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所在平台: Udemy |
课程主页: https://www.udemy.com/course/a-complete-course-on-complex-analysis/
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课程名称：复杂分析完备课程 课程概述：本课程是一门关于复杂分析的完整课程，所有主题都以详细但简单易懂的方式进行讲解。课程专为科学和工程领域的大学及学院学生设计，同时也适合准备各种竞争考试的学生。整个课程分为两个部分： 第一部分： - 复变量函数 - 解析函数 - 柯西-黎曼方程及其示例 - 利用Milne Thomson方法构造解析函数 - 简单连通域与多连通域 - 柯西定理及其证明 - 柯西定理在多连通域中的扩展及其示例 - 柯西积分公式及其证明 - 柯西积分公式的示例 - Morera定理 - 幂级数及其收敛半径 第二部分： - 泰勒级数与洛朗级数及相关示例 - 残数及柯西残数定理 - 柯西残数定理的应用 - 极点与奇点 - Contour积分 - 双线性或Mobius变换 复杂数是实数的扩展，复杂分析主要讨论复杂变量。该课程旨在为科学和工程学生奠定一个扎实的基础，以理解基本概念和发展操作技能，同时确保学生在完成此课程后能应对复杂变量在后续课程中的高级应用。
This is a complete course on complex analysis in which all the topics are explained in detailed but simple and easy manner. This course is designed for university and college level students of science and engineering stream as well as for the students who are preparing for various competitive exams. The whole curriculum is divided into two parts.Part 1Functions of Complex variables, Analytic Function, Cauchy Riemann EquationsSome examples of Cauchy Riemann EquationsMilne Thomson Method to construct Analytic functionSimply and Multiply Connected Domains, Cauchy's theorem and its proof, extension of Cauchy's theorem for multiply connected domainSome examples of Cauchy's theoremCauchy's Integral Formula with its proofSome examples of Cauchy's integral formulaMorera's TheoremPower series and Radius of ConvergencePart 2Taylor's series and Laurent's series and some examples based on theseResidues and Cauchy's Residue TheoremSome applications of Cauchy's residue theoremPoles and SingularitiesContour IntegrationBi linear or Mobius TransformationComplex numbers are just extension of real numbers. In complex Analysis mostly we discuss about complex variables. This course on Complex Analysis is taught to the students of science and engineering with the task of meeting two objectives: one, it must create a sound foundation based on the understanding of fundamental concepts and development of manipulative skills, and second it must reach far enough so that the student who completes such a course will be prepared to tackle relatively advanced applications of the subject in subsequent courses that utilize complex variables.
