I saw a book on my brother's bookshelf and I decided to look through it and to me it looked pretty complicated (it's physics). On the first page I encountered the Rayleigh-Jeans formula:
$$u(v) \space dv = \dfrac{8\pi v^2 kT}{c^3} dv$$
I have a couple of (mathematical) questions regarding this:
What kind of formula is this? I understand the fraction, the $u(v)$ part resembles the regular $f(x) = ..$ you encounter in basic math often, but the $dv$ in the beginning and end confuse me. I am familair with integrals, but this seems to be something else. A differential equation?
How do you work with these kinds of formulas? At my level of physics/mathematics you just have to plug in data (like $k, T, v, c, \pi$) and you get an answer. What do you have to do here, with the $dv$ part, in order to get the 'answer'?
The Rayleigh Jeans formula is the classical (non-quantum mechanical in this context) result for the black body radiation.
The quantity $u(\nu)d\nu$ is the spectral radiance $u(\nu)$ per unit frequency $d\nu$. You can see that $u(\nu)=K\nu^2$ for some $K>0$ so
$$ \lim_{\nu\to\infty} u(\nu)=+\infty$$
These infinite radiance result is not experimentally allowed, and it's called the ultraviolet catastrophe. Its solution is due to Max Planck, via Planck's formula, one of the first (if not the first) quantum mechanical results ever.
I still propose the migration to physics.SE because it is a physics question (hence the physics tag) and people there will provide you much more insightul answers than mine.