(0:00) Exam 3 date change. (0:32) Review expansion and visualization of f(z) = z/(z^2 + z - 12) as a Laurent series in a disk centered at z = 0 and an annulus centered at z = 0. (11:20) Find the Laurent series centered at z = -4 (converging on a punctured disk of radius 7 centered at -4). (27:13) The pole at z = -4 has order 1. (27:59) New example with a pole of order 2 at z = -4.
Based on "Fundamentals of Complex Analysis, with Applications to Engineering and Science", by E.B. Saff and A.D. Snider (3rd Edition). "Visual Complex Analysis", by Tristan Needham, is also referred to a lot. Mathematica is often used, especially to visualize complex analytic (conformal) mappings.