ABSTRACT
It turns out to be useful, especially in evaluating various types of integrals, to consider functions that have more than one “singularity.” This chapter discusses functions with multiple singularities, the concept of residue, and the residue theorem. The index or winding number of a curve about a point is also discussed along with a set of examples of the index of a curve. The chapter provides a method for calculating residues and a summary charts of laurent series and residues. The charts summarizes key ideas about Laurent coefficients and the second of which contains key ideas about residues. Applications to the calculation of definite integrals and sums and evaluation of definite integrals are analyzed with examples.
