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[6]{x+5}: \[\sqrt[6]{x+5}\]
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.
Relation Symbols
Some symbols that are useful for relationships.
Greek Letters
Greek alphabet for LaTeX, more info on Wikipedia.
Accent Symbols
Useful Symbols
More Symbols
An extremely detailed list of symbols can be found over here: The Comprehensive LaTeX Symbol List