2 Contour integration

In the remaining of the course, we will spend all our time studying integration of

complex functions. At first, you might think this is just an obvious generalization

of integration of real functions. This is not true. Starting from Cauchy’s theorem,

beautiful and amazing properties of complex integration comes one after another.

Using these, we can prove many interesting properties of holomorphic functions

as well as do lots of integrals we previously were not able to do.