On 03/09/2013 04:45 PM, Brian Martin wrote:
> Is there a simple way to plot the graphics for 4.3-3? 
Dear Brian,

The solution u(r,theta,t) can be found on this blackboard image:

http://www.math.utah.edu/~gustafso/s2013/3150/blackboardPhotos/blackboard-8mar2013/blackboard-4.3-3-nonsymmDrumhead-solution-800x600.jpg

The plotting effort is a filmstrip of three frames, at times t=0,1,3.

Each frame is a 3D graphic, plane r-theta against vertical axis u for fixed t (t=0,1,3).

To make one frame, say for t=1, truncate the series answer for u(r,theta,t=1) to four terms (N=4). Then you will need values for alpha_{0 n} for n=1,2,3,4. Get them from a table of zeros of the Bessel function of order zero, J_0(x). Similarly, you will need values for alpha_{1 n} for n=1,2,3,4, zeros of the Bessel function of order one, J_1(x).

If you can use maple, either your private copy, or remote connection to the UofU, then this example shows how to get the values of the zeros of J_1 (similar for J_0):

N:=4: alpha1:=evalf([BesselJZeros(1,1..N)]);

Interdependence of Fourier coefficients on J_0, J_1 and the zeros of these Bessel functions is complex. See the other blackboard images for 4.3-3 from 8 Mar 2013,
posted in the course web site for lecture links 8 March.

Best. Dr. G.