Complex Variables with Applications
MIT OpenCourseWare's course on complex analysis and its engineering applications. Topics include complex algebra and functions, analyticity, contour integration and Cauchy's theorem, singularities, Taylor and Laurent series, residues and their use in evaluating integrals, multivalued functions, two dimensional potential theory, Fourier analysis and Laplace transforms. Materials include lecture notes, assignments, and exams from MIT's mathematics department, following the structure of an undergraduate applied math course rather than a pure theory treatment. The course builds from foundational definitions of complex functions toward tools engineers and physicists use to solve boundary value problems and evaluate real integrals through residue calculus. No certificate is offered since this is open courseware, but the full set of course materials is freely downloadable for self-study.