Prof. Tobias Colding
OCW has published multiple versions of this subject.
Colding, Tobias. 18.152 Introduction to Partial Differential Equations, Fall 2005. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/courses/mathematics/18-152-introduction-to-partial-differential-equations-fall-2005 (Accessed). License: Creative Commons BY-NC-SA