ahmedazizkhelifi

Plain:

\begin{matrix}
1 & 2 & 3\\
a & b & c
\end{matrix}

Round brackets:
\begin{pmatrix}
1 & 2 & 3\\

ahmedazizkhelifi

To insert a mathematical formula we use the dollar symbol $, as follows:

Euler's identity: $ e^{i \pi} + 1 = 0 $

To isolate and center the formulas and enter in math display mode, we use 2 dollars symbol:
$$
...
$$

ahmedazizkhelifi

Simple integral:
$$\int_{a}^b f(x)dx$$

Double integral:
$$\int_{a}^b\int_{c}^d f(x,y)\,dxdy$$	

Triple integral:
$$\iiint$$	

Quadruple integral:

ahmedazizkhelifi

Product:
$$\prod_{j=1}^k A_{\alpha_j}$$
Double product:
$$\prod^k_{i=1}\prod^l_{j=1}\,A_i A_j$$	

ahmedazizkhelifi

Sum from 0 to +inf:

$$\sum_{j=0}^{+\infty} A_{j}$$

Double sum:
$$\sum^k_{i=1}\sum^{l+1}_{j=1}\,A_i A_j$$	


Taylor expansion of $e^x$:
$$ e^x  = \sum_{k=0}^{n}\, \frac{x^k}{k!} + o(x^n) $$ 

ahmedazizkhelifi

#limit
Limit at plus infinity	: $$\lim_{x \to +\infty} f(x)$$ 
Limit at minus infinity	: $$\lim_{x \to -\infty} f(x)$$	
Limit at $\alpha$  : $$\lim_{x \to \alpha} f(x)$$

Max : $$\max_{x \in [a,b]}f(x)$$	
Min : $$\min_{x \in [\alpha,\beta]}f(x)$$	
Sup : $$\sup_{x \in \mathbb{R}}f(x)$$	
Inf : $$\inf_{x > s}f(x)$$	

ahmedazizkhelifi

First order derivative : $$f'(x)$$ 
K-th order derivative  : $$f^{(k)}(x)$$
Partial firt order deivative	: $$\frac{\partial f}{\partial x}$$
Partial k-th order derivative	: $$\frac{\partial^{k} f}{\partial x^k}$$

ahmedazizkhelifi

$$
\underbrace{\ln \left( \frac{5}{6} \right)}_{\simeq -0.1823}
< \overbrace{\exp (2)}^{\simeq 7.3890}
$$

ahmedazizkhelifi

$$
sign(x) = \left\{
    \begin{array}\\
        1 & \mbox{if } \ x \in \mathbf{N}^* \\
        0 & \mbox{if } \ x = 0 \\
        -1 & \mbox{else.}
    \end{array}
\right.
$$

ahmedazizkhelifi

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