留数定理及其应用毕业论文.doc

合肥师范学院2014届本科生毕业论文（设计） PAGE PAGE 18 学号：1007410101 学号：1007410101 本科毕业论文（设计） (2014 届) 留数定理及其应用 院 系 数学与统计学院 专 业 数学与应用数学 姓 名 指导教师 职 称 摘要 留数定理是复积分和复级数理论相结合的重要产物之一，只有正确理解并掌握孤立奇点的概念，进一步研究孤立奇点的分类，还有函数在孤立奇点的留数概念，才能解决一些实际问题中涉及留数的应用。理解并掌握留数的计算方法，尤其是极点处留数的求解方法，以及实际求解中会应用留数求一些实积分。我们现在所学习还有研究的留数理论就是是柯西积分理论的延续，泰勒级数和洛朗级数与其密切联系，是研究解析函数的重要工具。留数在复变函数论本身和实际应用中都是有其重要地位的，尤其是与计算周线积分的问题密切相关。此外，我们还可以运用留数理论已知条件去解决“大范围”的积分计算问题，也可以访问一个函数的零点分布区域问题。 关键词：留数理论；留数的计算；积分；留数的应用 ABSTRACT Residue theorem is the combination of the theory of integral and series, need to correct understanding of the concept and the classification of isolated singularity of isolated singularity and function in the isolated singularity residue concept. Mastering the residue method, especially in pole residue, practice with residue and some solid points. Residue is one of important concepts in the theory of complex function, and analytic function in the isolated singularity, cauchy composite Laurent expansion of closed circuit theorem and so on all are closely linked. Now research of residue theory is a continuation of cauchy integral theory. The insert in the middle of the Taylor series and Laurent series is a powerful tool to study analytic function. Residue in the complex variable function theory and practical application is important it and calculating contour integral (or boil down to examine cycle line integral) problems have close relationship. In addition the residue theory, we have conditions to solve the problem of large scale integral calculation, can also examine zero point of function in the area of distribution Key words：Residue theory; The calculation of residue; Integral; The application of residue 目录 TOC \o 1-2 \h \u HYPERLINK \l _Toc3129 摘要 l _Toc15401 ABSTRACT l _Toc25441 1.引言 l _Toc24781 2．留数 l _Toc11834 2.1留数的定义及留数定理 l _Toc14159 2.2留数的求法 l _Toc15960 2.3函数在无穷远点的留数 l _Toc22171