\documentclass[11pt]{article}

\newcommand{\piRsquare}{\pi r^2} % This is my own macro !!!

\title{My Sample \LaTeX{} Document} % used by \maketitle
\author{\L\"{a}rs Schl{\oe}ff\d{o}ng\"{e}n, } % used by \maketitle
\date{July 14, 2005} % used by \maketitle

\begin{document}
\maketitle % automatic title!

I typed this file with a plain text editor. The source file is a mix of
normal text and typesetting commands.

The area of a circle is $\pi r^2$; again, that is $\piRsquare$.  My
score on the last exam\footnote{May 23} was $95 \pm 5$.

\section{Formulas, inline vs.\ displayed}

I insert an inline formula by surrounding it with a pair of single \$
symbols; what is $x = 3 \times 5$?  For a \emph{displayed} formula, use
double-\$ before and after.

$$\mu^{\alpha+3} + (\alpha^{\beta}+\theta_{\gamma}+\delta+\zeta)$$

\subsection{Numbered formulae}

Use the \emph{equation} environment to get numbered formulae, e.g.,
\begin{equation}
  y_{i+1} = x_{i}^{2n} - \sqrt{5}x_{i-1}^{n} + \sqrt{x_{i-2}^7} -1
\end{equation}

\begin{equation}
  \frac{\partial u}{\partial t} + \nabla^{4}u + \nabla^{2}u +
  \frac12    |\nabla u|^{2}~ =~ c^2
\end{equation}

\section{Acknowledgments}

Thanks to my buddies {\AE}schyulus and Chlo\"{e}, who helped me define
the macro \verb9\piRsquare9 which is $\piRsquare$.  The end.

\end{document}             % End of document.
