Movies for 
  Introduction to Partial Differential Equations
      by Peter J. Olver

Movies can be viewed at    
         http : // www.math.umn.edu/~olver/mov.html

3D Wave Equation Movies:   Figures 12.10, 12.11, 12.12.

General plotting routine

pl[t_] := Print[Plot[u[t,x],{x,(Subscript[x, 0]),(Subscript[x, 1])},PlotRange ->{(Subscript[y, 0]),(Subscript[y, 1])},AspectRatio -> asp,Ticks -> None,PlotStyle -> {Thickness[th],Hue[hu]}]]

th = .004; hu = .6;

Figure 12.10. Wave equation solution u(t,r) due to an initial velocity of the unit ball

Determine fundamental solution

u//ClearAll;

u[t_,r_] := Which[t<1-r ,t,(t>Abs[1-r] )&& (t<r+1),((1-(((r-t))^2))/(4 r )),True,0]

Set plotting parameters and routine

(Subscript[x, 0]) =0;(Subscript[x, 1])=3;(Subscript[y, 0]) = -.1; (Subscript[y, 1]) =1.1; asp = Automatic;

Set time range

ti= 0;tf =2.1; δt = .01;ts = Range[ti,tf,δt];

Plot movie  — evaluate Notebook to generate output

pl /@ ts;

Figure 12.11. Wave equation solution u(t,r) due to an initial displacement of the unit ball

Determine solution

u//ClearAll;

u[t_,r_] := Which[t<1-r ,1,(t>Abs[1-r] )&& (t<r+1),((r-t)/(2 r )),True,0]

Set plotting parameters and routine

(Subscript[x, 0]) =0;(Subscript[x, 1])=4;(Subscript[y, 0]) = -2.1; (Subscript[y, 1]) =2.1; asp = Automatic;

Set time range

ti= 0;tf =2.6; δt = .01;ts = Range[ti,tf,δt];

Plot movie  — evaluate Notebook to generate output

Figure 12.12. Solution to the two-dimensional wave equation for a concentrated impulse

Determine solution

u//ClearAll;

u[t_,r_] := Which[r<t ,(1/(2π(Sqrt[(t^2) - (r^2)]))),True,0]

Set plotting parameters and routine

(Subscript[x, 0]) =0;(Subscript[x, 1])=3;(Subscript[y, 0]) = -.1; (Subscript[y, 1]) =2.1; asp = Automatic;

Set time range

ti = δt = .01; tf = 2.6;ts = Range[ti,tf,δt];

Plot movie  — evaluate Notebook to generate output

pl/@ ts;