Prof. Steven G. Johnson
This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems.
OCW has published multiple versions of this subject.
Johnson, Steven. 18.303 Linear Partial Differential Equations: Analysis and Numerics, Fall 2010. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-analysis-and-numerics-fall-2010 (Accessed). License: Creative Commons BY-NC-SA