“复变函数论”中奇偶性的原理与应用  

作　　者：万莉莉 

机构地区：[1]西南科技大学数理学院,四川绵阳621010

出　　处：《科技风》2025年第2期95-97,共3页

基　　金：西南科技大学龙山人才项目(18LZX655)。

摘　　要：函数是数学的主要研究对象,而奇偶性是函数的一种重要特性,通过研究函数的奇偶性可以加强学生对函数概念与性质的理解,培养数学思维和创新能力.“复变函数论”是理工科本科生必修的数学基础课程,在自然科学的各个领域都有着广泛的应用.现有文献主要集中于研究实变量函数的奇偶性及其应用,对复变函数的奇偶性讨论较少.本文利用函数的奇偶性,系统研究复变函数中的积分、求导及留数等相关问题,以指导大学数学教学,改进教师的教学方法,提高学生的思维水平和计算效率,并体现数学之美.Function is the main research object of mathematics and parity is an important characteristic of function.By studying the parity,students can strengthen their understanding of the concept and property of function,and cultivate mathematical thinking and innovation ability.Complex function theory,as a compulsory mathematical basic course for undergraduate students of science and engineering,has been widely used in various fields of natural science.The existing literature mainly focus on the research of real variable function and there is little discussion on the parity of complex variable function.This paper uses the parity of function to study the problems of integration,derivation and residue in complex variable function systematically,so as to guide college mathematical education,improve teachers’teaching methods,promote students’thinking level and computing ability,and reflect the beauty of mathematics.

关 键 词：复变函数 奇偶性 复积分 解析函数 留数 

分 类 号：G63[文化科学—教育学]