ABSTRACT
This chapter provides the reader with a brief introduction to the theory of integration in complex analysis. It deals primarily with rectifiable paths, that is, paths of "finite length." A complete proof of the Cauchy-Goursat theorem is quite difficult and is omitted in abbreviated introduction to complex integration. The chapter examines briefly the relationship between analytic functions and power series. The principal result is the following, which states that an analytic function can be represented locally by a power series. Power series representations of functions are especially useful since they are easily subject to many analytic operations. This is essentially due to the fact that a power series converges uniformly on every compact subset of its disk of convergence. Independence of path in a region is equivalent to the line integral along closed paths being equal to 0.
