\usepackage{amssymb, amsmath}
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The following commands are defined in the amsmath package; in other
words, to typeset with these commands, the document class should
start with
\documentclass{article} % article document
class
\usepackage{amssymb, amsmath}
Note:
-
Inline
-
math environment open and close with $
-
Examples: $ a + b $, $ a/b $
-
Displayed
-
math environment open with \[ and closed with \]
-
Examples:
-
\[
-
\frac{1 + 2x}{x + y + xz}
-
\]
-
Arithmatic
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The arithmetic operations such as +, -, *, /, fraction (\frac)
-
Examples: $a + b$, $x - y$, $a \cdot b$, $x \times y$
-
Subscripts and superscripts
-
Subscripts are typed with _ (underscore) and superscripts are
typed with ^ (caret).
-
Remember to enclose the subscripts and superscripts with { and }.
-
Examples: $a^2$, $a_i$, $x_{ij}$
-
Accents (in math environment)
-
There are four most often used math accents:
-
$\bar{a}$
-
$\hat{a}$
-
$\tilde{a}$
-
$\vec{a}$
-
Binomial coefficients
-
Use \binom{ }{ } for the binomial coefficients
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Example: $ \binom{n}{k} $
-
Congruences
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The two most important (examples) forms are:
-
$a \equiv v \pmod{\theta}$
-
$a \equiv v \pod{\theta}$
-
Delimiters
-
These are parenthesis-like symbols that vertically expand to enclose a
formular.
-
Examples:
-
\[
-
\left( \frac{1 + x}{2 + y^{2}} \right) ^{2}
-
\]
-
\[
-
\left| \frac{a + b}{2} \right|,
-
\quad \left\| A^{2} \right\|
-
\]
-
Operators
-
Such as trig functions, limit; for instance, to typeset the sine function
sin x
-
type: $\sin x$.
-
Examples:
-
\[
-
\lim{x \to 0} f(x) = 0
-
\]
-
Ellipses
-
vertical dots: \vdots
-
low dots: \ldots
-
centered dots: \cdots
-
Note: \vdot, \ldot, \cdot produce a single dot.
-
Integrals
-
The command for an integral is \int; the lower limit is a subscript and
the upper limit is a superscript.
-
Example: $\int_{0}^{2 \pi} \cos x \, dx$
-
Matrices
-
The amsmath package provide you with a matrix environment.
The matrix elements are separated by &; the rows are separted by \\.
(View these matrices.)
-
The basic matrix (without parenthese)
\[
\begin{matrix}
a + b + c & uv
& x - y & 27 \\
a + b
& u + v & z
& 134
\end{matrix}
\]
-
use pmatrix for matrix with parentheses
\[
\begin{pmatrix}
x + y + z
& xy \\
2x + xy
& xz
\end{pmatrix}
\begin{pmatrix}
223
& 43 \\
34
& 15
\end{pmatrix}
\]
-
use bmatrix for matrix with brakets
-
use vmatrix for matrix with vertical lines
-
use Vmatrix for matrix with double vertical lines
-
Roots
-
\sqrt produces the square root.
-
For nth squart root, use \sqrt[n]{ }
-
Examples: $\sqrt{a + 2b}$
-
Sums and products
-
The command for sum is \sum and for product is \prod .
-
Examples: $\prod_{i = 1}^{n} x_{i}^2$
-
Text
-
Place text in a formula with an \mbox command
-
Example:
- \[
- a = b \mbox{by assumption}
- \]
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