Cauchy-Goursat theorem (variational approach)

Azram, Mohammad and Daoud, Jamal Ibrahim and Elfaki, Faiz Ahmed Mohamed (2010) Cauchy-Goursat theorem (variational approach). In: IIUM Research, Invention and Innovation Exhibition 2010 , 26-27th Jan, 2010, CAC, IIUM. (Unpublished)

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Abstract

In this article, we have presented a simple and un-conventional proof of a basic but important Cauchy-Goursat theorem of complex integral calculus. The pivotal idea is to sub-divide the region bounded by the simple closed curve by infinitely large number of different simple omotopically closed curves between two fixed points on the boundary. Beauty of the method is that one can easily see the significant roll of singularities and analyticity requirements. We suspect that our approach can be utilized to derive simpler proof for Green’s, Stoke’s theorems and the generalization to Gauss’s divergence theorem

Item Type:	Conference or Workshop Item (Poster)
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering > Department of Science
Depositing User:	Prof Mohammad Azram
Date Deposited:	24 Dec 2011 07:18
Last Modified:	24 Dec 2011 07:18
URI:	http://irep.iium.edu.my/id/eprint/12145

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