LaTeX Guide

A comprehensive reference for mathematical notation.

Algebra & Fundamentals

Fractions & Roots

\frac{a}{b} + \sqrt{x} + \sqrt[n]{y}

Polynomials & Equations

P(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_0

Quadratic Equations

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

Logarithms

\log_b(x) = y \iff b^y = x

Calculus & Analysis

Differentiations

\frac{d}{dx}(x^n) = nx^{n-1}

Integrations

\int \sin(x) \, dx = -\cos(x) + C

Limits & Continuity

\lim_{x \to \infty} \left( 1 + \frac{1}{x} \right)^x = e

Differential Equations

\frac{d^2y}{dx^2} + k^2y = 0

Trigonometry

Fundamental Identities

\sin^2 \theta + \cos^2 \theta = 1, \quad 1 + \tan^2 \theta = \sec^2 \theta

Compound Angles

\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B

Double & Half Angles

\cos 2\theta = 2\cos^2 \theta - 1, \quad \tan \frac{\theta}{2} = \frac{1 - \cos \theta}{\sin \theta}

Laws of Sines & Cosines

\frac{a}{\sin A} = \frac{b}{\sin B}, \quad c^2 = a^2 + b^2 - 2ab \cos C

Geometry & Shapes

Geometric Figures

\bigcirc \text{ (Circle)}, \quad \square \text{ (Square)}, \quad \triangle \text{ (Triangle)}, \quad \lozenge \text{ (Rhombus)}

Angles & Lines

\angle A = 60^\circ, \quad L_1 \parallel L_2, \quad AB \perp CD

Similarity & Congruence

\triangle ABC \sim \triangle DEF, \quad \triangle ABC \cong \triangle DEF

Arc & Segment

\text{Arc } \stackrel{\frown}{AB}, \quad \text{Ray } \overrightarrow{AB}, \quad \text{Line } \overleftrightarrow{AB}

Science (Physics & Chemistry)

Physics Formulas

E = mc^2, \quad F = G \frac{m_1 m_2}{r^2}, \quad \lambda = \frac{h}{p}

Chemical Reactions

2H_2 + O_2 \longrightarrow 2H_2O, \quad \Delta H < 0

Atomic Notation

{}_{6}^{12}C, \quad {}_{-1}^{0}e, \quad \alpha = {}_{2}^{4}He

Equilibrium

A + B \rightleftharpoons C + D, \quad K_c = \frac{[C][D]}{[A][B]}

Modern & Discrete Math

Boolean Algebra

A \cdot (B + C) = A \cdot B + A \cdot C

Matrices & Determinants

A^{-1} = \frac{1}{|A|} \text{adj}(A)

Probability & Stats

P(A|B) = \frac{P(A \cap B)}{P(B)}

Quick Symbols Reference

\pi
\infty
\pm
\times
\div
\neq
\leq
\geq
\mu
\rho
\omega
\tau
\phi
\psi
\lambda
\Delta
\longrightarrow
\rightleftharpoons
\uparrow
\downarrow
\partial
\nabla
\hbar
\AA

Pro Tip: New to LaTeX?

If you find typing LaTeX code difficult, don't worry! You can use a visual math editor to build your formulas. Simply visit the MathLive Visual Editor, design your equation using their intuitive interface, and then copy the LaTeX code back into our editor. It's a great way to learn and work faster!