MAT 461 Complex Analysis

This course explores the calculus of complex-valued functions of a complex variable. Topics covered include basic properties of complex numbers and algebraic operations on them; complex-valued versions of exponential, logarithmic, and trigonometric functions; limits and continuity of complex functions; differentiation and the Cauchy-Riemann conditions; evaluating contour integrals using the Cauchy-Goursat Theorem and Cauchy Integral Formula; Taylor and Laurent series representations of complex functions; and evaluating residues of isolated singular points.  Prerequisite(s): MAT 290   3 hour(s).