In this section we shall investigate two dimensional equations deﬁned on rectangular domains. We shall either look at ﬁnite rectangles, when we have two space variables, or at semi-inﬁnite rectangles when one of the variables is time. We shall study all three diﬀerent types of equation.
Thumbnail: A visualization of a solution to the two-dimensional heat equation with temperature represented by the third dimension. Imaged used wth permission (Public Domain; Oleg Alexandrov). The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.