LaTeX

LAH-tehk

Usage in Markdown

Surround notation with single $ for inline display. Place $$ in line before and after notation for block display.

Inline: $a+b$ becomes $a + b$
Block:
```
$$
a+b
$$
```
$a + b$

Syntax/Terminology

control sequences — prefixed with \
- also called “commands” or “macros”
- two kinds:
  - Control words — backslash \ + some word: \begin, \frac, \times
  - Control symbols — backslash \ + some symbol: \\, \,, \!

Formatting

Grouping

curly braces {} group content as a single unit
required when a subscript or superscript is more than one character
without braces, $x^10$ renders as $x^{1} 0$ where only the 1 is superscript

Spacing

Command ⇅	Size ⇅	Example ⇅	Output ⇅
`\,`	Thin space	$\int f(x)\,dx$	$\int f (x) d x$
`\quad`	Medium space	$a \quad b$	$a b$
`\qquad`	Large space	$a \qquad b$	$a b$
`\!`	Negative thin space	$a\!b$	$a b$

Text & Style

Command ⇅	Purpose ⇅	Example ⇅	Output ⇅
`\text{}`	Normal text	$x \text{ if } x > 0$	$x if x > 0$
`\mathbf{}`	Bold face	$\mathbf{v}$	$v$
`\mathrm{}`	Upright (“roman”)	$\mathrm{pH}$	$pH$
`\mathbb{}`	Blackboard bold	$\mathbb{R}$	$R$
`\displaystyle`	Full-size in inline mode	$\displaystyle\sum_{k=1}^n$	$k = 1 \sum n$

Auto-Sizing Delimiters

\left and \right scale delimiters to fit content
they must always be paired
- use . as an invisible match if necessary

Example ⇅	Output ⇅
$\left(\frac{a}{b}\right)$	$(\frac{a}{b})$
$\left.\frac{df}{dx}\right\rvert_{a}$	$\frac{df}{d x}_{a}$

Other

usually used to highlight final answer or key result
$\boxed{x=5}$ → $x = 5$

Alignment

aligned

use \begin{aligned} ... \end{aligned} to align multiple lines
& marks the alignment point(s)
\\ marks end of each line
- except the last line, adds extra blank space

ex. place & before the = character to align all equations

$$
\begin{aligned}
2x + 3y &= 7 \\
x - y &= 1
\end{aligned}
$$

2 x + 3 y x - y = 7 = 1

gathered

use gathered when lines should be centered, not aligned at a specific point

$$
\begin{gathered}
  f(x) = x^2 + 2x + 1 \\
  x \in \mathbb{R}
\end{gathered}
$$

f (x) = x^{2} + 2 x + 1 x \in R

Notation

Arithmetic

Notation ⇅	Example ⇅	Output ⇅
Multiplication	$a \times b$	$a \times b$
	$a \ast b$	$a * b$
	$a \cdot b$	$a \cdot b$
Division	$a / b$	$a / b$
	$a \div b$	$a \div b$
	$\frac{a}{b}$	$\frac{a}{b}$
Plus or Minus	$\pm a$	$\pm a$
Roots	$\sqrt{a}$	$a$
	$\sqrt[n]{a}$	$n a$

Equality

Notation ⇅	Example ⇅	Output ⇅
Not Equal	$a \neq b$	$a \neq = b$
Equivalent	$a \equiv b$	$a \equiv b$
Proportional	$a \propto b $	$a \propto b$
Approx.	$a \approx b$	$a \approx b$

Comparison

Notation ⇅	Example ⇅	Output ⇅
Less Than or Equal	$a \leq b$	$a \leq b$
Greater than or Equal	$a \geq b$	$a \geq b$
Much Smaller Than	$a \ll b$	$a ≪ b$
Much Larger Than	$a \gg b$	$a ≫ b$

Algebra

Notation ⇅	Example ⇅	Output ⇅
Absolute Value	$\lvert a \rvert$	$∣ a ∣$
Function Of	$f(x)=x^2$	$f (x) = x^{2}$
Delta	$\Delta x$	$Δ x$
Pi	$\pi$	$π$
Sum	$\sum_{k=3}^5$	$\sum_{k = 3}^{5}$
	$\displaystyle\sum_{k=3}^5$	$k = 3 \sum 5$
Product	$\prod_{x=2}^4$	$\prod_{x = 2}^{4}$
	$\displaystyle\prod_{x=2}^4$	$x = 2 \prod 4$

Angles

Notation ⇅	Example ⇅	Output ⇅
Angle	$\angle$	$∠$
Degree	$30\degree45\rq40\rq\rq$	$30°4 5^{'} 4 0^{''}$
Radians	$2\pi rad$	$2 π r a d$

