扩展劳伦系列及其应用

G. Adhikari
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引用次数: 0

摘要

在尼泊尔,大学开设了许多数学课程。其中,复杂分析是最强大的。在复分析中,洛朗级数展开是一个众所周知的主题,因为它可以用来寻找复函数在奇点周围的残数。结果表明,计算函数在其奇异点周围的洛朗级数是计算函数沿奇异点周围的任何闭合轮廓的积分以及函数的残数的有效方法。学习洛朗级数的概念可能是困难的,许多学生努力发展足够的理解,推理和解决问题的能力。因此,本文给出了多个实际的例子,其中一个函数的洛朗级数被发现,然后利用洛朗级数的理论计算函数的积分在任何封闭的轮廓上围绕该函数的奇点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
EXPANDING THE LAURENT SERIES WITH ITS APPLICATIONS
In Nepal, there are many mathematics subjects taught at university level. Among them, complex analysis is the most powerful. In complex analysis, the Laurent series expansion is a well-known subject because it may be used to find the residues of complex functions around their singularities. It turns out that computing the Laurent series of a function around its singularities is an effective way to calculate the integral of the function along any closed contour around the singularities as well as the residue of the function. Learning the Laurent series concepts can be difficult, and many students struggle to develop adequate understanding, reasoning, and problem-solving skills. Therefore, this article presents multiple practical examples where the Laurent series of a function is found and then utilized to compute the integral of the function over any closed contour around the singularities of the function, based on the theory of the Laurent series.
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