Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 2, 20 February 2023
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Complex Analysis and its Several Applications
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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
References
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.
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 International Conference on Computing Innovation and Applied Physics (CONF-CIAP 2022)
- ISBN (Print)
- 978-1-915371-13-3
- ISBN (Online)
- 978-1-915371-14-0
- Published Date
- 20 February 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/2/20220087
- Copyright
- © 2023 The Author(s)
- 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