0
votes
0answers
49 views

where $\nabla^2V = 0$ , evaluate $\int_S V d\Omega /4\pi$

Where $\nabla^2 V = 0$ in 3 dimensional Euclidean space, it is a well-known fact that $${\int_S V(\vec{r'}) d\Omega'\over 4\pi}=V(\vec{a})$$ where $\vec{a}$ is the center of a sphere $S$ of radius ...
2
votes
1answer
228 views

Dealing with a non-linear oscillator

This is a problem for my classical mechanics course, but it seems more math, so thats why I am asking this here. So I am given the following equation: $$\ddot x+(x^2+\dot x^2-1)\dot x +x=0$$ $$\dot ...
4
votes
1answer
225 views

Solving laplace's equation for an inviscid and incompresible fluid

Background I'm working on a 2D inviscid, incompressible fluid sim using vortex methods (that is, treating vortex as discrete particles), and I'm trying to (numerically) solve the no-through boundary ...
1
vote
1answer
221 views

Discontinuity of double-layer potentials

I'm currently reading about solutions to boundary-value problems for Laplace's equation, and I'm a bit confused with regards to the discontinuity properties of double-layer potentials. So the text ...
14
votes
2answers
814 views

Why are harmonic functions called harmonic functions?

Are they related to harmonic series in any way? Or something else? Wikipedia didn't help.