0
votes
0answers
47 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 ...
1
vote
1answer
208 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
792 views

Why are harmonic functions called harmonic functions?

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