Elegant Theory of Complex Analysis

Research Article
Open access

Elegant Theory of Complex Analysis

Yisun Chen 1*
  • 1 Shanghai Foreign Language School Affiliated to SISU    
  • *corresponding author fz0528@shisu.edu.cn
Published on 20 February 2023 | https://doi.org/10.54254/2753-8818/2/20220086
TNS Vol.2
ISSN (Print): 2753-8826
ISSN (Online): 2753-8818
ISBN (Print): 978-1-915371-13-3
ISBN (Online): 978-1-915371-14-0

Abstract

A complex number is an element in a number system containing both real numbers and the imaginary unit 𝑖, satisfying 𝑖^2 = −1. Since their discovery, complex numbers have been a powerful means of mathematical calculation. Complex analysis is a part of mathematical analysis that investigates complex numbers and their analyticity, holomorphicity, etc. Many renowned mathematical giants once had their own research in complex analysis, such as Cauchy, Gauss, Euler, etc. On the grounds that it deals with functions of complex numbers, complex analysis is a helpful area in the whole mathematics field. There are plenty of applications of complex analysis in both the mathematical field and the physics field. In this paper, the history of complex numbers and complex analysis is presented. Also, some contents of complex variables are shown, including the basic properties of complex numbers, the derivative and integral of functions of complex numbers, and several critical theorems in the area of complex analysis.

Keywords:

Complex variables, Complex analysis, Complex number

Chen,Y. (2023). Elegant Theory of Complex Analysis. Theoretical and Natural Science,2,224-231.
Export citation

References

[1]. Linda Cummings, Stefan Llewellyn Smith, Paul Martin, and Bartosz Protas. (2015) Modern Applications of Complex Variables: Modeling, Theory and Computation

[2]. Edgardo V. Gerck, Ed Gerck. (2019) Overview of Complex Analysis and Applications https://www.researchgate.net/publication/331025041_Overview_of_Complex_Analysis_and_Applications

[3]. R. Wegmann. (2005) Methods for numerical conformal mapping. In Handbook of complex analysis, geometric function theory, (R. Kuehnau, ed.), vol. 2, 351–477, Elsevier.

[4]. S. Olver.(2012) A general framework for solving Riemann–Hilbert problems numerically, Numer. Math. 122, 305–340.

[5]. Bagni, G. T. (2009) Bombelli’s Algebra (1572) and a new mathematical object. For the Learning of Mathematics.

[6]. Berlinghoff, W. P. and Gouvea, F. Q. (2002) Math through the ages. Farmington, Maine: Oxton House Publishers, LLC.

[7]. Cardano, H. (1545). Artis magnae, sive de regulis algebraicis, liber unus. (n.p.): Joh. Petreius, Ch. 37, Rule II.

[8]. Hodgkin, L. (2005) A history of mathematics: From Mesopotamia to modernity. New York, New York: Oxford University Press.

[9]. Burton, D. M. (2011) The history of mathematics: An introduction. New York, New York: The McGraw-Hill Companies, Inc.

[10]. Christen Peters. (2018) The Reality of the Complex: The Discovery and Development of Imaginary Numbers.

[11]. Kline, M. (1972). Mathematical Thought from Ancient to Modern Times. Vols. 1-3. New York: Oxford University Press.

[12]. A. S. Fokas.(2008) A unified approach to boundary value problems, SIAM, Philadelphia

Cite this article

Chen,Y. (2023). Elegant Theory of Complex Analysis. Theoretical and Natural Science,2,224-231.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

Disclaimer/Publisher's Note

The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of EWA Publishing and/or the editor(s). EWA Publishing and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

About volume

Volume title: Proceedings of the International Conference on Computing Innovation and Applied Physics (CONF-CIAP 2022)

ISBN：978-1-915371-13-3(Print) / 978-1-915371-14-0(Online)
Editor：Michael Harre, Marwan Omar, Roman Bauer
Conference website: https://www.confciap.org/
Conference date: 4 August 2022
Series: Theoretical and Natural Science
Volume number: Vol.2
ISSN：2753-8818(Print) / 2753-8826(Online)

© 2024 by the author(s). Licensee EWA Publishing, Oxford, UK. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license. Authors who publish this series agree to the following terms:
1. Authors retain copyright and grant the series right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this series.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the series's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this series.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See Open access policy for details).

References

[1]. Linda Cummings, Stefan Llewellyn Smith, Paul Martin, and Bartosz Protas. (2015) Modern Applications of Complex Variables: Modeling, Theory and Computation

[2]. Edgardo V. Gerck, Ed Gerck. (2019) Overview of Complex Analysis and Applications https://www.researchgate.net/publication/331025041_Overview_of_Complex_Analysis_and_Applications

[3]. R. Wegmann. (2005) Methods for numerical conformal mapping. In Handbook of complex analysis, geometric function theory, (R. Kuehnau, ed.), vol. 2, 351–477, Elsevier.

[4]. S. Olver.(2012) A general framework for solving Riemann–Hilbert problems numerically, Numer. Math. 122, 305–340.

[5]. Bagni, G. T. (2009) Bombelli’s Algebra (1572) and a new mathematical object. For the Learning of Mathematics.

[6]. Berlinghoff, W. P. and Gouvea, F. Q. (2002) Math through the ages. Farmington, Maine: Oxton House Publishers, LLC.

[7]. Cardano, H. (1545). Artis magnae, sive de regulis algebraicis, liber unus. (n.p.): Joh. Petreius, Ch. 37, Rule II.

[8]. Hodgkin, L. (2005) A history of mathematics: From Mesopotamia to modernity. New York, New York: Oxford University Press.

[9]. Burton, D. M. (2011) The history of mathematics: An introduction. New York, New York: The McGraw-Hill Companies, Inc.

[10]. Christen Peters. (2018) The Reality of the Complex: The Discovery and Development of Imaginary Numbers.

[11]. Kline, M. (1972). Mathematical Thought from Ancient to Modern Times. Vols. 1-3. New York: Oxford University Press.

[12]. A. S. Fokas.(2008) A unified approach to boundary value problems, SIAM, Philadelphia

For authors
Guide for authors Policies for authors Aims and scope Subscription Open access policy
For editors
Policies for editors Editorial board
For reviewers
Policies for reviewers Privacy policy

Cookies are used by this site.
Copyright © 2024 EWA Publishing, its licensors, and contributors. All rights reserved, including text and data mining, AI training, and similar technologies.