In this chapter we begin to look at the “Big Three PDEs”—the heat equation (or diffusion equation), the wave equation and Laplace’s equation (or the potential equation)—each in two independent variables. Each is a secondorder, linear, homogeneous PDE with constant coefficients. The general such equation is

auxx + buxy + cuyy + dux + fuy + gu = 0, (2.1)

where, again, u = u(x, y) and, of course, a, b, c, d, f and g are constants. We study equation (2.1) in detail in Section 5.4. In particular, there we’ll

classify these equations as in the following definition and give reasons for such a classification.