1. ## Conduction of Heat

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

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

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

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

How can I resolve ?

2. If you look around, you can find this worked out in a DE book or on line.

3. Originally Posted by Apprentice123
Find a general formula for the temperature $u(x,t)$ in the form of a series with general formula for the coefficients of the series.

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

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

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

How can I resolve ?
Here's another guy from Brazil that posted exactly the same question 2 minutes after you did. He received a (great!) reply.
See Conduction of Heat.

4. Zill's Differential Equations with Boundary Problems has this problem outlined. Except, they use k instead of ${\alpha}^{2}$.

That is all I meant. This is a common DE problem and can be found.

5. Originally Posted by galactus
Zill's Differential Equations with Boundary Problems has this problem outlined. Except, they use k instead of ${\alpha}^{2}$.

That is all I meant. This is a common DE problem and can be found.
Maybe TPH did it also... "better than the book".
See http://www.mathhelpforum.com/math-he...-equation.html. This thread is worth to be a sticky one I believe.