(* Beispiel p.324: 1-Treppe *)

c=1;
A[p_]=Sin[p]/(Pi p);
B[p_]=(1-Cos[p])/(Pi p);

u[t_]:=ListPlot[Table[{x,NIntegrate[(A[p]Cos[p x]+B[p] Sin[p x])Exp[-c^2p^2 t],{p,0.001,500}]},{x,-3,4,0.11}],PlotRange->{-0.2,1.2}];

Manipulate[u[t],{t,0,2,0.05}]

(* Beispiel mit 1-2-Treppe *)

A2[p_]=3Sin[p]/(Pi p);
B2[p_]=(1-Cos[p])/(Pi p);

u2[t_]:=ListPlot[Table[{x,NIntegrate[(A2[p]Cos[p x]+B2[p] Sin[p x])Exp[-c^2p^2 t],{p,0.001,500}]},{x,-3,4,0.11}],PlotRange->{-0.2,2.2}];

Manipulate[u2[t],{t,0,2,0.05}]