
Complex Analysis and its Several Applications
- 1 Shenzhen College of International Education, No.3 Antuoshan 6th street, Xiangmihu District, Futian, Shenzhen
- 2 Beijing 21st century international school, courtyard 46, No. 46, Enji West Street, Haidian District, Beijing
* Author to whom correspondence should be addressed.
Abstract
Complex analysis is important for science because it extends analytical methods from real variables to complex variables and complex numbers. Also, complex number has two independent components, one variable will not change when the other is changing, that are particularly useful when two variables must be dealt with simultaneously. In this essay, we are going to talk about the history chronologically such as who first introduced the idea of complex number, who first discovered the rule of complex number, and why complex analysis is important. Also, the essay includes some basics about the complex variable and complex analysis. For example, the definition of complex number, Cauchy-Riemann Equations, and Cauchy Goursat theorem can help us to get further known of the complex analysis and solve some basic analytic problems.
Keywords
Complex analysis, Complex number
[1]. L. V. Ahlfors. Conformal Invariants. McGraw-Hill, New York, 1973.
[2]. L. V. Ahlfors. Complex Analysis. McGraw-Hill, New York, third edition, 1979.
[3]. G. B. Airy. On the intensity of light in the neighbourhood of a caustic. Transactions of the Cambridge Philosophical Society, 6:379– 402, 1838.
[4]. J. Bak and D. J. Newman. Complex Analysis. Springer-Verlag, New York, second edition, 1997.
[5]. B. Blank, An Imaginary Tale Book Review, in Notices of the AMS Volume 46, Number 10, November 1999, pp. 1233-1236.
[6]. H. Dym and H. P. McKean: Fourier Series and Integrals, Academic Press, 1972.
[7]. T. W. Körner: Fourier Analysis, Cambridge University Press, 1988.
[8]. J. S. Walker: Fourier Analysis, Oxford University Press, 1988.
[9]. E.T. Whittaker and G.N. Watson. A Course in Modern Analysis. Cambridge University Press, 1927.
[10]. E.M. Stein and R. Shakarchi, Complex Analysis, Princeton University Press, 2003.
Cite this article
Zhang,J.;Zhang,M. (2023). Complex Analysis and its Several Applications. Theoretical and Natural Science,2,232-237.
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)
© 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).