On the wikipedia page for the Cauchy-Goursat theorem it says:
If one assumes that the partial derivatives of a holomorphic function are continuous, the Cauchy integral theorem can be proved as a direct consequence of Green's theorem and the fact that the real and imaginary parts of $f=u+iv$ must satisfy the Cauchy–Riemann equations in the region bounded by $\gamma$, and moreover in the open neighborhood U of this region. Cauchy provided this proof, but it was later proved by Goursat without requiring techniques from vector calculus, or the continuity of partial derivatives.
But there is no reference given, and I couldn't find it on the internet. Where could I find Goursat's proof? Is it very complicated?
Best Answer
Stein et al. - Complex Analysis
http://press.princeton.edu/chapters/s02_7563.pdf