学习柯西积分定理及留数定理的体会

On Cauchy's Theorem and Residue Theorem of Complex Variable Functions

本文利用在闭区域上解析的函数其导数必连续这一结论,证明柯西积分定理、闭路变形原理及复合闭路定理.总结复变函数的留数定理与物理上电通量的高斯定理的相似性.

Based on the result that if a function is analytic on a closed domain then its derivative must be continuous on the domain,we prove Cauchy's theorem,the principle of deformation of path,and Cauchy's theorem for multiply connected regions.We summarize the similarity between the residue theorem and Gauss theorem of electric flux in Physics.