Mathematics 174 -- Applied Mathematics 2

March 14, 2000

The Green's Function for the operator on , for the boundary conditions

and

> PSGreen:=(N,x,x0) -> -(2/Pi)*add(sin(n*x)*sin(n*x0)/n^2,n=1..N);

Warning, `n` in call to `add` is not local

> plot3d(PSGreen(200,x,x0),x=0..Pi,x0=0..Pi,axes=BOXED,grid=[100,100]);

The slice of the above graph in the plane . Note the point ( ) where

the function fails to be differentiable:

> plot(PSGreen(200,x,Pi-x),x=0..Pi,scaling=CONSTRAINED);

There is a similar point for each slice by a plane parallel to this one, which accounts for the

"ridge" that is visible in the surface plot.