I just solved the heat equation but my solution is not the same as the solution given.
Concretely, I am solving
$$ u_t (x,t) = D u_{xx}(x,t) $$ for $x \in (0,1) , t > 0$
with boundary conditions
$$ u_x (0,t) = u_x(1,t) = 0$$
This are equations pertaining to a wire of length $1$ with heat capacity $D>0$.
The problem I have is that I assumed that the period was $1$ because the length of the wire is given as $1$ but the solution I have to this exercise assumes $P=2$ and then for example integrates the Fourier coefficients from $-1$ to $1$.
I don't understand what's going on here.
Why is the period $2$ and not $1$?