# Analysis of the Residue Theorem and Its Applications

• Yuntong Li

## Keywords:

Residue theorem; Definite integral; Logarithmic residue; Complex analysis.

## Abstract

Residue theorem is a useful tool for studying complex variable function. Residue theorem can be widely used in various disciplines, and it helps people solve a lot of practical problems. The residue theorem plays an important role in both mathematics and physics. It can not only make integral easier, but also solve problems that related to thermodynamics, optics, and electricity. In practice, it is usually complicated to solve the definite integral by using substitution, partial integration method and so on. Although these methods can calculate the solution, the computational workload is too large and complex. Using residue theorem to transform integral formulas can help people solve integrals easily. The method of using the residue theorem to solve the integral is more convenient than some traditional methods. In this paper, some applications of residue theorem are introduced. Further, it also gives some examples for calculating the integral by using residue theorem and logarithmic residue theorem.

## References

Yu Jinqing, Wang Shuhong, Deng Mingli. Cauchy in The Early Development of Complex Analysis, Mathematics in Practice and Theory, 2012, 42(24): 274-277.

Zhou Yunqing, Huang Wentao. Further Discussion Two Classes of Infinite integrals Solved by the Residue Theorem. College Physics, 2022, 42(9): 24-27+42.

Zhou Wenping, Liu Yifan, Song Tielei. Two types of infinite integrals handled by residue theorem. Physics and Engineering, 2022, 32(1): 56-59.

Li Qing, Lin Shiyou. A Generalization of the Residue Theorem. Journal of Qiongzhou College, 2013, 20(05): 30-35.

James Ward Brown, Ruel V. Churchill. Complex Variables and Application (Ninth Edition), 2018.

Yang Ping, Jing Fu. Engineering Mathematics, Xidian University Press, 2015.

Yang Lunbiao, Hao Zhifeng. Complex Function, Beijing: Science Press, 2004.

Zhong Yuquan. Function Theory of Complex Variables, Beijing: Higher Education Press, 2013.

Shen Yanwei. Residue Theorem and Its Applications. Journal of Tonghua Normal College, 2017, 38(06): 24-26.

Zhang Zhongcheng, Wang Cheng. Generalization and Application of Logarithmic Residue Theorem, Journal of Yangze University, 2006, (04): 470-471.

29-03-2024

Articles

## How to Cite

Li, Y. (2024). Analysis of the Residue Theorem and Its Applications. Highlights in Science, Engineering and Technology, 88, 439-444. https://doi.org/10.54097/njxsv644