14.2 Cylindrical Coordinates


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.

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 ...

Get Advanced Engineering Mathematics, 7th Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.