1. The problem statement, all variables and given/known data Solve the heat equation ut=uxx on the interval 0 < x < 1 with no-flux boundary conditions. Use the initial condition u(x,0)=cos ∏x 2. Relevant equations We eventually get u(x,t)= B0 + ƩBncos(n∏x/L)exp(-n2∏2σ2t/L2) where L=1 and σ=1 in our case. B0 is given by (1/L)∫[0,L]u(x,0)dx and Bn by (2/L)∫[0,L]u(x,0)cos(n∏x/L)dx 3. The attempt at a solution Well, I keep getting Bn = (2/L)∫[0,L]u(x,0)cos(n∏x)dx = 0 after using the trig identity cos(u)cos(v)=(1/2)(cos(u+v)+cos(u-v)). What's happening here? I've checked my steps many times.