浅谈复积分的计算方法摘要.docx

文档介绍：浅谈复积分的计算方法
摘要
复积分即是指复变函数积分•在复变函数的分析理论屮，复积分是研究解析函数的重 分的计算中理论上处于关键地位，因此，对复积分及其计算的研究显得尤为重要•复变函 数中的积分不仅是研究解析函数的重要工具，也是它的后继课程积分变换的基础，所以就 复变函数的积分计算方法进行总结和探讨是十分必耍的•柯西积分公式、柯西高阶导数公 ，而且 可以用来计算实积分，它把实积分和复积分的相关知识有机的结合起来.
本文讨论了留数定理与复变函数积分Z间的内在联系，并举例说明了留数定理、柯西 积分定理、柯西积分公式和柯西高阶导数公式Z间的密切关系•本文将利用复变函数积分 基本原理，利用儿种复积分的基本求法，针对每一种计算方法给出例子，并通过柯西积分 定理、柯西积分公式、柯酋高阶导数公式、留数定理等來计算复积分，从中揭示诸多方法 的内在联系，对复积分的计算方法作岀较系统的归纳总结，从中概括岀求复变函数积分的 解题方法和技巧•复变函数中积分分闭曲线和非闭曲线两类•本文就这两种积分的计算方 法进行总结和探讨.
关键词：复积分；柯西积分定理；柯西积分公式；留数定理
Discussion on the computational methods of complex integration
ABSTRACT
Complex integration entails Complex integration」n the analysis of the complex function theory,Complex integration is an important tool for analytic important properties of analytic functions must use the complex function points to prove that the Cauchy integral theorem in a key position in the calculation of the complex integral theory,Therefore,Complex integral calculation is particularly important ..The integral in the complex variable function is not only an important tool for the study of analytic functions,Also the basis for its successor course integral transforms , integral calculation of the complex function method summary and discussion is very integral formula , Cauchy order derivative formula and residue theorem has played a significant role in the calculation of complex residue theorem can not only be used to calculate the complex integration,A nd can be used to calculate the real integral,It organic combination of real integral and complex integration of knowledge ..
This paper discusses the intrinsic link between the stay theorem Complex integration,And illustrates the residue theorem, the close relationship between the Cauchy integral theorem, Cauchy integral formula and the Cauchy higher derivative article will use the basic principles of Complex integration,Th