## Heat Conduction

Find a formula for the temperature $u(x,t)$ in the form of a series with general formula for the coefficients of the series.

$\alpha^2 \frac{ \partial^2 u}{ \partial x^2} = \frac{\partial u}{\partial t}$ and $0 ; $t>0$

$u(0,t) = 0$ and $\frac{\partial u}{\partial x}(L,t) = 0$ and $t>0$

$u(x,0) = f(x)$

$f(x)$ is assumed to be piecewise continuous and periodic of period 2L