# Thread: laplace equation in polar coordinates

1. ## laplace equation in polar coordinates

Hi members,

in changin from cartesian to polar coordinates they use:

x=r*cos(phi)
y=r*sin(phi)
then using the chain rule delta u/delta r=delta u/delta x.delta x/delta r+delta u/delta y.delta y/delta r
My question:
Delta x/delta r=cos(phi) (here delta means partial derivative)

Is it delta x=delta r*cos(phi).How is it calculated????

Thank you

2. ## Re: laplace equation in polar coordinates

You seem to be wanting to go from $\frac{\partial x}{\partial r}= cos(\phi)$ to $\partial x= \partial r cos(\phi)$. You can't do that! $\frac{\partial x}{\partial r}$ is defined as single quantity, not as a fraction.
(In ordinary derivatives, $y'= \frac{dy}{dx}$ is also defined as a single quantity but then we define "differentials" so that we can treat it as a fraction, $dy= y' dx$, but we cannot do that with partial derivatives.)

3. ## Re: laplace equation in polar coordinates

a quick application of google works wonders....

https://www.math.ucdavis.edu/~saito/.../polar-lap.pdf