英语翻译摘要：留数定理是复变函数中重要的工具与概念,需要正确理解孤立奇点的概念与孤立奇点的分类和函数在孤立奇点的留数概念.掌握留数的计算法,特别是极点处留数的求,实际中会用

Question

英语翻译
摘要：留数定理是复变函数中重要的工具与概念,需要正确理解孤立奇点的概念与孤立奇点的分类和函数在孤立奇点的留数概念.掌握留数的计算法,特别是极点处留数的求,实际中会用留数求一些实积分.留数是复变函数论中重要的概念之一,它与解析函数在孤立奇点处的洛朗展开式、柯西复合闭路定理等都有密切的联系.现在研究的留数理论就是是柯西积分理论的继续,中间插入的泰勒级数和洛朗级数是研究解析函数的有力工具.在计算复函数沿闭曲线的积分时,常常转化为函数在各个孤立奇点处的留数,因此在实际问题和理论研究中都有很广泛的应用.而留数本身的计算及其应用一直是学习的重点和难点,这里进行简单的归纳总结和推广

Answer 1

The residue theorem of complex variable function is an important tool and concept, need to understand the concept of the isolated singularity and isolated singularity classification and function in the isolated singularity of the residue concept. Master residue calculation method, especially a pole residue and, actually using the residue of some real integrals. The residue is of complex variable function one of the important concept, it and analytic function in isolated singular point Laurent expansion, Cauchy composite closed theorem are closely linked. Now the study of residue theory are Cauchy integral theory continued, inserted in the middle of the Taylor series and Laurent series is a powerful tool in studying the analytic function. In the calculation of complex functions along the closed curve points, often converted to function in various isolated singular point residue, so in practical and theoretical research have very extensive application. Calculation and application of the residue itself is always the emphasis and difficulty in learning, there are simple summary and promotion