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\newcommand{\RR}{\mathbb{R}}
\newcommand{\CC}{\mathbb{C}}
\title{Prova latex}
\author{}
\begin{document}
 \maketitle
 \section{I numeri reali $\RR$ }
 In questa sezione introduciamo l'insieme $A$ definito come
 $$\{ x\in \RR: \vert x\vert \leq 1\}$$
 $\RR$ $\CC$
 $$
A= \left (\begin{matrix}
a_{11} & a_{12}& a_{13}& \dots& a_{1i}&\dots & a_{1n} \\
a_{21}& a_{22}& a_{23}& \dots& a_{2i}&\dots & a_{1n}\\
...& ...& .....& \dots& ....&\dots &......\\
a_{i1}& a_{i2}& a_{i3}& \dots& a_{ii}&\dots & a_{in}\\
...& ...& .....& \dots& ....&\dots &......\\
a_{n1}& a_{n2}& a_{n3}& \dots & a_{ni}&\dots & a_{nn}
\end{matrix}\right)
$$
$$\sum_{i=1}^n a_n$$
$$\frac 1{2c}$$
$$\prod_{i=1}^n a_n$$
$$Df(x)= (f_{x_1}( x),f_{x_2}( x),\dots, f_{x_n}( x))$$
$$Df= \bigg(\frac  {\partial f} { \partial x_1},\frac {\partial f}{ \partial x_2},\dots,\frac  {\partial f} { \partial x_n}\bigg)$$
 $$\int_a^b f(x) dx$$
 $$\Delta f(x)=0$$
  \subsection{ Seconda}
  $$\frac {\partial^2 }  {\partial x^2} f $$
  \begin{equation}\label{wave}
    u_{tt}=\Delta u
     \end{equation}
     \subsubsection{terza}
        $$x_n\to x \iff\,\,\forall \epsilon>0\,\, \exists N : \vert x_n-x\vert <\epsilon\,\, \forall n>N $$
La formula \eqref{wave}....
 \end{document}