Linear Partial Differential Equations: Analysis and Numerics
MIT OpenCourseWare offers the analytical and computational foundations of linear partial differential equations, covering heat and diffusion equations, wave equations, and the Poisson equation. The analytical side treats PDEs through the lens of linear algebra, drawing out the analogy with finite-dimensional matrix problems. The numerical side works through finite-difference and finite-element methods that turn PDEs into matrix problems a computer can solve, with homework assignments built around the free, open-source Julia language. Materials include lecture notes, assignments, and the course's problem sets as published on MIT OCW, aimed at science and engineering students who already have some linear algebra background. There is no instructor interaction or certificate, since OCW is a self-study archive of MIT's actual course materials, but the full syllabus and assignments are available to work through at your own pace.