Laurent Series and the Residue Theorem

Abstract

In this chapter, we investigate the behavior of a function at points where the function fails to be analytic. While such functions cannot be expanded in a Taylor series, we show that a Laurent series expansion is possible. Also, we introduce the notion of isolated and non-isolated singularities and discuss different ways of characterizing isolated singularities. The complex integration machinery that was built in Chapter 7 and developed in Chapter 8 is now ready to be utilized in order to evaluate definite integrals of real-valued functions.