sea-budgets


Mathematics

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.