# Latex & HTML Tips

Syntax of Latex is:

$latexExpressions “$”
where
Expressions: “\command”

Latex equation designer (change “$…$” to “$..$

https://www.food4rhino.com/resource/latex-equation-designer#lg=1&slide=1

Latex Convert Tool : https://v.ixigua.com/ePw8K3t/

The list of Latex symbols is here:

http://kogler.wordpress.com/2008/03/21/latex-use-of-math-symbols-formulas-and-equations/

Examples:
Color: &fg=rrggbb
Font Size : &s = 4

\mathbb{N}\subset \mathbb{ Z }\subset \mathbb{ Q }\subset \mathbb{ R} \subset \mathbb{ C }
}&fg=00bb00&s=3

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

\boxed {
{\mathbb {S}^1 } \simeq {\mathbb {A}^1 } \Big/ { \langle \tau , {\tau}^{-1} \rangle}
}&fg=aa0000&s=3

$\boxed { {\mathbb {S}^1 } \simeq {\mathbb {A}^1 } \Big/ { \langle \tau , {\tau}^{-1} \rangle} }$

x^2 + y^2 &fg=aa0000&s=4
$x^2 + y^2$

$x^2 + ax + b = 0$

$a = - (x_1 + x_2)$

$b = x_1. x_2$

$x_1 \to x_2$

$x_2 \to x_1$

$a = - (x_2+ x_1)$

$b = x_2. x_1$

x= \frac{-b \pm \sqrt{b^{2}-4ac} }{2a}

$\boxed{x= \frac{-b \pm \sqrt{b^{2}-4ac} }{2a}}$

\binom{n}{k}
= \frac { n^{\underline {k}}}
{k^{\underline {k}}}

$\displaystyle \boxed { \binom{n}{k} = \frac { n^{\underline {k}}} {k^{\underline {k}}} }$

F(x) = \underbrace {0 }_{F_{0}}
+ \underbrace { \frac {r-s}{r-s}}_{F_{1}}x +
\underbrace { \frac {r^2-s^2}{r-s}}_{F_{2}}x^2 +… \underbrace { \frac {r^n-s^n}{r-s}}_{F_{n}}x^n

$\boxed { F(x) = \underbrace {0 }_{F_{0}} + \underbrace { \frac {r-s}{r-s}}_{F_{1}}x + \underbrace { \frac {r^2-s^2}{r-s}}_{F_{2}}x^2 +... \underbrace { \frac {r^n-s^n}{r-s}}_{F_{n}}x^n }$

F_{n}= \frac{1} {\sqrt {5}}\left(\bigl( \frac {1+ \sqrt {5}}{2} \bigr)^n – \bigl( \frac {1-\sqrt {5}}{2} \bigr)^n\right)
&fg=aa0000&s=1

$\boxed { F_{n}= \frac{1} {\sqrt {5}}\left(\bigl( \frac {1+ \sqrt {5}}{2} \bigr)^n - \bigl( \frac {1-\sqrt {5}}{2} \bigr)^n\right) }$

W_{\ell} = \displaystyle \bigoplus \limits_{0 \leq i < \ell } \mathbb{C}v_i \text{ and } a \in \mathbb{C}^{*}

$\boxed{ W_{\ell} = \displaystyle \bigoplus \limits_{0 \leq i < \ell } \mathbb{C}v_i \text{ and } a \in \mathbb{C}^{*} }$

\: space

\begin{array}{|l|l|l|}
\hline
x & – \infty \rightarrow \: \: \: \: 0 & 0 \:\:\:\:\: \rightarrow \:\:3 \rightarrow \:\:\: +\infty \\
\hline
f'(x) & \:\: \: \: \:\: \: + & \:\:\:\: – \:\:\:\:\:\:\:\:\: 0 \:\:\:\:\:\:\: + \\
\hline
f(x) & -\infty \nearrow +\infty & +\infty \searrow \: \frac{9}{2} \nearrow +\infty\\
\hline
\end{array}

$\begin{array}{|l|l|l|} \hline x & - \infty \rightarrow \: \: \: \: 0 & 0 \:\:\:\:\: \rightarrow \:\:3 \rightarrow \:\:\: +\infty \\ \hline f'(x) & \:\: \: \: \:\: \: + & \:\:\:\: - \:\:\:\:\:\:\:\:\: 0 \:\:\:\:\:\:\: + \\ \hline f(x) & -\infty \nearrow +\infty & +\infty \searrow \: \frac{9}{2} \nearrow +\infty\\ \hline \end{array}$

Faà di Bruno Fomula
(f\circ H)^{(n)} =\displaystyle\sum_{\sum_{j=1}^n j\,m_j=n}
\frac{n!}{m_!\ldots m_n!}\,
\bigl(f^{(m_1+\ldots+m_n)})\circ H\bigr)\,
\prod_{j=1}^n \left(\frac{H^{(j)}}{j!}\right)^{m_j}

