以初等多值函数为例对复变函数进行的教学探讨  

Discussion on the Teaching of Complex Variable Function by Taking Elementary Multi-valued Function as an Example

作　　者：侯利元 刘念平 HOU Liyuan;LIU Nianping(School of Mathematics and Science,Leshan Normal University,Leshan Sichuan 614000,China)

机构地区：[1]乐山师范学院,数理学院,四川乐山614000

出　　处：《乐山师范学院学报》2021年第12期110-115,共6页Journal of Leshan Normal University

基　　金：乐山师范学院学科建设重点科研项目“以事件触发、脉冲控制为基础的忆阻神经网络的同步控制”(LZD015);乐山师范学院一流本科课程建设与研究专项科研课题“‘常微分方程’课程的教学改革与实践”(KG2020-1-06);乐山师范学院学科建设重大科研项目“具有时空异构性的复杂网络模型及其动力学研究”(LZDP010)。

摘　　要：文章分析了复变函数的教学中经常存在的问题,学生学习动力不足,考核方式陈旧,教师对课程内容缺乏深层次的思考。之后以初等多值函数为例对复变函数的教学进行了分析,以期解决分析出的问题。在分析过程中重点对求单值解析分支的函数值问题进行了剖析,给出两种求函数值方法的比较,分析教材中的不足之处。最后给出复变函数这一课程的教学建议。Firstly,the problems that exist in the teaching of complex variable function are analyzed in this paper.The main problems listed in the paper are the lack of learning motivation of students,the obsolete assessment method and the lack of teachers’deep thinking on the course content.After that,this paper takes the chapter of elementary multi-valued function as an example for teaching analysis,and puts forward corresponding teaching suggestions in order to solve the problems just mentioned.In the process of analysis,the paper focuses on calculating the function value of the multi-valued function on the single-valued analytic branch,and gives the comparison of the two methods of calculating the function value,and analyzes the shortcomings in the textbook.Finally,some teaching suggestions on the course of complex function are given.

关 键 词：复变函数 多值函数 单值解析分支 

分 类 号：O231[理学—运筹学与控制论] TP273[理学—数学]