Complex Analysis

3 Credits.

This course presents complex analysis with a rigorous approach that also emphasizes problem solving techniques and applications. The major topics covered are holomorphic functions, contour integrals, Cauchy integral theorem and residue integration, Laurent series, argument principle, conformal mappings, harmonic functions. Several topics are explored in the context of analog and digital signal processing including: Fourier transforms for functions over the reals and the integers, Laplace and z-transforms, Jordan’s lemma and inverse transforms computed via residue integration, reflection principle for lines and circles.