柯西积分定理的初等证明  

Elementary proof of Cauchy integral theorem

作　　者：王信松[1] 张节松[2] 

机构地区：[1]天津城市建设学院基础学科部,天津300384 [2]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《安徽大学学报（自然科学版）》2011年第5期6-9,共4页Journal of Anhui University(Natural Science Edition)

基　　金：安徽省教育厅自然科学基金资助项目(2006KJ069A)

摘　　要：利用数学分析的知识构造一个简单的恒同逼近函数,由此用分析中的逼近思想,成功地用满足柯西-黎曼条件的连续可微的函数逼近一般的可微函数,给出了柯西积分定理的一个初等证明,克服了复变函数论中这一关键性定理证明繁琐或者超纲的困难.In this paper,a simple identity approximation function was constructed by using the knowledge of mathematic analysis,thereby,applying the approximation idea in analysis,we successfully obtained that ordinary differential functions were well approximated by continuously differentiable functions satisfying the Cauchy-Riemann equations,and an elementary proof of Cauchy integral theorem was presented,which overcame some troublesome or over-syllabus difficulties in the proof of the theorem in the text of complex variable functions,and was also beneficial to the teaching.

关 键 词：解析函数 柯西积分定理 单连同区域 

分 类 号：O174.5[理学—数学]