
temperature problem
slab of material $\displaystyle 1 \leq x \leq 1$ is initally at a temperature given by
$\displaystyle T = T_{0}(1 + x) \ for \ 1 \leq x \leq 0$
$\displaystyle = T_{0}(1  x) \ for \ 0 < x \leq 1$,
and the surfaces $\displaystyle x = \pm 1$ are maintained at zero temperature.
Show that the temperature is
$\displaystyle T=\frac{8T_{0}}{\pi^{2}} \sum^{\infty}_{n=0} \frac{1}{(2n+1)^2} cos \frac{(2n+1) \pi x}{2} exp[k(n+ \frac{1}{2})^2 \pi^2 t]$

Re: temperature problem
Have you tried separation of variables?
Note: For those that are reading this post, I'm sure the OP meant to include the governing PDE
$\displaystyle T_t = kT_{xx}$

Re: temperature problem