# Markdown

# Heading 1


## 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) -->
<!-- ![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)

## 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:
$$\iiint$$

$$\iiiint$$

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}