Probability & Statistics

Notation ⇅	Example ⇅	Output ⇅
Probability	$P(A)$ , $\Pr(A)$	$P (A)$ , $Pr (A)$
Intersection	$P(A \cap B)$	$P (A \cap B)$
Union	$P(A \cup B)$	$P (A \cup B)$
Conditional	$P(A \mid B)$	$P (A ∣ B)$
Median	$\tilde{x}$	$\tilde{x}$
Population Mean	$\overline{x}$	$\overline{x}$
	$\langle x \rangle$	$⟨ x ⟩$

Linear Algebra

Vectors

Notation ⇅	Example ⇅	Output ⇅
Vector	$\mathbf{v}$	$v$
	$\vec{v}$	$v$
Column Vector	$\mathbf{v}=\begin{pmatrix}4\cr5\cr6\end{pmatrix}$	$v = 456$
Row Vector	$\mathbf{v}^T = \begin{pmatrix}1&2&3\end{pmatrix}$	$v^{T} = (123)$
Norm	$\lVert \mathbf{v} \rVert$	$∥ v ∥$

Matrices

Notation ⇅	Example ⇅	Output ⇅
Matrix	$A=\begin{bmatrix}1&2&3\cr4&5&6\end{bmatrix}$	$A = [142536]$
Hadamard Product	$A \circ B$	$A \circ B$
Kronecker Product	$A \otimes B$	$A \otimes B$

Calculus

Notation ⇅	Example ⇅	Output ⇅
Limit	$\lim_{x \to \infty} f(x)$	$lim_{x \to \infty} f (x)$
Derivative Definition	$\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$	$lim_{h \to 0} \frac{f ( x + h ) - f ( x )}{h}$
Partial Derivative	$\frac{\partial f}{\partial x}$	$\frac{\partial f}{\partial x}$
Evaluated At	$\left. \frac{df}{dx} \right\rvert_{x=a}$	$\frac{df}{d x}_{x = a}$
Evaluated Between	$\left. F(x) \right\rvert_a^b$	$F (x) ∣_{a}^{b}$
Integration	$\int f(x) \, dx$	$\int f (x) d x$
Definite Integral	$\int_a^b f(x) \, dx$	$\int_{a}^{b} f (x) d x$
Double Integral	$\iint f \, dA$	$\iint f d A$
Triple Integral	$\iiint f \, dV$	$∭ f d V$
Closed Line Integral	$\oint \mathbf{F} \cdot d\mathbf{r}$	$\oint F \cdot d r$
Gradient	$\nabla f$	$\nabla f$
Infinity	$\infty$	$\infty$
Piecewise Function	$f(x) = \begin{cases} x^2 & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}$	$f (x) = {x^{2} - x if x \geq 0 if x < 0$
Dot Notation (Time)	$\dot{f}$ $\ddot{f}$	$\dot{f}$ $\ddot{f}$
Primes	$f'$ $f''$	$f^{'}$ $f^{''}$

Chemistry

Requires the mhchem LaTex extension. Standard LaTeX treats letters as italic variables and requires verbose workarounds like adding \text{} around every element symbol.

Notation ⇅	Example ⇅	Output ⇅
Chemical Formula	$\ce{H2SO4}$	$H X_{2} SO X_{4}$
Isotope	$\ce{^{14}_{6}C}$	$X_{6}^{14} X_{26}^{214} C$
Ions	$\ce{Ca^2+}$	$Ca X^{2 +}$
	$\ce{Cl-}$	$Cl X^{-}$
Reaction	$\ce{2H2 + O2 -> 2H2O}$	$2 H X_{2} + O X_{2} 2 H X_{2} O$
Reaction Conditions	$\ce{N2 + 3H2 ->[\Delta] 2NH3}$	$N X_{2} + 3 H X_{2} Δ 2 NH X_{3}$
Reversible Reaction	$\ce{A <=> B}$	$A B$
Equilibrium Constant	$K_{eq} = \frac{\ce{[C][D]}}{\ce{[A][B]}}$	$K_{e q} = \frac{[ C ] [ D ]}{[ A ] [ B ]}$
Precipitation	$\ce{Ag+ + Cl- -> AgCl v}$	$Ag X^{+} + Cl X^{-} AgCl ↓$
Physical Units	$\pu{8.314 J mol-1 K-1}$	$8.314 J mo l^{- 1} K^{- 1}$
Bonds	$\ce{A\bond{~}B\bond{~-}C}$	$A - - - - B - - - - - C$
Radical Dot	$\ce{OCO^{.-}}$	$OCO X^{∙ -}$
Arrow with Text	$\ce{A ->[{text above}][{text below}] B}$	$A text above text below B$
Escaped Braces	$\ce{[\{(X2)3\}2]^3+}$	$[{(X X_{2}) X_{3}} X_{2}] X^{3 +}$

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