function u = P16forward(N)
% P16FORWARD   compute and plot parts of forward heat equation problem
% requires circu.m
h = 1/N;   x = (0:h:1-h)';
%  H  is discretization of   -d^2/dx^2 + 3 I   because heat eqn is   0 = u'' - 3 u + f
H = - (1/(h*h)) * circu([-2 1 zeros(1,N-3) 1]') + 3 * eye(N);
c = [5 1 4];
f = c(1) * exp(-20*abs(x-.4)) + c(2) * exp(-40*abs(x-.5)) + c(3) * exp(-20*abs(x-.75));
u = H \ f;
plot(x,f,'o-',x,10*u,'*-')  
legend('heat source f(x)','temperature soln, scaled for clarity: 10 * u(x)')