丁韫， 杨晓春^*

（  大连海事大学数学系；  ）

摘要： 本文主要对复积分这个知识点做了探讨。文中就复积分的概念及相关问题的处理、复积分特点、复积分的计算等方面做了讨论。内容涉及到了多值函数积分，被积函数的单值化问题，一般有界函数可积性问题，解析函数积分计算的计算问题，积分与路径的关系，及利用留数计算积分问题等等。关注点主要放在如何在面对一个与Riemann积分有较大差异的情况下，在构建复积分知识的继承性和差异的合理性解决方面的思维模式。
关键词： 复积分的概念；多值函数；单值解析分值；积分计算；留数.

DING Yun， YANG Xiaochun^*

（  Mathematics Department of Dalian Maritime University；  ）

Abstract： The paper discuss the knowledge of complex integrals which is about the concept of complex integrals and the dealings of some related problems, the significance of complex integrals and the computation of complex integrals as well. In the middle of the discussion, it concerns the integrals of multiple valued function, the uniformization of integrand, integrability of the general bounded function, the computation of integral of the analytic function, the relation between integral and path of integral, and compute an integrals by using residue. We pay more attention to the thinking pattern of constructing the succession of the knowledge of complex integrals and the dealing of rationality of the difference when integral we facing is quite different from Riemann integrals.

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