# 
# Numerical Mathematics and Computing, Fifth Edition
# Ward Cheney & David Kincaid
# Brooks/Cole Publ. Co.
# (c) 2004
#
# file:  heat
#
# Parabolic PDE: heat equation
# 
su := u = sum(c[n]*exp(-(n*Pi)^2*t)*sin(n*Pi*x), n=1..N);
Diff(u,x,x) - Diff(u,t) = eval(subs(su, diff(u,x,x) - diff(u,t)));