1: Introduction to Partial Differential Equations — Read

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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.

1.1: Ordinary Diﬀerential Equations
ODE’s are equations involving an unknown function and its derivatives, where the function depends on a single variable, e.g., the equation for a particle moving at constant velocity.
1.2: PDE’s

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).

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