Complex Variables and Integral Transforms课程：前往报名学习
Let's take you into the magic world of complex numbers and complex functions. Join us, enjoy your study!
开设学校：北京交通大学；学科：理学、
Let's take you into the magic world of complex numbers and complex functions. Join us, enjoy your study!
-Lecture 1 - Complex Number and Functions
-Lecture 2 - Algebraic operations of complex numbers
-Lecture 3 - Geometrical Representations in complex plane
-Lecture 4 - Representations of triangle and exponent
-Lecture 5 - Product, quotient and deMoivre's formula
-Lecture 6 - Roots of complex number
-Lecture 7 - Concept of Domain
-Lecture 8 - Funtions of complex variables
-Lecture 9 - Geometrical explanations for functions of complex number
-Lecture 10 - Limit and continuity of complex functions
-Exercise 1
-Discussing topics for Chapter 1
-Lecture 1 - Derivative of complex functions
-Lecture 2 - Concept of analytic function
-Lecture 3 - Equivalent conditions for analytic function
-Lecture 4 - Cauchy-Riemann equations
-Lecture 5 - Exponential function and Logarithmic function
-Lecture 6 - Trigonometric function and hyperbolic function
-Exercise 2
-Discussing topics for Chapter 2
-Lecture 1 - Definition of complex integral
-Lecture 3 - Cauchy theorem in multiply connected domains
-Lecture 4 - Anti derivative and indefinite integral
-Lecture 5 - Cauchy integral formula
-Lecture 6 - Higher order derivatives of analytic functions
-Lecture 7 - Analytic functions and harmonic functions
-Exercise 3
-Discussing topics for Chapter 3
-Lecture 2 - Concept of power series
-Lecture 3 - Calculations of radius of convergence
-Lecture 5 -Series with both positive and negative terms
-Lecture 7 - Applications of Laurent Expantions
-Exercise 4
-Discussing topics for Chapter 4
-Lecture 1 - Isolated singular points
-Lecture 3 - Residues and its calculations
-Lecture 4 - Rules for calculating residue I
-Lecture 5 - Rules for calculating residue II
-Lecture 6 - Applications of residue - I
-Lecture 7 - Applications of residue - II
-Lecture 8 - Applications of residue - Examples
-Exercise 5
-Discussing topics for Chapter 5
-Lecture 1 - Concept of conformal mapping
-Lecture 2 - Geometrical explanations of the derivative
-Lecture 3 - Fractional linear mapping I
-Lecture 4 - Fractional linear mapping II
-Lecture 5 - Determine the fractional linear mapping
-Lecture 6 - Determine the fractional linear mapping - examples
-Lecture 7 - Some special mappings
-Exercise 6
-Discussing topics for Chapter 6
-Lecture 1 - Fourier integral formula
-Lecture 2 - Fourier transform and its inverse - I
-Lecture 3 - Fourier transform and its inverse - II
-Lecture 4 - Properties of fourier transform
-Lecture 5 - Convolution and applications of fourier transform
-Exercise 7
-Discussing topics for Chapter 7
-Lecture 1 - Concept of Laplace transform
-Lecture 2 - Properties of Laplace transform - I
-Lecture 3 - Properties of Laplace transform - II
-Lecture 4 - Inverse of Laplace transform
-Lecture 5 - Applications of Laplace transform
-Exercise 8
黄晓鸣，北京交通大学理学院副教授，硕士研究生导师，主要研究方向为数字图像处理，医学影像重建，计算机网络及应用。1988年毕业于中国科学院系统科学研究所，获理学硕士学位。曾作为访问学者在芬兰图尔库大学工作一年多。发表20余篇论文或著作，主持多项计算机应用系统（软硬件）的设计和开发，先后参与多项国家自然科学基金面上项目，指导硕士研究生20余人。长期工作在教学一线，主讲过的研究生和本科生课程包括：数理方程与特殊函数、数字图像处理，数据结构与算法，复变函数与积分变换，离散数学，数据库原理等。
郑神州，北京交通大学理学院教授，博士生导师，主要研究方向为偏微分方程理论及应用。1997年于复旦大学获理学博士学位，2005年评为教授。曾访问过中科院应用所、系统所、南开大学陈所，肯塔基大学、芝加哥大学、普渡大学、得克萨斯大学，西班牙巴斯克应用数学中心等。在Transactions of AMS,J. Functional Anal.,JDE, manus.math., Proceedings of AMS等国际知名刊物发表了130余篇论文, 其中SCI论文90余篇。主持完成多项国家自然科学基金面上等项目，指导博士、硕士生40余人。长期在教学一线，1998年获北京市优秀青年骨干教师称号，2014年参加项目获中国铁道学会科技奖二等奖，是北京交通大学“数学物理方程”课建设负责人。
