Math 314 Lecture 29: Monday, November 15th 1999.
Today we looked at solving the potential equation in a disk. This involved
separating variables using polar coordinates, with a boundary condition at
the edge of the disk and continuity conditions with respect to angles. (The
solutions must be continuous when going through a full cycle of theta.)
The angle problem turned out to be a degenerate eigenvalue problem with two
different eigenfunctions (cosine and sine) corresponding to the same eigenvalue.
The radial problem turned out to be a Cauchy-Euler equation, and the boundary
condition led to a Fourier series.
A simple example was then summed and plotted in Maple. This involved specifying the function
parametrically in cylindrical coordinates. Both a 3-D Plot and a
Contour Plot were done.
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Revised 23 November 1999 by
John Hebron.