I found a cool html equation editor online based on a superset of the LaTeX markup language that allows me to code some important equations you should know about. You can find the site Here . You can also click on any equation to see its LaTeX source.

### Fourier Expansion of a periodic function in three dimensions

$n(\vec{r}) = \sum_{\mathbf{G}}n_{\mathbf{G}}exp(i{\mathbf{G}}\cdot {\mathbf{r}}) \qquad \qquad (1)$

This equation is quite important, and I’m using it right now in my Solid State physics class to help define crystal structure. The constants $n_{\mathbf{G}}$ may be found by the following correlary function:

$n_{\mathbf{G}} = V^{-1}_C \int_{cell}dVn({\mathbf{r}})exp(-i{\mathbf{G}}\cdot {\mathbf{r}}) \qquad \qquad(2)$

### Maxwell’s equations of electricity and magnetism

These bad boys will solve anything to to with E and M; including optics.

Name Equation
Gauss’ Law $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$
Gauss’ Law for Magnetism $\nabla \cdot \mathbf{B}=0$
Maxwell – Faraday Equation $\nabla \times \mathbf{E}=-\frac{\partial \mathbf{B}}{\partial t}$
Ampere’s Law $\nabla \times \mathbf{B}= \mu _0\mathbf{J}+\mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}$

…more later