Instructor question A simple model for heating in a plate is to consider the temperature only on a finite lattice of points. We assume that each of these points is the average of its neighbors. If we have a rectangular grid then we take the average of the neighbors on either side and above and below. See sketch 1 below. Consider the case where there are 9 points in a 3x3 grid. If the outside edges are fixed, what system of equations do we need to solve in order to find all the interior temperatures? See sketch 2 below.