Originally Posted by

**Spec** Transform Laplace's equation to polar coordinates.

$\displaystyle \frac{\partial^2{u}}{\partial{x^2}} + \frac{\partial^2{u}}{\partial{y^2}} = 0$

$\displaystyle u(x, y) = u(rcos\varphi + rsin\varphi)$

$\displaystyle \left\{\begin{array}{cc}\frac{\partial{u}}{\partia l{r}} = cos\varphi \frac{\partial{u}}{\partial{x}} + sin\varphi \frac{\partial{u}}{\partial{y}}\\ \frac{\partial{u}}{\partial{\varphi}} = rcos\varphi \frac{\partial{u}}{\partial{y}} - rsin\varphi \frac{\partial{u}}{\partial{x}}\end{array}\right. $

Now what?