文档介绍：论文题目：
复变函数的孤立奇点及其应用
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2011年4月7日
复变函数的孤立奇点及其应用
摘要
孤立奇点的应用在复变函数的教学以及学****中有着重要的作用。而留数的计算是复变函数中经常碰到的问题，本文主要探讨了孤立奇点在留数计算中的应用。函数在不同的孤立奇点的不同类型处，其计算的方法也不同，所以首先我们要对其做出判断。再根据孤立奇点类型的不同对应不同的留数求法，分别从可去奇点，本质奇点处留数的求法，极点处留数的求法，无穷远点的留数的求法，其中在本文中因为考虑极点处的留数求法又根据：单极点、二阶极点、阶极点的求法不同，结合例子给出极点阶数的判断方法。另外，还采用了变量替换的方法，增加了一个计算留数的公式。

关键字：孤立奇点；可去奇点；极点；本质奇点；留数；
Isolated singularities and its application
Abstract
Isolated singular point in the application of complex function of teaching and learning plays an important role. The residue of the calculation is complex function often encounter problems, the paper focused on a singular point in isolation remain in the calculation of the number of applications. Different functions in the isolation of the different types of singular point, the calculation methods are also different, so first of all we have to make their judgement. According to isolate different types of singular point to different stay for a few, were to go from the singular point is, in essence, to stay a few critical points for the law, the number of Poles seeking to stay the law, infinite number of points to stay for the law, which in this paper In view of the Poles to stay for a few in accordance with law: a unipolar point, second-order pole, the pole-order solution different, with examples given pole order of the judgemen