Latex Cheat Sheet

Inline math uses $...$

Display math uses:

$$
...
$$

---

Variables

Output	LaTeX
$x$	x
$x_1$	x_1
$x_{long}$	x_{long}
$x^2$	x^2
$x^{10}$	x^{10}
$x_i^2$	x_i^2

---

Fractions

Output	LaTeX
$\frac{a}{b}$	\frac{a}{b}
$\frac{a}{b}$	\dfrac{a}{b}

---

Square Roots

Output	LaTeX
$\sqrt{x}$	\sqrt{x}
$\sqrt[n]{x}$	\sqrt[n]{x}

---

Parentheses

Automatically sized delimiters:

Output	LaTeX
$\left(x\right)$	\left(x\right)
$\left[\frac{a}{b}\right]$	\left[\frac{a}{b}\right]
\left{x\right}	\left\{x\right\}
x\right	x\right

---

Greek Letters

Output	LaTeX
$\alpha$	\alpha
$\beta$	\beta
$\gamma$	\gamma
$\delta$	\delta
$ϵ$	\epsilon
$\theta$	\theta
$\lambda$	\lambda
$\mu$	\mu
$\pi$	\pi
$\rho$	\rho
$\sigma$	\sigma
$\tau$	\tau
$\varphi$	\phi
$\omega$	\omega
$\Gamma$	\Gamma
$\Delta$	\Delta
$\Theta$	\Theta
$\Lambda$	\Lambda
$\Pi$	\Pi
$\Sigma$	\Sigma
$\Phi$	\Phi
$\Omega$	\Omega

---

Arithmetic

Output	LaTeX
$a+b$	a+b
$a-b$	a-b
$a\cdot b$	a\cdot b
$a\times b$	a\times b
$\frac{a}{b}$	\frac{a}{b}

---

Comparison

Output	LaTeX
$=$	=
$\ne$	\neq
$<$	<
$>$	>
$\le$	\le
$\ge$	\ge
$\approx$	\approx
$\equiv$	\equiv
$\propto$	\propto

---

Logic

Output	LaTeX
$\wedge$	\land
$\vee$	\lor
$\neg$	\neg
$\forall$	\forall
$\exists$	\exists
$\therefore$	\therefore
$\because$	\because
$⟹$	\implies
$⟺$	\iff

---

Sets

Output	LaTeX
$\in$	\in
$\notin$	\notin
$\subset$	\subset
$\subseteq$	\subseteq
$\supseteq$	\supseteq
$\cup$	\cup
$\cap$	\cap
$\varnothing$	\emptyset
$\mathbb{N}$	\mathbb{N}
$\mathbb{Z}$	\mathbb{Z}
$\mathbb{Q}$	\mathbb{Q}
$\mathbb{R}$	\mathbb{R}
$\mathbb{C}$	\mathbb{C}

---

Calculus

Output	LaTeX
${\lim }_{x\to 0}$	\lim_{x\to0}
${\sum }_{i=0}^n$	\sum_{i=0}^{n}
${\prod }_{i=1}^n$	\prod_{i=1}^{n}
${\int }_a^b$	\int_a^b
$\oint$	\oint
$\partial$	\partial
$\nabla$	\nabla
$\infty$	\infty

---

Derivatives

Output	LaTeX
$\frac{dy}{dx}$	\frac{dy}{dx}
$\frac{\partial f}{\partial x}$	\frac{\partial f}{\partial x}
$\dot{x}$	\dot{x}
$\ddot{x}$	\ddot{x}

---

Vectors

Output	LaTeX
$\vec{v}$	\vec{v}
$\overrightarrow{AB}$	\overrightarrow{AB}
$\mathbf{v}$	\mathbf{v}
$\hat{x}$	\hat{x}
$\bar{x}$	\bar{x}

---

Matrices

$$
\begin{bmatrix}
1 & 2 \\
3 & 4
\end{bmatrix}
$$

Produces

$$\left[\begin{array}{ccc}1& 23& 4\end{array}\right]$$

Other environments:

• pmatrix → ()
• bmatrix → []
• Bmatrix → {}
• vmatrix → |
• Vmatrix → ||

---

Cases

$$
f(x)=
\begin{cases}
x^2 & x>0\\
0 & x=0\\
-x & x<0
\end{cases}
$$

$$f(x)=\{\begin{array}{ll}{x}^2& x>0\\ 0& x=0\\ -x& x<0\end{array}$$

---

Alignment

$$
\begin{aligned}
a+b &= c\\
x+y &= z
\end{aligned}
$$

$$\begin{array}{rl}a+b& =c\\ x+y& =z\end{array}$$

---

Decorations

Output	LaTeX
$\overline{AB}$	\overline{AB}
$\underline{x}$	\underline{x}
$\widehat{ABC}$	\widehat{ABC}
$\tilde{f}$	\widetilde{f}
$\cancel{x}$*	\cancel{x}

*Requires the cancel package (not available in all renderers).

---

Common Functions

Output	LaTeX
$\sin$	\sin
$\cos$	\cos
$\tan$	\tan
$\log$	\log
$\ln$	\ln
$\exp$	\exp
$\max$	\max
$\min$	\min

---

Spacing

Output	LaTeX
$a,b$	a\,b
$a;b$	a\;b
$ab$	a\quad b
$ab$	a\qquad b

---

Text Inside Math

\text{Speed}

Example:

$$v=10\text{ m/s}$$

---

Useful Symbols

Output	LaTeX
$\to$	\rightarrow
$\Rightarrow$	\Rightarrow
$\leftarrow$	\leftarrow
$\leftrightarrow$	\leftrightarrow
$\mapsto$	\mapsto
$\circ$	\circ
$\bullet$	\bullet
$\angle$	\angle
$\perp$	\perp
$\parallel$	\parallel
$°$*	^\circ

---

Most Used Commands

^        Superscript
 
_        Subscript
 
\frac{}{}
 
\sqrt{}
 
\sum
 
\prod
 
\int
 
\lim
 
\partial
 
\nabla
 
\vec{}
 
\mathbf{}
 
\mathbb{}
 
\left ... \right
 
\begin{cases}
 
\begin{aligned}
 
\begin{bmatrix}

Inline math uses $...$

Display math uses:

$$
...
$$