Complex Analysis: Hands On

Material relevant from a physicist’s point of view is addressed in this chapter. The emphasis is on understanding Cauchy’s theorem, the residue theorem, etc. by following a numerical approach—performing hands-on computations. I have found that students appreciate this and understand analytic functions, and singularities better if a concrete numerical approach is adopted in addition to the standard methods. Python programmes and figures elucidate the content. Figures show the properties of poles and essential singularities; why is it called essential? Its nasty behaviour is made explicit. Topics such as analytic continuation and the stationary phase approximation are also discussed.