz-Christoffel Transformation
7.6 Applications in Electrostatics,Heat Flow,and Fluid Mechanics
7.7 Further Physical Applications of Conformal Mapping
Summary
8 The Transorms of Applied Mathematics
8.1 Fourier Series(The Finite Fourier Transform)
8.2 The Fourier Transform
8.3 The Laplace Transform
8.4 The z-Transform
8.5 Cauchy Integrals and the Hilbert Transform
Summary
A Numerical Construction of Confomal Maps
A.1 The Schwarz-Christoffel Parameter Problem
A.2 Examples
A.3 Numerical Integration
A.4 Conformal Mapping of Smooth Domains
A.5 Conformal Mapping Software
B Table of Conformal Mappings
B.1 Mobius Transformations
B.2 Other Transformations
Answers to Odd-Numbered Problems
Index
1 Complex Numbers
1.1 The Algebra of Complex Numbers
1.2 Point Representation of Complex Numbers
1.3 Vectors and Polar Forms
1.4 The Complex Exponential
1.5 Powers and Roots
1.6 Planar Sets
1.7 The Riemann Sphere and Stereographic Projection
Summary
2 Analytic Functions
2.1 Functions of a Complex Variable
2.2 Limits and Continuity
2.3 Analyticity
2.4 The Cauchy-Riemann Equations
2.5 Harmonic Functions
2.6 *Steady-State Temperature as a Harmonic Function
2.7 *Iterated Maps:Julia and Mandelbrot Sets
Summary
3 Elementary Eunctions
3.1 Polynomials and Rational Functions
3.2 The Exponential,Trigonometric,and Hyperbolic Functions
3.3 The Logarithmic Function
3.4 Washers,Wedges,and Walls
3.5 Complex Powers and Inverse Trigonometric Functions
3.6 *Application to Oscillating Systems
Summary
4 Complex Integration
4.1 Contours
4.2 Contour Integrals
4.3 Independence of Path
4.4 Cauchy's Integral Theorem
4.4a Deformation of Contours Approach
4.4b Vector Analysis Approach
4.5 Cauchy's Intergral Formula and Its Consequences
4.6 Bounds for Analytic Functions
4.7 *Applications to Harmonic Functions
Summary
5 Series Representations for Analytic Functions
5.1 Sequences and Series
5.2 Taylor Series
5.3 Power Series
5.4 *Mathematical Theory of Convergence
5.5 Laurent Series
5.6 Zeros and Singularities
5.7 The Point at Infinity
5.8 *Analytic Continuation
Summary
6 Residue Theory
6.1 The Residue Theorem
6.2 Trigonometric Integrals over[0,2π]
6.3 Improper Integrals of Certain Functions over
6.4 Improper Integrals Involving Trigonometric Functions
6.5 Indented Contours
6.6 Integrals Involving Multiple-Valued Functions
6.7 The Argument Principle and Rouche's Theorem
Summary
7 Conformal Mapping
7.1 Invariance of Laplace's Equation
7.2 Geometric Considerations
7.3 Mobius Transformations
7.4 Mobius Transformations,Continued
7.5 The Schwarz-Christoffel Transformation
7.6 Applications in Electrostatics,Heat Flow,and Fluid Mechanics
7.7 Further Physical Applications of Conformal Mapping
Summary
8 The Transorms of Applied Mathematics
8.1 Fourier Series(The Finite Fourier Transform)
8.2 The Fourier Transform
8.3 The Laplace Transform
8.4 The z-Transform
8.5 Cauchy Integrals and the Hilbert Transform
Summary
A Numerical Construction of Confomal Maps
A.1 The Schwarz-Christoffel Parameter Problem
A.2 Examples
A.3 Numerical Integration
A.4 Conformal Mapping of Smooth Domains
A.5 Conformal Mapping Software
B Table of Conformal Mappings
B.1 Mobius Transformations
B.2 Other Transformations
Answers to Odd-Numbered Problems
Index
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