LaTeX:Commands

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This page introduces various useful commands for rendering math in LaTeX, as well as instructions for building your own commands.

Subscripts and Superscripts

Subscripts and superscripts (such as exponents) can be made using the underscore _ and caret ^ symbols respectively.

Symbol	Command	Symbol	Command
	2^2		a_i
	2^{23}		n_{i-1}
	a^{i+1}_3		x^{3^2}
	2^{a_i}		2^a_i

Notice that we can apply both a subscript and a superscript at the same time. For subscripts or superscripts with more than one character, you must surround what you want to be the exponent/superscript with curly braces. For example, x^10 produces , while x^{10} produces .

Math Commands

Here are some commonly used math commands in LaTeX:

Fractions

Symbol	Command
	\frac{1}{2} or \frac12
	\frac{2}{x+2}
	\frac{1+\frac{1}{x}}{3x + 2}

Notice that with fractions with a 1-digit numerator and a 1-digit denominator, we can simply group the numerator and the denominator together as one number. However, for fractions with either a numerator or a denominator that requires more than one character (or if the numerator starts with a letter), you need to surround everything in curly brackets.

Use \cfrac for continued fractions.

Expression	Command
	\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1}}}}

Radicals

Symbol	Command
	\sqrt{3}
	\sqrt{x+y}
	\sqrt{x+\frac{1}{2}}
	\sqrt[3]{3}
	\sqrt[n]{x}

Sums, Products, Limits and Logarithms

Use the commands \sum, \prod, \lim, and \log respectively. To denote lower and upper bounds, or the base of the logarithm, use _ and ^ in the same way they are used for subscripts and superscripts. (Lower and upper bounds for integrals work the same way, as you'll see in the calculus section)

Symbol	Command
	\sum_{i=1}^{\infty}\frac{1}{i}
	\prod_{n=1}^5\frac{n}{n-1}
	\lim_{x\to\infty}\frac{1}{x}
	\lim\limits_{x\to\infty}\frac{1}{x}
	\log_n n^2

Some of these are prettier in display mode:

Symbol	Command
	\sum_{i=1}^{\infty}\frac{1}{i}
	\prod_{n=1}^5\frac{n}{n-1}
	\lim_{x\to\infty}\frac{1}{x}

Note that we can use sums, products, and logarithms without _ or ^ modifiers.

Symbol	Command
	\sum\frac{1}{i}
	\prod\frac{n}{n-1}
	\log n^2
	\ln e

Mods

Symbol	Command
	9\equiv 3 \bmod{6}
	9\equiv 3 \pmod{6}
	9\equiv 3 \mod{6}
	9\equiv 3 \pod{6}

Combinations

Symbol	Command
	\binom{1}{1}
	\binom{n-1}{r-1}

These often look better in display mode:

Symbol	Command
	\dbinom{9}{3}
	\dbinom{n-1}{r-1}

Trigonometric Functions

Most of these are just the abbreviation of the trigonometric function with simply a backslash added before the abbreviation.

Symbol	Command	Symbol	Command	Symbol	Command
	\cos		\sin		\tan
	\sec		\csc		\cot
	\arccos		\arcsin		\arctan
	\cosh		\sinh		\tanh
	\coth

Here are a couple examples:

Symbol	Command
	\cos^2 x +\sin^2 x = 1
	\cos 90^\circ = 0

Calculus

Below are examples of calculus expressions rendered in LaTeX. Most of these commands have been introduced before. Notice how definite integrals are rendered (and the difference between inline math and display mode for definite integrals). The \, in the integrals makes a small space before the dx.

Symbol	Command
	\frac{d}{dx}\left(x^2\right) = 2x
	\int 2x\,dx = x^2+C
	\int^5_1 2x\,dx = 24
	\frac{\partial^2U}{\partial x^2} + \frac{\partial^2U}{\partial y^2}
	\frac{1}{4\pi}\oint_\Sigma\frac{1}{r}\frac{\partial U}{\partial n} ds

Overline and Underline

Symbol	Command
	\overline{a+bi}
	\underline{747}

LaTeX

Other Functions

Symbol	Command	Symbol	Command	Symbol	Command
	\arg		\deg		\det
	\dim		\exp		\gcd
	\hom		\inf		\ker
	\lg		\liminf		\limsup
	\max		\min		\Pr
	\sup		\smiley

Some of these commands take subscripts in the same way sums, products, and logarithms do. Some render differently in display mode and inline math mode.

Symbol	Command	Symbol	Command	Symbol	Command
	\dim_x		\gcd_x		\inf_x
	\liminf_x		\limsup_x		\max_x
	\min_x		\Pr_x		\sup_x

Matrices

We can build an array or matrix with the \begin{array}…\end{array} commands, and use \left and \right to properly size the delimiters around the matrix:

The characteristic polynomial $f(\lambda)$ of the
$3 \times 3$ matrix
\[
\left(
\begin{array}{ccc}
a & b & c <br />d & e & f <br />g & h & i \end{array}
\right)\]
is given by the equation
\[ f(\lambda)
= \left|
\begin{array}{ccc}
\lambda - a & -b & -c <br />-d & \lambda - e & -f <br />-g & -h & \lambda - i \end{array}
\right|.\]

More simply, we can use the shortcut matrix environments in the amsmath package:

The characteristic polynomial $f(\lambda)$ of the
$3 \times 3$ matrix
\[
\begin{pmatrix}
a & b & c
= \begin{vmatrix}
\lambda - a & -b & -c <br />-d & \lambda - e & -f <br />-g & -h & \lambda - i
\end{vmaix}.\]

You can read more about how the array environment works here (it works the same as tabular).

We can also use this environment to typeset any mathematics that calls for multiple columns, such as piecewise-defined functions like this one:

\[ f(x) = \left\{ \begin{array}{ll}
x+7 & \mbox{if $5< x$};<br />x^2-3 & \mbox{if $-3 \le x \le 5$};<br />-x & \mbox{if $x < -3$}.\end{array} \right. \]

Text Styles in Math Mode

You can render letters in various styles in math mode. Below are examples; you should be able to use these with any letters. The \mathbb requires the amsfonts package to be included in your document's preamble. Do not try to do \mathbb{year}. You'll get , and that looks nothing like it!

So

$$n^2 + 5 = 30\text{ so we have }n=\pm5$$

gives

How to Build Your Own Commands

The command> \documength $\hypot{3}{4}$ (Error compiling LaTeX. Unknown error_msg). sqrt[3]{2}\cbrt{2}$.

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The \newcommand dputs will be sent to the cois called. f purposes, not just for making math commands you'll ue a lot easier to call. For example, try this:

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C.\ #4\hfill D.\ #5\hfill E.\ NOTA}

\begin{document}

\prob{Evaluateum_{fty \frac{1}{

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