Proofs and Applications of Cauchy-Goursat Theorem and Cauchy’s Integral Formula

Weilin Zhang

2025

Abstract

This article focuses on some basis formulae and theorems of complex analysis in further mathematics. Complex variable function is a kind of function which contains complex number as its independent variables on the complex plane instead of real number in the real plane. This essay attempts to prove the two theorems found by Cauchy, i.e., Cauchy-Goursat theorem and Cauchy’s integral formula primarily and briefly by some approaches which the people who knows the complex analysis firstly can follow and understand. After that, there are several applications in the further mathematical aspects in this paper. This paper may contain some reverse applications about previous conclusions and use the idea of breaking down some harsh problems into many easier questions. This paper has gotten the steps to utilize and further understand the Cauchy-Goursat theorem and Cauchy’s integral formula. This article may assist the people who first takes up the further mathematics and complex analysis to realize the Cauchy-Goursat theorem and Cauchy’s integral formula and try to construct the confidence of mastering them in the future.

Paper Citation

in Harvard Style

Zhang W. (2025). Proofs and Applications of Cauchy-Goursat Theorem and Cauchy’s Integral Formula. In Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA; ISBN 978-989-758-774-0, SciTePress, pages 655-658. DOI: 10.5220/0013861200004708

in Bibtex Style

@conference{iampa25,
author={Weilin Zhang},
title={Proofs and Applications of Cauchy-Goursat Theorem and Cauchy’s Integral Formula},
booktitle={Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA},
year={2025},
pages={655-658},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013861200004708},
isbn={978-989-758-774-0},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA
TI - Proofs and Applications of Cauchy-Goursat Theorem and Cauchy’s Integral Formula
SN - 978-989-758-774-0
AU - Zhang W.
PY - 2025
SP - 655
EP - 658
DO - 10.5220/0013861200004708
PB - SciTePress