Laplace's equation Definition and 104 Threads

How to solve Laplace's equation in three dimensions? Please anyone suggest me

Hi I am not quit sure I have understand the laplace equation correctly. I hope some one can help me with it. As far as I understand if we are able to differentiate any function twice, then the function is harmonic. so we assume V(x,y) is harmonic because of the above. Does...

I was hesistant wheter to post this in the physics of math section but it's much of math problem I think. Suppose I have a function V(x,y,z) which obeys Laplace's equation over some path in space. That is to say, for some path parametrized by \vec{r}(t) = x(t)\hat{x} + y(t)\hat{y} +...

Can someone explain how to separate a multivariable differential equation into two independent differential equations? I'm having an issue solving for the potential in spherical co-ordinates in terms of r and theta.