# TeX Math Typesetting -- Showcase
Inline math flows with prose: the mass-energy relation $E = mc^2$,
the golden ratio $\varphi = \frac{1+\sqrt{5}}{2}$, a limit
$\lim_{x \to 0} \frac{\sin x}{x} = 1$, and a binomial
$\binom{n}{k} = \frac{n!}{k!(n-k)!}$ -- all on the baseline.
## Fractions and radicals
$$\frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$$
$$\sqrt[3]{\frac{x^2 + 1}{y - 2}} \qquad \frac{\partial^2 u}{\partial x^2}
+ \frac{\partial^2 u}{\partial y^2} = 0$$
## Big operators with limits
$$\int_{0}^{\infty} e^{-x^2}\,dx = \frac{\sqrt{\pi}}{2}
\qquad \prod_{i=1}^{n} i = n! \qquad \bigcup_{k=1}^{\infty} A_k$$
## Sub/superscript stacks
$$e^{i\pi} + 1 = 0 \qquad x^{y^{z}} \qquad a_{i_{j}} \qquad
\sum_{0 < i < n} x_i^{2}$$
## Delimiters that grow
$$\left( \frac{1}{1 - x^2} \right)^{n}
\qquad \left[ \sum_{k=0}^{N} \frac{1}{k!} \right]
\qquad \left\{ \frac{a}{b} \mid b \neq 0 \right\}$$
## Greek, accents, operators
$$\alpha\beta\gamma\delta\;\Gamma\Delta\Theta\Lambda\Phi\Omega
\qquad \hat{x}\;\bar{y}\;\vec{v}\;\tilde{n}\;\dot{q}
\qquad \nabla \times \mathbf{F} = \mu_0 \mathbf{J}$$
## Matrices and cases
$$A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}
\qquad
## A worked formula
The Schrodinger equation,
$$i\hbar \frac{\partial}{\partial t}\Psi(\mathbf{r}, t) =
\left[ -\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r}, t) \right]
\Psi(\mathbf{r}, t)$$
sits as its own centered block while this paragraph resumes normal
prose flow with an inline aside $\big(\Delta x\,\Delta p \ge \tfrac{\hbar}{2}\big)$ tucked in.
---
Robustness: unmatched `\frac{1}{`, a lone `$`, and `\unknowncmd` must
not break the export -- if you can read this line, nothing panicked.