
5: Separation of variables on rectangular domains

[ "article:topic-guide", "authorname:nwalet" ]

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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.