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. Image used with permission (CC-BY-SA-3.0; Wikipedia A1).