\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{amssymb,amsmath}

\begin{document}
\section{Simple equations on text}
\label{sec:eq-text}

Here you can see simple equations along with text $x$, $y$ and \(z\) are in math mode. This mode is known as \textbf{inline} mode and it is recommended to write short equations like: $-10 \leq x \leq 10$. Thus, if complex and long equations are required, it is recommended to use the equation environment.\par

\section{Equation environment}
\label{sec:environment}

Here we can find a way to write long equations like \eqref{eq:fraction}:
\begin{equation}
  \label{eq:fraction}
  f(t)=\sqrt{\frac{t-a}{t+a}}
\end{equation}
\noindent here $t$ is time in seconds.

More complex equations can be written using symbols and commands from math-mode. An example is the Fourier coefficients equations \eqref{eq:a0},\eqref{eq:an} and \eqref{eq:bn}:
\begin{align}
  a_0&=\frac{1}{T}\int_0^T f(t)dt  \label{eq:a0}\\
  a_n&=\frac{2}{T}\int_0^T f(t)\cdot \cos{\left(\frac{2\pi nt}{T}\right)}dt  \label{eq:an}\\
  b_n&=\frac{2}{T}\int_0^T f(t)\cdot \sin{\left(\frac{2\pi nt}{T}\right)}dt  \label{eq:bn}
\end{align}

Previous equations are used to define the Fourier series as:
\begin{equation}
  \label{eq:fourier}
  g(t)=a_0+\sum_{m=1}^{\infty}a_m \cos{\left(\frac{2\pi mt}{T}\right)}++\sum_{m=1}^{\infty}b_n \sin{\left(\frac{2\pi nt}{T}\right)}
\end{equation}

\begin{equation}
A=
\begin{pmatrix}
a & b& c\\
d & e &f
\end{pmatrix}
\end{equation}
\end{document}




