復變函數的孤立點及其應用

論文題目：復變函數的孤立奇點及其應用學生姓名：學生學號：專業班級：學院名稱：

2011年4月7日

復變函數的孤立奇點及其應用

摘要

孤立奇點的應用在函數的教學以及學習中有著重要的作用。而留數的計算是復變函數中經常碰到的問題，本文主要探討了孤立奇點在留數計算中的應用。函數在不同的孤立奇點的不同類型處，其計算的方法也不同，所以首先我們要對其做出判斷。再根據孤立奇點類型的不同對應不同的留數求法，分別從可去奇點，本質奇點處留數的求法，極點處留數的求法，無窮遠點的留數的求法，其中在本文中因為考慮極點處的留數求法又根據：單極點、二階極點、 階極點的求法不同，結合例子給出極點階數的判斷方法。另外，還采用了變量替換的方法，增加了一個計算留數的公式。

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 judgement means. In addition, the variables used to replace the method, an increase of a formula for calculating the number of stay.

Key words: isolated singular point; singular point to go; pole; nature of singularity and reservations

目 錄

摘 要…………………………………………………………………………………Ⅱ

Abstract…………………………………………………………………………Ⅱ

孤立奇點的定義---------------------------------------------------------------------------3

孤立奇點的判別方法-----------------------------------------------------------------------4

孤立奇點的應用-----------------------------------------------------------------------------6

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