Second order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second order linear PDE in two variables can be written in the form where A, B, C, D, E, F, and G are functions of x and y. A PDE written in this form is elliptic if with this naming convention inspired by the equation for a planar ellipse. The simplest nontrivial examples of elliptic PDE's are the Laplace equation, , and the Poisson equation, through a change of variables.