We discussed some variations of Cauchy's theorem, and their uses. We
derived Cauchy's Integral Formula, and used it to prove that if a
function f is analytic at a point then it has infinitely many
derivatives at that point. We also generalized the Integral Formula
to give analogous formulas not just for f but each derivative of f.
We derived Cauchy's Inequality and used this to derive Liouville's
theorem.

HW: sections 45,49, 52