latex

Basics

Inline Math: … or $ … $

Display Math: … or

Equation Environment:

\begin{equation} … \end{equation}

Greek Letters

Lowercase: \alpha, \beta, \gamma, \delta, \epsilon, \theta, \lambda, \mu, \pi, \sigma, \phi, \omega

Uppercase: \Gamma, \Delta, \Theta, \Lambda, \Pi, \Sigma, \Phi, \Omega

Superscripts and Subscripts

Power: x^2 produces $$ x^2 $$

Subscript: x_1 produces $$ x_1 $$

Fractions

Basic Fraction: \frac{a}{b} produces $$ \frac{a}{b} $$

Binomial Coefficient: \binom{n}{k} produces $$ \binom{n}{k} $$

Roots

Square Root: \sqrt{x} produces $$ \sqrt{x} $$

nth Root: \sqrt[n]{x} produces $$ \sqrt[n]{x} $$

Sums and Integrals

Summation: \sum_{i=1}^n produces $$ \sum_{i=1}^n $$

Integral: \int_{a}^{b} produces $$ \int_{a}^{b} $$

Functions

Standard Functions: \sin, \cos, \tan, \ln, \exp

Limits: \lim_{x \to \infty} produces $$ \lim_{x \to \infty} $$ Brackets and Parentheses

Standard: ( … ), [ … ], { … }

Adjustable Size: \left( … \right), \left[ … \right], \left{ … \right}

$$ \left( … \right), \left[ … \right], \left{ … \right} $$

Matrices

Basic Matrix:

\begin{matrix} a & b \ c & d \end{matrix}

$$ \begin{matrix} a & b \ c & d \end{matrix} $$

Bracketed Matrix:

\begin{bmatrix} a & b \ c & d \end{bmatrix}

$$\begin{bmatrix} a & b \ c & d \end{bmatrix}$$

Parenthesis Matrix:

\begin{pmatrix} a & b \ c & d \end{pmatrix}

$$ \begin{pmatrix} a & b \ c & d \end{pmatrix} $$

Symbols

Equality: =

Approximation:

\approx for $$\approx $$ \sim for $$ \sim $$ Inequalities: \leq, \geq, <, >

Arrow Symbols: \rightarrow, \leftarrow, \Rightarrow, \Leftarrow

Infinity: \infty $$ \infty $$

Partial Derivative: \partial

$$ \partial $$

Sets and Logic

Belongs To: \in for $$ \in $$ Subset: \subset, \subseteq

Union/Intersection: \cup, \cap

Empty Set: \emptyset

Logic Symbols: \land for , \lor for , \neg for

Special Notations

Vectors: \vec{v} for , \mathbf{v} for bold

Overline: \overline{x} produces

Hat: \hat{x} produces

Accents

Dot/Double Dot: \dot{x}, \ddot{x}

Bar: \bar{x} produces

Examples

1. Quadratic Formula:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

2. Limit Definition of Derivative:

$$ f’(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} $$

Basics

Superscripts and Subscripts

Power: x^2 produces $$ x^2 $$

Subscript: x_1 produces $$ x_1 $$

Fractions

Basic Fraction: \frac{a}{b}

Roots

Square Root: \sqrt{x} produces $$ \sqrt{x} $$

nth Root: \sqrt[n]{x} produces $$ \sqrt[n]{x} $$

Sums and Integrals

Summation: \sum_{i=1}^n produces $$ \sum_{i=1}^n $$

Integral: \int_{a}^{b} produces $$ \int_{a}^{b} $$

Functions

Standard Functions: \sin, \cos, \tan, \ln, \exp

Limits: \lim_{x \to \infty} produces $$ \lim_{x \to \infty} $$ Brackets and Parentheses

Standard: ( … ), [ … ], { … }

Adjustable Size: \left( … \right), \left[ … \right], \left{ … \right}

$$ \left( … \right), \left[ … \right], \left{ … \right} $$

Matrices

Basic Matrix:

\begin{matrix} a & b \ c & d \end{matrix}

$$ \begin{matrix} a & b \ c & d \end{matrix} $$

Bracketed Matrix:

\begin{bmatrix} a & b \ c & d \end{bmatrix}

$$\begin{bmatrix} a & b \ c & d \end{bmatrix}$$

Parenthesis Matrix:

\begin{pmatrix} a & b \ c & d \end{pmatrix}

$$ \begin{pmatrix} a & b \ c & d \end{pmatrix} $$

Symbols

Equality: =

Approximation:

\approx for $$\approx $$ \sim for $$ \sim $$ Inequalities: \leq, \geq, <, >

Arrow Symbols: \rightarrow, \leftarrow, \Rightarrow, \Leftarrow

Infinity: \infty $$ \infty $$

Partial Derivative: \partial

$$ \partial $$

Sets and Logic

Belongs To: \in for $$ \in $$ Subset: \subset, \subseteq

Union/Intersection: \cup, \cap

Empty Set: \emptyset

Logic Symbols: \land for , \lor for , \neg for

Special Notations

Vectors: \vec{v} for , \mathbf{v} for bold

Overline: \overline{x} produces

Hat: \hat{x} produces

Accents

Dot/Double Dot: \dot{x}, \ddot{x}

Bar: \bar{x} produces

Examples

1. Quadratic Formula:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

2. Limit Definition of Derivative:

$$ f’(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} $$

$\mathbf{a} \times \mathbf{b}$