Partial Differential Equations

PDEs are how you describe systems that vary continuously in both space and time — heat spreading through a rod, waves on a string, steady-state potentials on a disk — and this course is about turning those physical setups into equations you can actually solve. You'll classify first- and second-order equations, push the three canonical ones (heat, wave, Laplace) through characteristics, separation of variables, Fourier methods, and Green's functions, with two midterms, five quizzes, and a final keeping you honest. It sits downstream of ODEs and advanced calculus, and it's the analytical backbone for anything you'll later do in mathematical physics, numerical analysis, or applied modeling.