Markdown

Headings

# Heading 1
## Heading 2
### Heading 3
#### Heading 4
##### Heading 5
###### Heading 6

Heading 1

Heading 2

Heading 3

Heading 4

Heading 5
Heading 6

Paragraph

This is a paragraph of text.   

This is another paragraph of text.

This is a paragraph of text.

This is another paragraph of text.

Line breaks

This is a text.     
This is another text.

This is a text.
This is another text.

Mark emphasis

Emphasis, aka italics, with *asterisks* or _underscores_.

Strong emphasis, aka bold, with **asterisks** or __underscores__.

Combined emphasis with **asterisks and _underscores_**.

Strikethrough uses two tildes ~ . ~~Scratch this.~~

Emphasis, aka italics, with asterisks or underscores.

Strong emphasis, aka bold, with asterisks or underscores.

Combined emphasis with asterisks and underscores.

Strikethrough uses two tildes ~ . Scratch this.

Lists

1. Item 1
2. Item 2 ( we can type 1. and the markdown will automatically numerate them) 
* First Item
  * Nested item 1
  * Nested item 2
    1. Keep going
    1. Yes

* Second Item
- First Item
- Second Item
  1. Item 1
  2. Item 2 ( we can type 1. and the markdown will automatically numerate them)
  • First Item

    • Nested item 1
    • Nested item 2
      1. Keep going
      2. Yes
  • Second Item

  • First Item
  • Second Item
<!-- [Text](link) -->
[Link Text](https://medium.com/@ahmedazizkhelifi "Optional Title")
<!-- ![Alt Text](image path "title") -->
![Alt Text](https://miro.medium.com/max/80/0*PRNVc7bjff0Jj1pm.png "Optional Title")
<!-- [![Alt Text](image path "title")](link) -->
[![Alt Text](https://miro.medium.com/max/80/0*PRNVc7bjff0Jj1pm.png "Optional Title")](https://medium.com/@ahmedazizkhelifi)

Link Text Alt Text Alt Text

Horizontal Rule

Reading articles on Medium is awesome.

---
Sure !!

Reading articles on Medium is awesome.


Sure !!

Table

| Id | Label    | Price |
|--- |----------| ------|
| 01 | Markdown | \$1600 |
| 02 | is       |   \$12 |
| 03 | AWESOME  |  \$999 |
Id Label Price
01 Markdown \$1600
02 is \$12
03 AWESOME \$999

Code and Syntax Highlighting

```python
def staySafe(Coronavirus)
  if not home:
    return home

```python
def staySafe(Coronavirus)
  if not home:
    return home

Blockquotes

> This is a blockquote.
>  
> This is part of the same blockquote.

Quote break
> This is a new blockquote.

This is a blockquote. This is part of the same blockquote.

Quote break

This is a new blockquote.

LaTeX

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:
$$
...
$$


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

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: $$ ... $$

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

Important Note

$$
\frac{arg 1}{arg 2} \\
x^2\\
e^{i\pi}\\
A_i\\
B_{ij}\\
\sqrt[n]{arg}   
$$
$$ \frac{arg 1}{arg 2} \\ x^2\\ e^{i\pi}\\ A_i\\ B_{ij}\\ \sqrt[n]{arg} $$

Greek Letters:

Given : $\pi = 3.14$ , $\alpha = \frac{3\pi}{4}\, rad$
$$
\omega = 2\pi f \\
f = \frac{c}{\lambda}\\
\lambda_0=\theta^2+\delta\\
\Delta\lambda = \frac{1}{\lambda^2}
$$

Given : $\pi = 3.14$ , $\alpha = \frac{3\pi}{4}\, rad$ $$ \omega = 2\pi f \\ f = \frac{c}{\lambda}\\ \lambda_0=\theta^2+\delta\\ \Delta\lambda = \frac{1}{\lambda^2} $$

