In this course we shall consider so-called linear Partial Differential Equations (P.D.E.’s). This chapter is intended to give a short definition of such equations, and a few of their properties. However, before introducing a new set of definitions, let me remind you of the so-called ordinary differential equations ( O.D.E.’s) you have encountered in many physical problems.
Thumbnail: Visualization of heat transfer in a pump casing, created by solving the heat equation. Heat is being generated internally in the casing and being cooled at the boundary, providing asteady state temperature distribution. (CC-BY-SA-3.0; Wikipedia A1).