Dr. Matthew Hancock
This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods and tools for solving these PDEs, such as separation of variables, Fourier series and transforms, eigenvalue problems, and Green's functions.
OCW has published multiple versions of this subject.
Hancock, Matthew. 18.303 Linear Partial Differential Equations, Fall 2006. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-fall-2006 (Accessed). License: Creative Commons BY-NC-SA