Mathematics - Complex Analysis - Cauchy's theorem and residues - Contour Integration and Residues

12 steps: (1) CONTOUR INTEGRAL: ∮_C f(z)dz = integral of f along a curve C in ℂ. (2) CAUCHY'S THEOREM: if f is analytic inside and on C, then ∮_C f(z)dz = 0! (3) Stunning consequence: the integral depends ONLY on what's inside the contour. (4) CAUCHY'S INTEGRAL FORMULA: f(a) = (1/2πi)∮_C f(z)/(z-a)d