Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 5, 25 May 2023
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Complex Analysis and Residue Theorem
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Abstract
The study of the properties of analytical functions is described as complex analysis. The residue theorem is an important conclusion in complex analysis. This paper introduces the origin of imaginary numbers from Cardano Formula defines the conversion of complex number formats from the Euler Theorem, and proves the intermediate theorem Cauchy Integral Formula before reaching our final conclusion and the goal of the paper, Residue Theorem. The name of the theorem comes from the concept of residue, which is defined using a function’s Laurent series. We could then derive the Residue Theorem from the Cauchy Integral Theorem, also called the Cauchy-Goursat Theorem. We will be able to formalize our prior, ad hoc method of computing integrals over contours encompassing singularities. Additionally, it is a theorem that may be applied to zero-pole qualities and curved integral properties. The Residue Theorem is the basis of many essential mathematical facts revolving around line integrals, particularly in solving ODEs and PDEs and describing physics models.
Keywords
residue theorem, complex analysis, residue.
References
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Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 2nd International Conference on Computing Innovation and Applied Physics (CONF-CIAP 2023)
- ISBN (Print)
- 978-1-915371-53-9
- ISBN (Online)
- 978-1-915371-54-6
- Published Date
- 25 May 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/5/20230307
- Copyright
- 25 May 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited