%ULYSSIS 2024-2025
%This work is licensed under Creative Commons BY-SA-NC 4.0

\documentclass[12pt,a4paper]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}


\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

\author{Simon Maenaut} % Presented by Natasha Philippe 
\title{ULYSSIS LaTeX Workshop - Mathematics}
\date{October 2024}

\usepackage{hyperref}
\usepackage[
    type={CC},
    modifier={by-nc-sa},
    version={4.0},
]{doclicense}

\begin{document}
\maketitle
\doclicenseThis

An inline mathematical environment inside a piece of text can be defined between dollar signs. For example, this is Pythagoras' formula: $a^2+b^2=c^2$. Superscripts can be written with the hat symbol and subscripts can be realised with an underscore: $C_1+C_2=C_3$. Multiple characters in a sub/superscript can realised with curly braces: $T_{t_0}^{n_0}$\\

Greek letters: $\alpha$, $\beta$, $\gamma$... as well as $\Pi$, $\Sigma$, ...\\

Mathematical environments can also be placed in between paragraphs as centred expressions:\\
\[  6 \leq 9  \]
\[ -1 \geq -2 \]

If you want to refer to specific expressions, you can use the ``equation'' environment:

\begin{equation}
a - 7 = 3
\label{eq:a}
\end{equation}

Equation \ref{eq:a} implies that $a=10$.\\

Many different special symbols and operations are supported.
$$ + - = ! / ( ) [ ] < > | ' : $$

\newpage

Logical symbols:
\[ \forall x \in \mathbb{R} : \exists \epsilon \geq 0 \]

Trigonometric functions:
\[ \cos (2\theta) = \cos^2 \theta - \sin^2 \theta \]

Fractions:
\[ \frac{3}{4} \]
\[ \left(\frac{3}{4}\right)^2 \]

Limits:
\[ \lim_{x \to \infty} \exp(-x) = 0 \]

Square roots:
\[ \sqrt{2} \]

Sums and series:
\[ \sum_{k=1}^{n} k = \frac{n(n+1)}{2} \]

Integrals:
\[ \int _{a}^{b} f(x) \, dx \]

% Looking up several difference.

% Wiki's like: http://en.wikibooks.org/wiki/LaTeX/Mathematics
% Drawing > recognise: http://detexify.kirelabs.org/classify.html

We can type an equation directly in \LaTeX.
\[ \int_{-\infty }^{\infty }e^{-x^{2}}\,dx={\sqrt {\pi }} \]

We can also copy equations from Wikipedia by selecting the expression (click and drag over it with the cursor), copy it (ctrl+c) and paste (ctrl+v).

\begin{equation*}
{\displaystyle \left.\operatorname {div} \mathbf {F} \right|_{p}=\lim _{V\rightarrow \{p\}}\iint _{S(V)}{\frac {\mathbf {F} \cdot \mathbf {\hat {n}} }{|V|}}\,dS}
\end{equation*}

\end{document}

ULYSSIS 2025 Natasha Philippe activiteiten@ulyssis.org