MathJax

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References

Example

When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are
\[ x = {-b \pm \sqrt{b^2-4ac} \over 2a}. \]

Modes

Inline mode

\(\sum_{i=0}^n i^2=\frac{(n^2+n)(2n+1)}{6}\) = \(\sum_{i=0}^n i^2=\frac{(n^2+n)(2n+1)}{6}\)

Display mode

$$\sum_{i=0}^n i^2=\frac{(n^2+n)(2n+1)}{6}$$ \[\sum_{i=0}^n i^2=\frac{(n^2+n)(2n+1)}{6}\]

Mode enforcement

\(\displaystyle \lim_{t \to 0} \int_t^1 f(t)\, dt \;\) vs \( \; \lim_{t \to 0} \int_t^1 f(t)\, dt\).

enforced with \displaystyle inside text mode and with \textstyle inside display mode

Syntax

Greek letters

\(\alpha \beta \Delta \Omega \) = \alpha \beta \Delta \Omega

Parentheses

\( (1) \) = (1)
\( [1] \) = [1]
\( \{1\} \) = \{1\}
\( |1| \) = |1|
\( \|1\| \) = \|1\|
\( \lvert{1}\rvert \) = \lvert{x}\rvert
\( \lVert{1}\rVert \) = \lVert{x}\rVert

\(\left( \frac{x}{y} \right) \) = \left( \right)
\(\left[ \frac{x}{y} \right] \) = \left[ \right]
\(\left\{ \frac{x}{y} \right\} \) = \left\{ \right\}
\(\left| \frac{x}{y} \right| \) = \left| \right|
\(\lvert \frac{x}{y} \rvert \) = \lvert \rvert
\(\left\vert \frac{x}{y} \right\vert \) = \left\vert \right\vert
\(\lVert \frac{x}{y} \rVert \) = \lVert \rVert
\(\left\Vert \frac{x}{y} \right\Vert \) = \left\Vert \right\Vert
\(\left\langle \frac{x}{y} \right\rangle \) = \left\langle \right\rangle
\( \binom nk \) = \binom nk

Invisible parentheses with .:
\(\left. \frac{x}{y} \right\} \) = \left. \right\}

Sums, integrals, etc

\(\sum_1^ni^2\) = \sum_1^ni^2
\(\sum_{i=1}^\infty x^2\) = \sum_{i=1}^\infty x^2
\(\iint_{i=1}^\infty x^2\) = \iint_{i=1}^\infty x^2
\(\prod_{i=1}^n x^2\) = \prod_{i=1}^n x^2

Fractions

\(\frac ab\) = \frac ab
\(\dfrac ab\) = \dfrac ab = in displaymode!
\(\frac{a+1}{b+1}\) = \frac{a+1}{b+1}
\(\sqrt[3] \frac{x^3}{b}\) = \sqrt[3] \frac{x^3}{b}
\(x^\frac 23\) = x^\frac 23

\(\lim_{x\to 0} \) =\lim_{x\to 0}
\(\displaystyle\lim_{x\to 0} \) =\displaystyle\lim_{x\to 0}

\(\hat x \) = \hat x
\(\widehat {xy} \) = \widehat {xy}
\(\bar x \) = \bar x

\(\vec x \) = \vec x
\(\overrightarrow {xyz} \) = \overrightarrow {xyz}
\(\lvert x \rvert \) = \lvert x \rvert
\(\lVert x \rVert \) = \lVert x \rVert
\( _5C_3 \) = _5C_3

Matrices

matrix

\( \begin{matrix} 1 & x \\ 1 & y \end{matrix} \) = \begin{matrix} 1 & x \\ 1 & y \end{matrix}

pmatrix (parentheses)

\( \begin{pmatrix} 1 & x \\ 1 & y \end{pmatrix} \) = \begin{pmatrix} 1 & x \\ 1 & y \end{pmatrix}

bmatrix (curved bracket)

\( \begin{bmatrix} 1 & x \\ 1 & y \end{bmatrix} \) = \begin{bmatrix} 1 & x \\ 1 & y \end{bmatrix}

Bmatrix (square Bracket)

\( \begin{Bmatrix} 1 & x \\ 1 & y \end{Bmatrix} \) = \begin{Bmatrix} 1 & x \\ 1 & y \end{Bmatrix}

vmatrix (vertical line)

