ABSTRACT
If f is a holomorphic function on an open disc W in the complex plane, and if γ : [a, b]→W is a C1 curve in W with γ(a) = γ(b), then∮
f(z) dz = 0 . (3.1)
This is the Cauchy integral theorem. It is central and fundamental to the theory of complex functions. All of the principal results about holomorphic functions stem from this simple integral formula. We shall spend a good deal of our time in this text studying the Cauchy theorem and its consequences.
