# Advanced examples of notation

## MathJax

You can enable MathJax by setting latex: true on a page or globally in the _config.yml. Some examples:

Euler’s formula relates the complex exponential function to the trigonometric functions.

$e^{i\theta}=\cos(\theta)+i\sin(\theta)$

The Euler-Lagrange differential equation is the fundamental equation of calculus of variations.

$\frac{\mathrm{d}}{\mathrm{d}t} \left ( \frac{\partial L}{\partial \dot{q}} \right ) = \frac{\partial L}{\partial q}$

The Schrödinger equation describes how the quantum state of a quantum system changes with time.

$i\hbar\frac{\partial}{\partial t} \Psi(\mathbf{r},t) = \left [ \frac{-\hbar^2}{2\mu}\nabla^2 + V(\mathbf{r},t)\right ] \Psi(\mathbf{r},t)$

## Code

Embed code by putting {% highlight language %} {% endhighlight %} blocks around it.

## Gists (WARNING: this method is not currently javascript free)

With the jekyll-gist plugin, which is preinstalled on Github Pages, you can embed gists simply by using the gist command:

<script src="https://gist.github.com/5555251.js?file=gist.md"></script>


## Images

Upload an image to the assets folder and embed it with ![title](/assets/name.jpg)). Keep in mind that the path needs to be adjusted if Jekyll is run inside a subfolder.

The .large wrapper can be used to increase the width of an image or iframe.

Flower by Tj Holowaychuk

Swiss Alps by René Reichelt

## Embedded content

You can also embed a lot of stuff, for example from YouTube, using the embed.html include.

<div class="large">
<div style="position: relative; margin: 1.5em 0; padding-bottom: 56.25%;">
<iframe style="position: absolute;" src="https://www.youtube.com/embed/_C0A5zX-iqM"
allow="autoplay; encrypted-media"
width="100%"
height="100%"
frameborder="1"
allowfullscreen>
</iframe>
</div>

</div>