Development of Efficient Algorithms for the Computation of Complex Integrals Based on Mathematical Theorems

Yuldasheva Shakhlo Otabekovna

Development of Efficient Algorithms for the Computation of Complex Integrals Based on Mathematical Theorems

Authors

Yuldasheva Shakhlo Otabekovna Master’s Student, Navoi State University

Keywords:

complex integral, analytic function, Cauchy’s theorem, residue theorem, contour integrals, numerical integration, Python programming, algorithms, mathematical analysis, singularities

Abstract

The computation of complex integrals is widely applied in mathematical analysis, as well as in physics, engineering, and computer science. This article analyzes the main theorems used in the evaluation of complex integrals and efficient computational algorithms implemented in the Python programming language. The practical application of these theorems, along with numerical and graphical methods for evaluating integrals, is also presented.

References

Churchill, R.V., Brown, J.W. Complex Variables and Applications. 9th Edition. McGraw-Hill, 2014.

Ahlfors, L.V. Complex Analysis. McGraw-Hill, 1979.

Ablowitz, M.J., Fokas, A.S. Complex Variables: Introduction and Applications. Cambridge University Press, 2003.

Press, W.H., et al. Numerical Recipes: The Art of Scientific Computing. 3rd Edition. Cambridge University Press, 2007.

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Published

2026-04-15

How to Cite

Yuldasheva Shakhlo Otabekovna. (2026). Development of Efficient Algorithms for the Computation of Complex Integrals Based on Mathematical Theorems. INTERNATIONAL JOURNAL OF SOCIAL SCIENCE & INTERDISCIPLINARY RESEARCH ISSN: 2277-3630 Impact Factor: 8.036, 13(04), 59–63. Retrieved from https://www.gejournal.net/index.php/IJSSIR/article/view/2901