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...
| Main Authors: | , , |
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| Format: | Proceeding Paper |
| Language: | English |
| Published: |
2010
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/12145/ http://irep.iium.edu.my/12145/1/IRIIE_%28Cauchy%29.pdf |
| _version_ | 1848777407180308480 |
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| 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 |
| building | IIUM Repository |
| collection | Online Access |
| 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 |
| first_indexed | 2025-11-14T14:45:29Z |
| format | Proceeding Paper |
| id | iium-12145 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:45:29Z |
| publishDate | 2010 |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 Proceeding Paper 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 |
| spellingShingle | QA Mathematics Azram, Mohammad Daoud, Jamal Ibrahim Elfaki, Faiz Ahmed Mohamed Cauchy-Goursat theorem (variational approach) |
| title | 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_short | Cauchy-Goursat theorem (variational approach) |
| title_sort | cauchy-goursat theorem (variational approach) |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/12145/ http://irep.iium.edu.my/12145/ http://irep.iium.edu.my/12145/1/IRIIE_%28Cauchy%29.pdf |