This chapter takes a look at some important properties of basic partial differential equations (PDEs) that govern physical processes such as heat conduction, fluid flow, solid mechanics, etcetera.
The question is not to solve the equations; that can be done numerically, and for much more general problems than for which an analytical solution exists. Instead, the purpose is to recognize it if a numerical computation produces a solution that is grossly incorrect. To do so, some knowledge about the qualitative behavior of solutions of PDEs is useful.
Another objective is to examine what data (initial and boundary conditions) are required to solve a PDE. This is needed to determine whether a failing computation attempts to compute a solution without having sufficient data. Clearly, without the required data, no correct computation is possible.
A third objective is to introduce the names of the most basic partial differential equations, such as the ``heat equation'', the ``wave equation'', and the ``Laplace equation'', and how they can be classified.