Introduction to Partial Differential Equations
MIT OpenCourseWare offers this introduction to the three canonical types of partial differential equations: diffusion, elliptic, and hyperbolic. The course covers the mathematical tools used to analyze each type, including separation of variables, Fourier series, Green's functions, and characteristics, alongside real-world examples such as heat flow and wave propagation. Materials include lecture notes, problem sets, and exams drawn from the MIT mathematics curriculum, giving a full semester's worth of structured coursework rather than a single lecture. The course assumes prior exposure to ordinary differential equations and multivariable calculus and builds toward applying these equation types to physical and engineering problems. As with other MIT OCW offerings, all materials are free to use and there is no certificate attached, since OCW publishes course content rather than running a graded, credentialed platform.