MATH 524 Complex Variables
Field of complex numbers. Elementary functions in complex variables: polynomials, rational, trigonometric and exponential functions. Limits and continuity. The complex derivative, Cauchy-Riemann equations. Analytic and harmonic functions. Complex integration, Cauchy's integral formula. Taylor and Laurent series. Residue theory. Uniform convergence. Analytic continuation. Conformal mapping. Prerequisite: 221.