## 复变函数奇点的分类及其确定

The Classification and Judgment of the Singularity in the Complex Function
Abstract: In this paper, through the study of functions of a complex variable, the paper gives the singularities of its classification and determination method. First the paper introduces the definition of complex variable function in singularity. Then the related theorems and conclusions are given, the classification of isolated singular points, and the three major types of Isolated Singularities are judged. Through several special examples, we had further recognition of isolated singularity judgment, and grasp the method of Isolated Singularities of judgment. Of course, the judgment methods for some special cases are understood.
Keywords: Singularity; Isolated Singular Point; Removable Singularity; Poles; Essential Singularity

1 基础知识    3
2 奇点的分类    5
2.1 孤立奇点的三种类型    5
2.2 函数的零点与极点的关系    6
2.3 奇点的分类    7
3 三类孤立奇点的判定    8
3.1 相关定理    8
3.2 孤立奇点的判断方法    8
3.2.1可去奇点    8
3.2.2极点    10 源`自*六)维[论*文'网www.lwfree.cn
3.2.3本质奇点    11
4 应用举例    12
4.1两函数四则运算的奇点类型的举例    12
4.2孤立奇点在留数定理中的应用    13
5 结束语    15

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