Section 4.2 Example1
with(plots):
u:=(r,y,t)->-2*sum(sin(100.*BesselJZeros(0,n)*t)*BesselJ(0,BesselJZeros(0,n)*r)/BesselJ(1,BesselJZeros(0,1.*n))/evalf(BesselJZeros(0,n))^2,n=1..11LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=);
u(r,y,t);
addcoords(z_cylindrical,[r,theta,z],[r*cos(theta),r*sin(theta),z]);
animate(implicitplot3d,[z=u(r,y,t),r=0..1,y=0..2*Pi,z=-1..1,coords=z_cylindrical],t=0..10,
frames=50,color=red);
plot([BesselJ(0,x),BesselJ(1,x),BesselJ(2,x),BesselJ(3,x)],x=1..10);
BesselJ(1,BesselJZeros(0,2));
BesselJZeros(0,2);