```
using Plots
using LaTeXStrings
= (-2π):0.01:(2π)
x plot(x, exp.(sin.(x)); xlabel=L"$x$", ylabel=L"$e^{\sin(x)}$", legend=false)
```

# Quarto

## Overview

In this tutorial, you will learn how to typeset mathematics and equations in Jupyter notebooks using LaTeX.

## Further Resourcesw

- Markdown Cheatsheet
- LaTeX Cheatsheet
- Mathpix Snpi allows you to convert images of equations to LaTeX code (there is a free tier)
- Detexify lets you draw a symbol and suggests the LaTeX code for the corresponding symbol

This tutorial was inspired and draws from Justin Bois’ tutorial.

## Inline Mathematics

To include mathematical notation within text, enclose the LaTeX within dollar signs `$`

. For example, to obtain the output

the objective function is \(4x + 7x\),

you would enter

`the objective function is $4x + 7x$`

.

You can enter subscripts and superscripts with `_`

and `^`

, respectively; to get

the function is \(f(x_i) = x_i^2\),

type

the function is

`$f(x_i) = x_i^2$`

.

If you want multiple characters to be enclosed in a subscript or superscript, enclose them in braces `{}`

:

\(e^{i \pi} - 1 = 0\) is produced by

`$e^{i \pi} - 1 = 0$`

.

To get special characters like \(\pi\) (or other Greek letters), precede their name (or sometimes a code) with a backslash: `$\pi$`

. There are a number of special characters like this, which you can find in cheatsheets like this one.

Bold characters, which you might use to denote vectors, can be rendered using `\mathbf`

:

\(\mathbf{a} \cdot \mathbf{b} = \sum_{i=1}^n a_i \times b_i\)

`$\mathbf{a} \cdot \mathbf{b} = \sum_{i=1}^n a_i \times b_i$`

Fractions can be displayed using `\frac{}{}`

, where the first bracket encloses the numerator and the second the denominator, as in

\(\frac{1}{2}\)

`$\frac{1}{2}$`

## Displaying Equations

To place equations or other mathematics on their own line(s), enclose the entire block in *two* dollar signs `$$`

. For example, the prior dot-product definition could be displayed as \[
\mathbf{a} \cdot \mathbf{b} = \sum_{i=1}^n a_i \times b_i
\] using

```
$$
\mathbf{a} \cdot \mathbf{b} = \sum_{i=1}^n a_i \times b_i
$$
```

Displaying equations on their own line(s) can improve the spacing of symbols like sums (as above) or fractions: compare the inline

\(x < \frac{1}{2}\)

to \[ x < \frac{1}{2}. \]

To display multiple related lines in a single block, there are two environments of note. The first will center all of the equations, and is obtained by enclosing the equations in `\begin{gather}`

and `\end{gather}`

. Each line should be separated with `\\`

:

\[ \begin{gather} x_1 + x_2 \leq 5 \\ y \leq \frac{1}{2}. \end{gather} \]

```
$$
\begin{gather}
x_1 + x_2 \leq 5 \\
y \leq \frac{1}{2}.
\end{gather}
$$
```

The second environment will let you align the equations as you wish instead of automatically centering them, and is used by enclosing the equations with `\begin{align}`

and `\end{align}`

, with an ampersand `&`

in front of the characters which will be used on each line to align the equations:

\[ \begin{align} x_1 + x_2 &\leq 5 \\ y &\leq \frac{1}{2}. \end{align} \]

```
$$
\begin{align}
x_1 + x_2 &\leq 5 \\
y &\leq \frac{1}{2}.
\end{align}
$$
```

## Sizing Parentheses or Brackets

By default, parentheses and brackets are sized for simple characters, but will look bad when used to surround fractions or sums, particularly when they are not used in-line: \[
x_n = (\frac{1}{2})^n.
\] To make this look better, use `\left`

and `\right`

around the left and right parentheses or brackets: \[
x_n = \left(\frac{1}{2}\right)^n
\]

```
$$
x_n = \left(\frac{1}{2}\right)^n.
$$
```

This is totally optional, but helps!

## Using LaTeX in Figures

You may want to use LaTeX in figures, for example if your \(x\)-axis should have a title like \(x\). To do this, load the `LaTeXStrings`

package and precede the relevant LaTeX-formatted string (within in-line dollar signs `$`

) with `L`

, as in: