This post is going to run some simple math tests.
We begin with the binomial theorem:
$$ (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^{k} $$
where the binomial expression is defined as:
$$ \binom{n}{k} = \dfrac{n!}{(n-k)! k!} $$
Next, we have a simple PDE:
$$ \dfrac{\partial \phi}{\partial t} + \nabla \cdot \mathbf{u} \phi = - \nabla \cdot J_{\phi} + S_{\phi} $$
We will see how this goes.