Many of the partial differential equations that describe physical systems involve derivatives with respect to space variables (x,y,z) or with respect to space and time variables (x,y,z,t). Such equations include the diffusion equation which describes the spread (diffusion) of energy throughout a material medium with diffusion factor K $$ \frac{{\partial \psi (x,y,z,t)}}{{\partial t}} - {\rm K}{\nabla^2}\psi (x,y,z,t) = f(x,y,z,t) $$ (8.1a) the wave equation which describes the propagation of a wave traveling at speed c $$ \frac{{{\partial^{ 2}}\psi (x,y,z,t)}}{{\partial {t^2}}} - {c^2}{\nabla^2}\psi (x,y,z,t) = f(x,y,z,t) $$ (8.1b) and Poisson’s equation which describes the electrostatic potential at any point in space due to a distribution of charge, the properties of which are embodied in ρ(x,y,z), the charge density (charge per unit volume). $$ {\nabla^2}\psi (x,y,z) = \frac{{\rho (x,y,z)}}{{{\varepsilon_0}}} $$ (8.1c)