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Constructs
LaTeX provides a number of commands to generate mathematical constructs.
Basics
1,2,3,\ldots
sequence
1+2+3+\cdots
sequence
\frac{a}{b}
fraction
\cfrac{a}{1+\cfrac{b}{c}}
continued fraction
^3/_7
simple fraction
\sqrt{x}
square root
\sqrt[n]{x}
nth root
a^b
exponentiation
a_b
subscript
|x|
absolute value
\ln(x)
natural log
\log_{a} b
logarithm
\binom{n}{k}
binomial
|x| = \begin{cases}
x & x\ge 0\\
-x & x<0
\end{cases}
piecewise function
\begin{equation} \begin{split} \label{x5} x &= a + b \\ &= c + d + e. \end{split} \end{equation}
multi-line equation
There are no rows in this table
Geometry and trigonometry
\angle 45^\circ
angle and degree
\triangle ABC
triangle
\overline{AB}
segment
\sin
sine
\cos
cosine
\tan
tangent
\cot
cotangent
\sec
secant
\csc
cosecant
\arcsin
arcsine
\arccos
arccosine
\arctan
arctangent
There are no rows in this table
Matrices and arrays
Matrices can be created using a number of environments, depending on the desired delimiter and spacing.
\begin{matrix}
a & b & c \\
d & e & f \\
g & h & i
\end{matrix}
matrix
\begin{pmatrix}
a & b & c \\
d & e & f \\
g & h & i
\end{pmatrix}
matrix (parentheses)
\begin{bmatrix}
a & b & c \\
d & e & f \\
g & h & i
\end{bmatrix}
matrix (brackets)
\begin{Bmatrix}
a & b & c \\
d & e & f \\
g & h & i
\end{Bmatrix}
matrix (braces)
\begin{vmatrix}
a & b & c \\
d & e & f \\
g & h & i
\end{vmatrix}
matrix (verts)
\begin{Vmatrix}
a & b & c \\
d & e & f \\
g & h & i
\end{Vmatrix}
matrix (double verts)
A_{m,n} =
\begin{pmatrix}
a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\
a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m,1} & a_{m,2} & \cdots & a_{m,n}
\end{pmatrix}
A_{m,n} =
\begin{pmatrix}
a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\
a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m,1} & a_{m,2} & \cdots & a_{m,n}
\end{pmatrix}
arbitrarily sized matrix with dots
n \cdot (
\begin{smallmatrix}
a & b\\
c & d
\end{smallmatrix}
)
small matrix
\begin{array}{l|r}
20 & -30\\
30 & -40
\end{array}
array
\left|
\begin{array}{ccc}
1 & 2 & 3\\
4 & 5 & 6\\
7 & 8 & 9
\end{array}
\right|
determinant
There are no rows in this table
Set theory
\angle 45^\circ
angle and degree
\triangle ABC
triangle
\overline{AB}
segment
\sin
sine
\cos
cosine
\tan
tangent
\cot
cotangent
\sec
secant
\csc
cosecant
\arcsin
arcsine
\arccos
arccosine
\arctan
arctangent
There are no rows in this table
Calculus
\frac{df}{dx}
derivative
f'
derivative
\frac{\partial f}{\partial x}
partial derivative
\int, \int_{-N}^{N} e^x dx
integral
\iint
double integral
\iiint
triple integral
\oint
contour integral
\lim_{x \to \infty}
limit
\sum_{n=1}^{\infty}a_n
summation
\prod_{n=1}^{\infty}a_n
product
There are no rows in this table
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