Important Note:

|Uppercase| LaTeX |Lowercase| LaTeX | 
|---------|-------|---------|-------|
|$\Delta$ |\\Delta|$\delta$ |\\delta|
|$\Omega$ |\\Omega|$\omega$ |\\omega|
Uppercase LaTeX Lowercase LaTeX
$\Delta$ \Delta $\delta$ \delta
$\Omega$ \Omega $\omega$ \omega

Roman Names:

$$
\sin(-\alpha)=-\sin(\alpha)\\
\arccos(x)=\arcsin(u)\\
\log_n(n)=1\\
\tan(x) = \frac{\sin(x)}{\cos(x)}
$$
$$ \sin(-\alpha)=-\sin(\alpha)\\ \arccos(x)=\arcsin(u)\\ \log_n(n)=1\\ \tan(x) = \frac{\sin(x)}{\cos(x)} $$

Other Symbols

Angles:

Left angle : $\langle$

Right angle : $\rangle$

Angle between two vectors u and v   : $\langle \vec{u},\vec{v}\rangle$  


$$ \vec{AB} \, \cdot \, \vec{CD} =0  \Rightarrow  \vec{AB} \, \perp\, \vec{CD}$$


##Sets and logic

$$\mathbb{N} \subset \mathbb{Z} \subset \mathbb{D} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}$$

Left angle : $\langle$

Right angle : $\rangle$

Angle between two vectors u and v : $\langle \vec{u},\vec{v}\rangle$

$$ \vec{AB} \, \cdot \, \vec{CD} =0 \Rightarrow \vec{AB} \, \perp\, \vec{CD}$$

Sets and logic

$$\mathbb{N} \subset \mathbb{Z} \subset \mathbb{D} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C}$$

Vertical curly braces:

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

\\

$$
 \left.
    \begin{array} \\
        \alpha^2 = \sqrt5 \\
        \alpha \geq 0 
    \end{array}
\right \} \alpha = 5 
$$
$$ sign(x) = \left\{ \begin{array}\\ 1 & \mbox{if } \ x \in \mathbf{N}^* \\ 0 & \mbox{if } \ x = 0 \\ -1 & \mbox{else.} \end{array} \right. $$

\

$$ \left. \begin{array} \\ \alpha^2 = \sqrt5 \\ \alpha \geq 0 \end{array} \right \} \alpha = 5 $$

Horizontal curly braces $\underbrace{}$

Horizontal curly braces $\underbrace{}$

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

Derivate

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

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

Limit $\lim$

Limit $\lim$

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 : $$\inf_{x > s}f(x)$$

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 : $$\inf_{x > s}f(x)$$

Sum $\sum$

Sum $\sum$

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

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

Product $\prod$

Product $\prod$

Product:

$$\prod_{j=1}^k A_{\alpha_j}$$

Double product:
$$\prod^k_{i=1}\prod^l_{j=1}\,A_i A_j$$

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

Integral : $\int$

Integral : $\int$

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:
$$\iiiint$$ 

Multiple integral :

$$\idotsint$$


Contour integral:
$$\oint$$

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: $$\iiiint$$

Multiple integral : $$\idotsint$$

Contour integral: $$\oint$$

Matrix

Plain:

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

Round brackets:
\begin{pmatrix}
1 & 2 & 3\\
a & b & c
\end{pmatrix}

Curly brackets:
\begin{Bmatrix}
1 & 2 & 3\\
a & b & c
\end{Bmatrix}   

Pipes:
\begin{vmatrix}
1 & 2 & 3\\
a & b & c
\end{vmatrix}

Double pipes
\begin{Vmatrix}
1 & 2 & 3\\
a & b & c
\end{Vmatrix}

Plain:

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

Round brackets: \begin{pmatrix} 1 & 2 & 3\\ a & b & c \end{pmatrix}

Curly brackets: \begin{Bmatrix} 1 & 2 & 3\ a & b & c \end{Bmatrix}

Pipes: \begin{vmatrix} 1 & 2 & 3\\ a & b & c \end{vmatrix}