Hi, another diff. eq problem:

In my notes, it suggests to use a similarity transformation to solve the heat equation in one dimension $\displaystyle \frac{\partial u}{\partial t} = D\frac{\partial^2 u}{\partial x^2}$.

So if $\displaystyle \xi = \frac{x}{2\sqrt{Dt}}$ and $\displaystyle u(x,t) = v(\xi)$, then:

$\displaystyle \frac{\partial u}{\partial t} = \frac{v}{\xi}\frac{\partial \xi}{\partial t} =. . .$

...What?

any help in explaining this would be much appreciated.