U:=sum(c(n)*sin(n*Pi*x/30)*cos(2*n*Pi*t/30),n=1..infinity);
F(x):=piecewise(x<=10,x/10,x>10,(30-x)/20);
plot(F(x),x=0..30);
assume(n,integer):
cn:=2/30*Int(f(x)*sin(n*Pi*x/30),x=0..30);
subs(Int=int,f=F,%):%;
simplify(%);
cn:=%;
Un:=subs(c(n)=cn,U);
fin1:=subs(infinity=300,%):
with(plots):
animate( plot, [fin1,x=0..30], t=0..30, frames=100 );
plot3d(fin1,x=0..30, t=0..100,axes=framed,lightmodel=light1,orientation=[-15,27],transparency=0.1);