# Problem 3.5-13, heat equation,
f1:=x->33*x;f2:=x->33*(Pi-x);
f:=x->piecewise(x<0,0,x<Pi/2,f1(x),x<Pi,f2(x),0):
u1:=x->-50*x/Pi+100;'f(x)'=eval(f(x));
assume(n,integer):
b[n]:=simplify((2/Pi)*int((f(x)-u1(x))*sin(n*x),x=0..Pi));
b:=unapply(b[n],n);
u2:=(x,t)->sum(b(n)*sin(n*x)*exp(-n^2*t),n=1..50);
u:=(x,t)->u1(x)+u2(x,t);
u(0,0,20);u(Pi,0,20);b(1),b(2),b(3);
plot3d(u(x,t),x=0..Pi,t=0..1.5,axes=boxed);
#u(x,0);