$\boxed{ (f\circ H)^{(n)} =\displaystyle\sum_{\sum_{j=1}^n j\,m_j=n} \frac{n!}{m_!\ldots m_n!}\, \bigl(f^{(m_1+\ldots+m_n)})\circ H\bigr)\, \prod_{j=1}^n \left(\frac{H^{(j)}}{j!}\right)^{m_j} }$

\text {text message}

p \mid 2^{p} – 2 \text{ for p prime}
\implies 2^{p} \equiv 2 \mod {p}

$\boxed {p \mid 2^{p} - 2 \text{ for p prime} \implies 2^{p} \equiv 2 \mod {p}}$

\displaystyle\sum_{n=2}^{n}{_n}C_r :

$\boxed{\displaystyle\sum_{n=2}^{n}{_n}C_r }$

\int \frac {dT}{T-T_s}=\int k.\mathrm{d}t:

$\boxed {\int \frac {dT}{T-T_s}=\int k.\mathrm{d}t}$
\displaystyle\int_{0}^{\infty}{e^{-ax}dx}=-\frac{1}{a}e^{-ax}\Bigr|_{0}^{\infty}=\frac{1}{a}

$\boxed{\displaystyle\int_{0}^{\infty}{e^{-ax}dx}=-\frac{1}{a}e^{-ax}\Bigr|_{0}^{\infty}=\frac{1}{a}}$
\boxed{n!=\int_{0}^{\infty}x^{n}e^{-x}dx}

$\boxed{n!=\int_{0}^{\infty}x^{n}e^{-x}dx}$

\displaystyle\int_{a}^{b} f(x) dx = \lim_{n\to\infty} \sum_{i=1}^{n} f(x_i)\Delta x

$\boxed{\displaystyle\int_{a}^{b} f(x) dx = \lim_{n\to\infty} \sum_{i=1}^{n} f(x_i)\Delta x}$
Piecewise function:
D(x) = \begin{cases} 1/b, & \text{if }x=a/b\in\mathbb{Q}\text{ rational} \\
0, & \text{if }x\text{ irrational}
\end{cases}

$\boxed{ D(x) = \begin{cases} 1/b, & \text{if }x=a/b\in\mathbb{Q}\text{ rational} \\ 0, & \text{if }x\text{ irrational} \end{cases} }$

\cos^2 x +\sin^2 x = 1
$\cos^2 x +\sin^2 x = 1$

\cos 90^\circ = 0
$\cos 90^\circ = 0$

Matrix

\begin{pmatrix}
a_{11} & 0 & \ldots & a_{1n}\\
0 & a_{22} & \ldots & a_{2n}\\
\vdots & \vdots & \ddots & \vdots\\
0 & 0 &\ldots & a_{nn}
\end{pmatrix}

$\begin{pmatrix} a_{11} & 0 & \ldots & a_{1n}\\ 0 & a_{22} & \ldots & a_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ 0 & 0 &\ldots & a_{nn} \end{pmatrix}$

\begin {bmatrix}
a & b \\
c & d
\end{bmatrix} = K

$\begin{bmatrix} a & b \\ c & d \end{bmatrix} = K$

\boxed{ \displaystyle { \vec a_{(M)} = \begin{pmatrix}
\ddot r – r {\dot{\theta}} ^2\\
2\dot r \dot \theta + r \ddot \theta \end {pmatrix}
\begin{pmatrix}
\vec e_r \\
\vec e_{\theta}
\end {pmatrix}}
}&fg=00aa00&s=3

$\boxed{ \displaystyle { \vec a_{(M)} = \begin{pmatrix} \ddot r - r {\dot{\theta}} ^2\\ 2\dot r \dot \theta + r \ddot \theta \end {pmatrix} \begin{pmatrix} \vec e_r \\ \vec e_{\theta} \end {pmatrix}} }$

\displaystyle\lim_{x\to a}f(x) = L
\iff
\forall \varepsilon >0, \exists \delta >0 such that
\boxed{0<|x-a|<\delta}
\implies |f(x)-L|< \varepsilon

$\displaystyle\lim_{x\to a}f(x) = L \iff$
$\forall \varepsilon >0, \exists \delta >0$ such that
$\boxed{0<|x-a|<\delta} \implies |f(x)-L|< \varepsilon$

0 \xrightarrow { } V_0 \xrightarrow {d_0} V_1 \xrightarrow {d_1} V_2 \xrightarrow { } 0

$0 \xrightarrow { } V_0 \xrightarrow {d_0} V_1 \xrightarrow {d_1} V_2 \xrightarrow { } 0$

Embedded Video Size Setting:

Table in HTML (non-latex)

 Description Worldwide APEC Percentage Apple 164,125 85,527 52.11% Orange 257,854 178,756 69.32%

HTML CODES

## One thought on “Latex & HTML Tips”

1. nice tip for matrix!