\( \begin{vmatrix} 1 & x \\ 1 & y \end{vmatrix} \) = \begin{vmatrix} 1 & x \\ 1 & y \end{vmatrix}

Vmatrix (Vertical lines)

\( \begin{Vmatrix} 1 & x \\ 1 & y \end{Vmatrix} \) = \begin{Vmatrix} 1 & x \\ 1 & y \end{Vmatrix}

Smallmatrix

\( \bigl(\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\bigr) \) \bigl(\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\bigr)

Arrays

\( \left[ \begin{array}{cc|c} 1 & 2 & 3 \\ \hline 1 & x & y \\ \end{array} \right] \) \left[ \begin{array}{cc|c} 1 & 2 & 3 \\ \hline 1 & x & y \\ \end{array} \right]

Alignment

\( \begin{align} a^2-b^2 & = (a+b)(a-b) \\ &= a^2 + ab -ab +b^2 \end{align} \)
\begin{align} a^2-b^2 & = (a+b)(a-b) \\ &= a^2 + ab -ab +b^2 \end{align}

Cases

\( f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases} \)
f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases}

Tables

\( \begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & \color{red}{125} \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array} \)
\begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array}

Table with Lines

\( \begin{array}{ |c|c|c| } \hline a & a^2 \pmod{5} & 2a^2 \pmod{5} \\ \hline 0 & 0 & 0 \\ 1 & 1 & 2 \\ 2 & 4 & 3 \\ \hline \end{array} \)
\( \begin{array}{ |c|c|c| } \hline a & a^2 \pmod{5} & 2a^2 \pmod{5} \\ \hline 0 & 0 & 0 \\ 1 & 1 & 2 \\ 2 & 4 & 3 \\ \hline \end{array} \)

Highlighted Box

\( \bbox[#ffe,5px,border:2px solid #fee] { e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n \qquad (1) } \)
$$ \bbox[yellow,5px,border:2px solid red] { e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n \qquad (1) } $$

Arrows

\( \implies \) = \implies
\( \impliedby \) = \impliedby
\( \iff \) = \iff
\( \mapsto \) = \mapsto
\( \to \) = \to
\( \gets \) \gets
\( \rightarrow \) = \rightarrow
\( \leftarrow \) = \leftarrow
\( \Rightarrow \) = \Rightarrow
\( \Leftarrow \) = \Leftarrow

Vector

\( \|\mathbf{v}\| \) = \|\mathbf{v}\|

Integral

\( \int_{a}^{b} \! f(x)\,\mathrm{d}x \) = \int_{a}^{b} \! f(x)\,\mathrm{d}x

Binomial

\( \binom nk \) = \binom nk

Underbrace

\( \underbrace{a_0+a_1+a_2+\cdots+a_n}_{x} \) = \( \underbrace{a_0+a_1+a_2+\cdots+a_n}_{x} \)

\( \overbrace{a_0+a_1+a_2+\cdots+a_n}^{x} \) = \( \overbrace{a_0+a_1+a_2+\cdots+a_n}_{x} \)

Alignment

Aligning e.g. "\(=\)" signs and "\(|\)":
\( \begin{align} 2+3x&=y &&|-2\\ 3x&=y-2 &&|\div 3\\ x&=\frac{y-2}{3} \end{align} \)
\( \begin{align}
2+3x&=y &&|-2\\
3x&=y-2 &&|\div 3\\
x&=\frac{y-2}{3}
\end{align}
\)

Fonts

\( \mathrm{ABCD abcd} \) = \mathrm{ABCD abcd} = rm=Roman font
\( \mathsf{ABCD abcd} \) = \mathsf{ABCD abcd} = sf=sans-serif
\( \mathtt{ABCD abcd} \) = \mathtt{ABCD abcd} = tt=typewriter
\( \mathbf{ABCD abcd} \) = \mathbf{ABCD abcd} = bf=boldface
\( \mathbb{ABCD abcd} \) = \mathbb{ABCD abcd} = bb=blackbord bold
\( \mathfrak{ABCD abcd} \) = \mathfrak{ABCD abcd} = frak=fraktur