留数概念的起源  

The Origin of the Concept of Residue

作　　者：王昌[1] 

机构地区：[1]西北大学数学与科学史研究中心,陕西西安710127

出　　处：《广西民族大学学报（自然科学版）》2008年第4期14-16,共3页Journal of Guangxi Minzu University ：Natural Science Edition

基　　金：国家自然科学基金资助项目(10771169)

摘　　要：采用历史分析和文献考证的方法,探讨和分析了柯西定义留数概念的原因及背景指明柯西从一些数学家的相关工作出发,在对C-R方程进行了讨论和分析之后,产生了他关于复积分问题的讨论.在处理了连续函数的复积分问题后,为了使复积分理论更加完善,他又开始讨论不连续函数的复积分,进而提出了留数概念.结论指出柯西的留数定义是他追求数学理论完美化的一种体现和产物.This paper studies and analyzes the reasons and the background of Cauchy defined the residue concept , in which we have used the method of historic analysis and literature review. The paper shows that Cauchy starts from some mathematician＇s related work, after discussion and analysis of the C-R equation, he has produced his discussion about the duplicate integral question. After having dealt with the continuous function duplicate integral issue, he starts to discuss the discontinuous function for the duplicate integral theory to be more perfect, then put forward the residue concept. The conclusion pointed out that the Cauchy＇s definition of residue is the manifestation and product of his persuit for the mathematical theory beautification.

关 键 词：柯西 复分析 留数 

分 类 号：O11[理学—数学]