Cauchy-Goursat theorem (variational approach)

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 curve...

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Main Authors:	Azram, Mohammad, Daoud, Jamal Ibrahim, Elfaki, Faiz Ahmed Mohamed
Format:	Conference or Workshop Item
Language:	English
Published:	2010
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/12145/ http://irep.iium.edu.my/12145/ http://irep.iium.edu.my/12145/1/IRIIE_%28Cauchy%29.pdf

id	iium-12145
recordtype	eprints
spelling	iium-121452011-12-23T23:18:22Z http://irep.iium.edu.my/12145/ Cauchy-Goursat theorem (variational approach) Azram, Mohammad Daoud, Jamal Ibrahim Elfaki, Faiz Ahmed Mohamed QA Mathematics 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 2010 Conference or Workshop Item NonPeerReviewed application/pdf en http://irep.iium.edu.my/12145/1/IRIIE_%28Cauchy%29.pdf 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 (Unpublished) http://www.iium.edu.my/irie/10/sub10/author/list_p.php
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Azram, Mohammad Daoud, Jamal Ibrahim Elfaki, Faiz Ahmed Mohamed Cauchy-Goursat theorem (variational approach)
description	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
format	Conference or Workshop Item
author	Azram, Mohammad Daoud, Jamal Ibrahim Elfaki, Faiz Ahmed Mohamed
author_facet	Azram, Mohammad Daoud, Jamal Ibrahim Elfaki, Faiz Ahmed Mohamed
author_sort	Azram, Mohammad
title	Cauchy-Goursat theorem (variational approach)
title_short	Cauchy-Goursat theorem (variational approach)
title_full	Cauchy-Goursat theorem (variational approach)
title_fullStr	Cauchy-Goursat theorem (variational approach)
title_full_unstemmed	Cauchy-Goursat theorem (variational approach)
title_sort	cauchy-goursat theorem (variational approach)
publishDate	2010
url	http://irep.iium.edu.my/12145/ http://irep.iium.edu.my/12145/ http://irep.iium.edu.my/12145/1/IRIIE_%28Cauchy%29.pdf
first_indexed	2023-09-18T20:21:23Z
last_indexed	2023-09-18T20:21:23Z
_version_	1777408130335899648

Cauchy-Goursat theorem (variational approach)

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