Solve the Dirichlet problem
$$\left\{ \begin{array}{l l} u_{t} - 2u - u_{xx} =0 & \quad \mbox{$0<x<1,t>0$}, \\ \quad u(x,0) = \begin{cases} x & \textrm{ if $0\le x\le 1/2$} \\ 1-x & \textrm{ if $1/2\le x\le 1$} \end{cases}, \\ \quad u(0,t) = u(1,t) = 0. \end{array} \right. $$
expressing the solution in terms of a Fourier sine series.
Also if anyone could help me solve this problem I would greatly appreciate it as well. Thanks!