Synopsis
《21世纪普通高等教育基础课规划教材：复变函数与积分变换》是根据国家教育部最新制定的高等学校《工科数学课程教学基本要求》，在历年主讲该课程时使用的自编讲义的基础上编写而成的。《21世纪普通高等教育基础课规划教材：复变函数与积分变换》内容包括复数与复变函数、解析函数、复变函数的积分、级数、留数、共形映射、傅里叶变换和拉普拉斯变换。《21世纪普通高等教育基础课规划教材：复变函数与积分变换》系统地介绍了复变函数与积分变换的基本理论、方法与应用。《21世纪普通高等教育基础课规划教材：复变函数与积分变换》可供高等工科院校的师生作为教材使用，也可作为从事实际工作的工程技术人员的参考读物。我们这里要介绍的是在工程技术中最常用的两类积分变换：傅里叶变换、拉普拉斯变换。用积分变换去求解微分方程或其他方程，是比较方便的，因为它能够将分析运算（如微分、积分）转化为代数运算，通过积分变换，原来的偏微分方程可以减少自变量的个数直至变成常微分方程；原来的常微分方程可以变成代数方程，从而积分变换成为微分方程和其他方程的重要解决方法之一。积分变换起源于19世纪的运算微积，英国著名的无线电工程师赫维赛德（Heaviside）在求解电工学、物理学等领域中的线性微分方程的过程中逐步形成了一种所谓的符号法，后来符号法又演变成现在的积分变换法。积分变换的理论和方法不仅在数学的诸多分支中得到广泛应用，而且作为一种研究工具在许多科学技术领域中，例如在物理学、力学、无线电技术以及信号处理等方面，无论是过去还是现在都在发挥着极为重要的作用。前言第1章复数与复变函数1.1复数的概念1.1.1复数1.1.2复数的运算1.2复数的几何表示1.3复球面与平面区域1.3.1复球面1.3.2复平面区域1.3.3曲线与连通域1.4复变函数的极限与连续性1.4.1复变函数的概念1.4.2复变函数的极限1.4.3复变函数的连续性习题一第2章解析函数2.1解析函数的概念2.1.1复变函数的导数与微分2.1.2解析函数2.2函数解析的充要条件2.3初等函数2.3.1指数函数2.3.2对数函数2.3.3幂函数2.3.4三角函数与双曲函数2.3.5反三角函数与反双曲函数习题二第3章复变函数的积分3.1复变函数积分的概念3.1.1复积分的概念3.1.2复积分的性质3.1.3复积分的计算3.2柯西-古萨（Cauchy-Goursat）定理与复合闭路定理3.2.1柯西-古萨定理3.2.2复合闭路定理3.3柯西积分公式与高阶导数公式3.3.1柯西积分公式3.3.2高阶导数公式3.4原函数与不定积分3.4.1原函数与不定积分3.4.2牛顿一莱布尼兹公式3.5解析函数与调和函数的关系3.5.1调和函数与共轭调和函数3.5.2共轭调和函数的求法习题三第4章级数4.1复数项级数4.1.1复数列4.1.2复数项级数4.2复变函数项级数与幂级数4.2.1复变函数项级数4.2.2幂级数4.2.3收敛半径的求法4.2.4幂级数的运算和性质4.3泰勒级数4.3.1泰勒定理、4.3.2常用函数的泰勒展开式4.4洛朗级数4.4.1洛朗级数的概念及收敛域
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Complex function and the integral transformation
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Machinery Industry Pub. Date :2009-6-1, 2009
ISBN 10: 7111266994
ISBN 13: 9787111266990
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Seller: liu xing, Nanjing, JS, China
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paperback. Condition: New. Ship out in 2 business day, And Fast shipping, Free Tracking number will be provided after the shipment.Pages Number: 189 Publisher: Machinery Industry Pub. Date :2009-6-1. This book is based on the latest Ministry of Education to develop the institutions of higher learning. the basic requirements of engineering mathematics teaching. speaker of the calendar year of the course handouts used self made on the basis of the preparation. This book includes: plural and complex function. analytic functions. complex function of the integral. series. residues. conformal mapping. Fourier transform and Laplace transform. This book systematically introduces complex variables and integral transformation of the basic theory. methods and applications. Book for teachers and students of engineering colleges as a textbook. can also be engaged in practical work as an engineering and technical personnel of readings. Contents: Preface Chapter 1 complex and the complex function of the concept of complex numbers 1.1.1 1.1 1.1.2 complex computing complex geometric representation of complex 1.3 1.2 Spherical and planar region complex re-spherical 1.3.2 1.3.1 1.3.3 complex plane area 1.4 curve and connected domain complex function limits and continuity of the concept of complex function 1.4.1 1.4.2 1.4.3 complex function of the limit of continuous complex function exercises an analytic function of 2.1 in Chapter 2 the concept of analytic functions 2.1.1 The derivative of complex function analytic functions and differential 2.1.2 2.2 function analysis of elementary functions necessary and sufficient conditions for 2.3 2.3.2 2.3.1 exponential power function of the number of function 2.3.3 2.3.4 Trigonometric and hyperbolic functions 2.3.5 Inverse trigonometric and inverse hyperbolic functions Problem 2 Chapter 3 complex function of the integral 3.1 The concept of integration of complex function 3.1.1 The concept of re-integration 3.1.2 3.1.3 re-integration complex nature of the calculation of 3.2 points Cauchy - the ancient Sa (Cauchy-Goursat) Theorem 3.2.1 the composite closed-Cauchy Theorem - Theorem 3.2.2 Composite closed the ancient Sa Theorem 3.3 Cauchy integral formula and higher order derivatives Equation 3.3.1 3.3.2 Cauchy integral formula 3.4-order derivative formula the original function and the original function and indefinite integral indefinite integral 3.4.1 3.4.2 Newton-Leibniz formula for analytic functions and harmonic functions 3.5 The relationship between harmonic functions conjugate 3.5.1 3.5.2 conjugate harmonic functions Method to harmonic functions of three exercises in Chapter 4 series 4.1 series plural items 4.1.2 4.1.1 plural plural items listed complex function series 4.2 series and power series term complex function key series 4.2.1 4.2. 2 radius of convergence of power series 4.2.3 4.2.4 Method to the nature of power series of operations and Taylor Theorem 4.3 Taylor Series 4.3.1. 4.3.2 Taylor expansion of commonly used functions 4.4 4.4.1 Laurent Laurent series series of concepts and convergence domain . . Chapter 5 Chapter 6 of the residue conformal mapping Fourier Transform Chapter 7 Chapter 8 Laplace Transform Appendix ReferencesFour Satisfaction guaranteed,or money back. Seller Inventory # L84717