In this section we are going to consider boundary-value problems involving forms of the heat and wave equation in polar coordinates and a form of Laplace’s equation in cylindrical coordinates. There is a commonality throughout the examples and most of the exercises—the boundary-value problem possesses radial symmetry.
The two-dimensional heat and wave equations
expressed in polar coordinates are, in turn,
where u = u(r θ, t). To solve a boundary-value problem involving either of ...