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LaTeX Math Guide

Complete reference for writing mathematical equations in LaTeX format

Quick Reference

Fractions: \frac{num}{den}
Powers: x^2 or x^{power}
Subscripts: x_1 or x_{index}
Square Root: \sqrt{x}
Greek Letters: \alpha, \beta, \gamma
Summation: \sum_{i=1}^n

Basic Mathematical Operations

Fractions

\frac{a}{b}
Simple fraction
\frac{x^2 + 1}{x - 1}
Complex fraction
\frac{\partial f}{\partial x}
Partial derivative
\frac{d}{dx}
Derivative operator

Powers and Subscripts

x^2
Simple power
x^{2n+1}
Complex power
x_1, x_2
Simple subscripts
x_{i+1}
Complex subscript
x_i^2
Both power and subscript
x_{i+1}^{2n}
Complex both

Roots and Radicals

\sqrt{x}
Square root
\sqrt{n}{x}
nth root
\sqrt{x^2 + y^2}
Complex expression
\sqrt{3}{x^3 + 1}
Cubic root

Greek Letters

Alpha\alpha
Beta\beta
Gamma\gamma
Delta\delta
Epsilon\epsilon
Zeta\zeta
Eta\eta
Theta\theta
Iota\iota
Kappa\kappa
Lambda\lambda
Mu\mu
Nu\nu
Xi\xi
Omicron\omicron
Pi\pi
Rho\rho
Sigma\sigma
Tau\tau
Upsilon\upsilon
Phi\phi
Chi\chi
Psi\psi
Omega\omega

Common Equations

Quadratic Formula
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Pythagorean Theorem
a^2 + b^2 = c^2
Einstein Mass-Energy
E = mc^2
Newton's Second Law
F = ma
Area of Circle
A = \pi r^2
Volume of Sphere
V = \frac{4}{3}\pi r^3
Derivative Definition
f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
Binomial Theorem
(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k
Euler's Identity
e^{i\pi} + 1 = 0

Tips and Best Practices

  • Use curly braces {} to group expressions: x^{2n+1}
  • Escape backslashes in strings: \\frac instead of \frac
  • Use \left( and \right) for auto-sizing parentheses
  • For inline math, use single $ symbols: $x^2$
  • For display math, use double $$ symbols: $$x^2 + y^2 = z^2$$

External Resources

LaTeX Math Guide - Akowe | Akowe