Numerical Methods for Partial Differential Equations
This MIT OpenCourseWare graduate course covers numerical methods for solving partial differential equations that arise in physical applications. Lectures and notes work through finite difference and finite element methods, stability and convergence analysis, and the mathematical theory underlying each technique, alongside methods for elliptic, parabolic, and hyperbolic equations. Materials include problem sets and lecture notes drawn from the course as taught at MIT, focusing on the ideas that connect different numerical schemes rather than treating each as an isolated recipe. The course assumes prior exposure to differential equations and linear algebra and is aimed at students who want to understand why a numerical method works, not just how to code it. As with other MIT OCW offerings, all materials are free to access and there is no certificate.