Prof. Jared Speck
OCW has published multiple versions of this subject.
Speck, Jared . 18.152 Introduction to Partial Differential Equations, Fall 2011. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/courses/mathematics/18-152-introduction-to-partial-differential-equations-fall-2011 (Accessed). License: Creative Commons BY-NC-SA