Introduction to Partial Differential Equations
MIT OpenCourseWare offers this advanced undergraduate course on partial differential equations, focusing on linear second order uniformly elliptic and parabolic equations. Topics include the maximum principle, existence and uniqueness of solutions, energy methods, Sobolev spaces, and weak solutions. The course includes lecture notes, problem sets with solutions, and exam materials covering the theoretical foundations needed to analyze equations like the Laplace, heat, and wave equations in a rigorous setting. Materials are freely available for self-study, with no certificate offered through MIT OpenCourseWare. The course assumes prior exposure to real analysis and ordinary differential equations, and builds toward the functional-analytic tools used in modern PDE theory.