Cauchy-Goursat theorem (variational approach) - Azram, Mohammad; Daoud, Jamal Ibrahim; Elfaki, Faiz Ahmed Mohamed (2010)
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