Application of residue theorem in mathematics

YuXuan Yan

doi:10.1117/12.2672673

28 March 2023 Application of residue theorem in mathematics

YuXuan Yan

Proceedings Volume 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022); 125970N (2023) https://doi.org/10.1117/12.2672673
Event: Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 2022, Nanjing, China

Abstract

Residue theorem is an important part of complex variable functions, and its theorems have been widely used in real life, such as mathematics, physics and computer fields, but because the residue theorem is the most difficult part of complex variable functions to understand, so some people don't know where to start when applying. However, when the original functions of some definite integral integrands are not easy to solve, using the remainder theorem to calculate these relatively difficult definite integrals is an effective method to solve the definite integral problem. This paper first gives the definition and derivation process of the residue theorem, discusses the simple calculation method of the residue theorem through examples, and then uses the residue theorem to deduce and calculate the integrals of rational fractions and rational trigonometric functions step by step, and obtain two common integrals for calculation. The method is hoped to be used in practice in the future.

Citation Download Citation

YuXuan Yan "Application of residue theorem in mathematics", Proc. SPIE 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 125970N (28 March 2023); https://doi.org/10.1117/12.2672673

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