A Study of Contour Integration: Methods and Their Applications

Urvashi Yadav¹ , Payal Shrivastava² , Garima Singh³

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.3 , pp.97-102, Jun-2024

Online published on Jun 30, 2024

Copyright © Urvashi Yadav, Payal Shrivastava, Garima Singh . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Complex analysis is a branch of mathematics that explores functions of complex numbers which consist of real and an imaginary part. One of its powerful techniques is contour integration , a technique for calculating integrals by following designated paths , or contour in the complex plane . This approach allows us to integrate functions that might be difficult or impossible to tackle using traditional real -variable methods .Contour integration and residues are indeed in complex analysis ,which are measure of functions behavior near its singularities ( points where the functions is not defined or is infinitely large )by using residue theorem ,a key principle in complex analytic ,we can measure complex integrals by combining the residues at these singularities , simplifying what might otherwise be a challenging problem .This technique finds applications in various fields ,including mathematics ,physics , engineering.

Key-Words / Index Term :
Contour , Contour integration, Cauchy integral Theorem, Residue theorem, Singularity

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