Week 7-8 : Calculus of Residues theorems
Cauchy's integral formula:
It is modefird form of Cauchy's integral theorem. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk, and it provides integral formulas for all derivatives of a holomorphic function. Cauchy's formula shows that, in complex analysis, "differentiation is equivalent to integration": complex differentiation, like integration, behaves well under uniform limits.
