Fundamental properties of complex integrals and series

Pengyu Jiang; Yanzhe Wang; Siyuan Zhai

doi:10.1117/12.2628130

22 April 2022 Fundamental properties of complex integrals and series

Pengyu Jiang, Yanzhe Wang, Siyuan Zhai

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121633R (2022) https://doi.org/10.1117/12.2628130
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

Complex number exists as the supplement of the real number set, providing mathematicians insights and practical ways to solve the problems whose solutions were beyond what mathematicians and physicians had known prior to the 18th century. Complex analysis is a subject that deals with the basic notions of mathematical analysis: differentiation and integration, going back to Newton, in the context of functions that are defined and take values in the complex plane. This essay provides a summary of geometric and algebraic properties of complex numbers to facilitate readers to comprehend the integral of complex functions. We’ll discuss about first, the basic definition and algebraic properties of complex number; second, operations and analysis of functions on complex plane; third, integrals along curves on complex planes. And at last, we’ll prove some theorems about complex series.

Citation Download Citation

Pengyu Jiang, Yanzhe Wang, and Siyuan Zhai "Fundamental properties of complex integrals and series", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121633R (22 April 2022); https://doi.org/10.1117/12.2628130

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