Complex Variables with Applications
Complex analysis builds around functions that have a complex derivative, and this MIT OpenCourseWare course covers the consequences of that single condition. Topics include analytic and harmonic functions, contour integration and the residue method for evaluating difficult real integrals, two-dimensional fluid flow modeled with complex potentials, and the use of Laplace and Fourier transforms in engineering and physics problems. Materials include lecture notes, problem sets with solutions, and exams drawn from MIT's Mathematics curriculum. The course assumes a background in calculus and treats complex variables as a practical toolkit rather than a purely abstract subject, showing how the theory simplifies computations that are hard or intractable using real analysis alone. As with other MIT OCW offerings, all materials are free to use and there is no certificate.