# LaTeX Overview

Just an overview and a reference to the most used functions.

## Simple formulars

Just write the symbols, like a = b : $a=b$

Power of x by using the ^-sign. Like a^2+b^2=c^2: $a^2+b^2=c^2$

Subscript and superscript by using _ and ^, like a_1^2=b_1^2+c_1^2: $a_1^2=b_1^2+c_1^2$

Grouping of symbols is done by curly brackets, like a_{ij}^{kl}: $a_{ij}^{kl}$

Grouping can be used for larger strings as well, like a_{index}^{matrix-counter}: $a_{index}^{matrix-counter}$

Fractions are done with the keyword \frac{}{}, where the brackets are the two parts, like \frac{1}{2} or \frac{a+b}{c+d}: $\frac{1}{2} \text{ or } \frac{a+b}{c+d}$

Text within the formular is done by \text{}, like a^2 \text{ or } b^2: $a^2 \text{ or } b^2$

Summarize some stuff with \sum_x^y{}, like \sum_{i=0}^{x}{x_i}: $\sum_{i=0}^{x}{x_i}$

Depending on the math forumular beeing a block (display mode like above) or being in inline mode, it looks slightly different, like the sum from before is $$\sum_{i=0}^{x}{x_i}$$ in inline style.

There are no spaces so you need to use \, for a short space, \: for a medium space and \; for a wide space, or a \! for reducing the space. Take this example: a+b\,+\:c\;+d\!x: $a+b\,+\:c\;+d\!x$

The square root is done with \sqrt{}, like \sqrt{2}=1.414 or c=\sqrt{a^2+b^2}: $\sqrt{2}=1.414 \text{ or } c=\sqrt{a^2+b^2}$

The n-th root is done by specifying an addition square(!) bracket, like \sqrt{x+5}: $\sqrt{x+5}$

Overlines and underlines are done like \overline{a^2+b^2} or \underline{a^2+b^2}: $\overline{a^2+b^2}$ or $\underline{a^2+b^2}$

A hat can be done over a symbol or over a whole group, like \hat{a} and \widehat{a^2+b^2}: $\hat{a} \text{ and } \widehat{a^2+b^2}$

Integrating some stuff is simply done by using \int_0^{\infty}{x \cdot dx}: $\int_0^{\infty}{x \cdot dx}$

A nice integral with the combination of multiple options (btw it is the Gaussian integral) \int_{-\infty}^{\infty} e^{-\frac{1}{2}t^2}dt = \sqrt{2 \cdot \pi}: $\int_{-\infty}^{\infty} e^{-\frac{1}{2}t^2}dt = \sqrt{2 \cdot \pi}$

Creating the products over a range, like \prod_{i=0}^{10}{x_i}: $\prod_{i=0}^{10}{x_i}$

The limes is done by \lim_{h-0}{\frac{f(x)}{h}}: $\lim_{h-0}{\frac{f(x)}{h}}$

Klammern kann man direkt verwenden oder mit \left und \right angeben. ${[(a+b)^2]^x}-3$

## General and Logic Symbols

Some symbols that are useful for logic operations.

$$\cup$$ : \cup
$$\cap$$ : \cap
$$\cdot$$ : \cdot
$$\circ$$ : \circ
$$\mp$$ : \mp
$$\pm$$ : \pm
$$\odot$$ : \odot
$$\oplus$$ : \oplus
$$\ominus$$ : \ominus
$$\otimes$$ : \otimes
$$\times$$ : \times
$$\sqcup$$ : \sqcup
$$\sqcap$$ : \sqcap
$$\star$$ : \star
$$\vee$$ : \vee
$$\wedge$$ : \wedge
$$\times$$ : \times

## Relation Symbols

Some symbols that are useful for relationships.

$$\approx$$ : \approx
$$\sim$$ : \sim
$$\equiv$$ : \equiv
$$\in$$ : \in
$$\napprox$$ : \napprox
$$\owns$$ : \owns
$$\parallel$$ : \parallel
$$\mid$$ : \mid
$$\neq$$ : \neq
$$\le$$ : \le
$$\ge$$ : \ge
$$\ll$$ : \ll
$$\gg$$ : \gg

## Greek Letters

$$\alpha$$ $$A$$ : \alpha A
$$\beta$$ $$B$$ : \beta B
$$\gamma$$ $$\Gamma$$ : \gamma \Gamma
$$\delta$$ $$\Delta$$ : \delta \Delta
$$\epsilon$$ $$\varepsilon$$ $$E$$ : \epsilon \varepsilon E
$$\zeta$$ $$Z$$ : \zeta Z
$$\eta$$ $$H$$ : \eta H
$$\theta$$ $$\vartheta$$ $$\Theta$$ : \theta \vartheta \Theta
$$\iota$$ $$I$$ : \iota I
$$\kappa$$ $$K$$ : \kappa K
$$\lambda$$ $$\Lambda$$ : \lambda \Lambda
$$\mu$$ $$M$$ : \mu M
$$\nu$$ $$N$$ : \nu N
$$\xi$$ $$\Xi$$ : \xi \Xi
$$\omicron$$ o $$O$$ : \omicron o O
$$\pi$$ $$\Pi$$ : \pi \Pi
$$\rho$$ $$\varrho$$ $$P$$ : \rho \varrho P
$$\sigma$$ $$\Sigma$$ : \sigma \Sigma
$$\tau$$ $$T$$: \tau T
$$\upsilon$$ $$\Upsilon$$ : \upsilon \Upsilon
$$\phi$$ $$\varphi$$ $$\Phi$$ : \phi \varphi \Phi
$$\chi$$ $$x$$ $$X$$ : \chi x X
$$\psi$$ $$\Psi$$ : \psi \Psi
$$\omega$$ $$\Omega$$ : \omega \Omega

## Accent Symbols

$$\acute{a}$$ : \acute{a}
$$\bar{a}$$ : \bar{a}
$$\breve{a}$$ : \breve{a}
$$\dot{a}$$ : \dot{a}
$$\grave{a}$$ : \grave{a}
$$\hat{a}$$ : \hat{a}
$$\ddot{a}$$ : \ddot{a}
$$\mathring{a}$$ : \mathring{a}

## Useful Symbols

$$\emptyset$$ : \emptyset
$$\infty$$ : \infty Infinity
$$\checkmark$$ : \checkmark

## More Symbols

An extremely detailed list of symbols can be found over here: The Comprehensive LaTeX Symbol List