Re. Cauchy Integral Formula. Please discuss how this might be useful in engineering and other scientific applications.

. Suppose C is a simple closed curve and the function f(z) is analytic on a region containing C and its interior. We assume C is oriented counterclockwise. Then for any values inside C Cauchy's Integral Formula applies. This is remarkable: it says that knowing the values of f on the boundary curve C means we know everything about f inside C!! This is probably unlike anything you have encountered with functions of real variables. Discuss how this might be useful in engineering and other scientific applications