柯西积分定理的初等证明

Elementary proof of Cauchy integral theorem

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.