ABSTRACT
This chapter discusses the basic result known as the residue theorem and then a number of examples of its application. Analytic function theory provides some powerful methods for calculating definite integrals. A slightly different application of the residue theorem leads to a method for calculating certain infinite sums. Occasionally an integral can be transformed to a more convenient form by using Cauchy's theorem to move the contour. The poles can be of finite or finite or infinite order. Branch points are not allowed in the region under consideration since the function must be single valued in this region. There are several ways to evaluate the residues. The minus sign in arises because the contour is traversed in the clockwise rather than the counterclockwise direction.
