# Mathjax v3

## Setup

You'll need to add the following lines in your layout (and discard KaTeX ones if there are any to avoid clashes):

<script>
MathJax = {
tex: {
inlineMath: [['\$$', '\$$']],
tags: 'all'
},
svg: {fontCache: 'global'}
};
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>

### Todo

• fix references

• environments with * should be ignored by Franklin and left to MathJax

• ...

## Demos

When $$a \neq 0$$, there are two solutions to $$ax^2+bx+c=0$$ and they are

$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$

## The Lorenz Equations

\begin{aligned} \dot{x} &= \sigma(y-x) \\ \dot{y} &= \rho x - y - xz \\ \dot{z} &= -\beta z + xy \end{aligned}

## Cauchy Schwarz

$\left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$

## Cross product

$\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \\ \end{vmatrix}$

## Rogers-Ramanujan

$1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for |q| < 1}.$

## Maxwell

\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &= \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &= 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &= \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} &= 0 \end{aligned}

## More inline

Finally, while display equations look good for a page of samples, the ability to mix math and text in a paragraph is also important. This expression $$\sqrt{3x-1}+(1+x)^2$$ is an example of an inline equation. As you see, MathJax equations can be used this way as well, without unduly disturbing the spacing between lines.

Here's one using the equation environment:

$$$x+1\over\sqrt{1-x^2}$$$

and one with equation* environment:

$\begin{equation*} x+1\over\sqrt{1-x^2} \end{equation*}$

This is a forward reference (9) for the following equation:

$x+1\over\sqrt{1-x^2}$

More math:

$x+1\over\sqrt{1-x^2}$