同一封闭曲线复积分的多种解法探究  

Various Approaches to Integrals on a Closed Contour

作　　者：江毅 JIANG Yi(Department of Mathematics,Fuzhou Institute of Technology,Fuzhou 350506,China)

机构地区：[1]福州理工学院数学系,福建福州350506

出　　处：《高等数学研究》2023年第3期47-50,共4页Studies in College Mathematics

基　　金：福建省教育厅中青年教师教育科研项目(JAT200890);福州理工学院一流本科课程《复变函数论》(LGJG2022012)。

摘　　要：在复分析中,对解析函数的研究及复积分的求解,一直贯穿着整个学科.众所周知,沿封闭曲线的复积分有多种求解方法:定积分的参数形式、柯西积分定理、柯西积分公式、洛朗级数、留数定理、对数留数法等.通过对同一道例题的求解,比较了这几种方法的利弊,揭示了柯西留数定理的技巧最灵活,适用的范围也最广.There are various approaches to a complex integral along the closed contour,such as the use of the parametric form of definite integral,Cauchy integral theorem,Cauchy integral formula,Laurent series,Cauchy residue theorem,logarithmic residue method,etc.Using an example,the advantages and disadvantages of these approaches are compared,which reveals that the Cauchy residue theorem is the most flexible technique and has the widest range of applications.

关 键 词：复积分 柯西积分定理 柯西积分公式 洛朗级数 柯西留数定理 

分 类 号：O174[理学—数学]