Chapter 18 · Partial Differential Equations
18.10
PDEs in Polar and Cylindrical Coordinates
On disks and cylinders, use polar coordinates. Separation gives Fourier series in the angle and Cauchy–Euler or Bessel equations in the radius, which is why drums don't sound like strings.
About 16 minutes
You'll learn to
- →Write the Laplacian in polar coordinates
- →Solve Laplace's equation on a disk
- →Explain why bounded solutions drop some terms
- →Describe the modes of a circular drum using Bessel functions