LaTeX Playground

Welcome to the LaTeX playground! Edit this content to see live preview of LaTeX and mhchem rendering.

Basic Math

Inline math: The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Display math:

$\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$

Fractions and Powers

$\frac{a}{b}$, $\frac{1}{\sqrt{2}}$, $x^2$, $x^{n+1}$, $e^{i\pi} + 1 = 0$

Greek Letters

$\alpha$, $\beta$, $\gamma$, $\delta$, $\epsilon$, $\theta$, $\lambda$, $\mu$, $\pi$, $\sigma$, $\phi$, $\psi$, $\omega$

$\Gamma$, $\Delta$, $\Theta$, $\Lambda$, $\Pi$, $\Sigma$, $\Phi$, $\Psi$, $\Omega$

Calculus

Derivatives: $\frac{d}{dx}f(x) = f'(x)$

Integrals: $\int_a^b f(x) dx$, $\oint_C f(z) dz$

Partial derivatives: $\frac{\partial f}{\partial x}$, $\nabla f$

Chemistry with mhchem

Simple molecules: $\ce{H2O}$, $\ce{CO2}$, $\ce{CH4}$, $\ce{NH3}$

Chemical reactions:

$\ce{2H2 + O2 -> 2H2O}$

$\ce{CaCO3 + 2HCl -> CaCl2 + H2O + CO2 ^}$

Equilibrium:

$\ce{N2 + 3H2 <=> 2NH3}$

Rate equations:

$\ce{A + B ->[k1] C}$

Complex molecules:

$\ce{CH3CH2OH}$, $\ce{C6H12O6}$

Ions and charges:

$\ce{Na+}$, $\ce{Cl-}$, $\ce{SO4^2-}$, $\ce{Fe^3+}$

Electron configurations:

$\ce{[Ar] 3d^10 4s^1}$

Physics

Force: $\vec{F} = m\vec{a}$

Energy: $E = mc^2$

Wave equation: $\psi(x,t) = Ae^{i(kx - \omega t)}$

Schrödinger equation:

$i\hbar\frac{\partial \psi}{\partial t} = \hat{H}\psi$

Maxwell's equations:

$\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}$

$\nabla \times \vec{B} = \mu_0\vec{J} + \mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t}$

Statistics

Normal distribution: $f(x) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$

Bayes' theorem: $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$

Set Theory

$A \cup B$, $A \cap B$, $A \subset B$, $x \in A$, $\emptyset$, $\mathbb{R}$, $\mathbb{N}$, $\mathbb{Z}$

Logic

$\forall x \in \mathbb{R}$, $\exists y \in \mathbb{N}$, $\land$, $\lor$, $\neg$, $\implies$, $\iff$

Try editing this content to test your own LaTeX!