\documentclass[12pt]{article}
\usepackage{graphicx,amsthm,fullpage}

\newtheorem*{theorem}{Theorem}  %This defines the "theorem environment" used below.

\title{Lab 2: Clairaut's Theorem}
\author{Put authors here}

\begin{document}

\maketitle

\section*{Introduction}

Introduction...

\begin{theorem}[Clairaut]
Suppose $f$ is defined on a disk $D$ that contains the point $(a,b)$.  If
the functions $f_{xy}$ and $f_{yx}$ are both continuous on $D$, then
$$f_{xy}(a,b) = f_{yx}(a,b).$$
\end{theorem}

...  We will consider a certain function that will not satisfy these hypotheses,
and will give an example of a function and a point for which 
$f_{xy}(a,b)\neq f_{yx}(a,b)$.

\section*{New Section}


Here is the function for you:
$$
f(x,y) = \left\{ \begin{array}{rl} 
  \displaystyle \frac{xy(x^2-y^2)}{x^2+y^2} & (x,y)\neq (0,0) \\
  0 & (x,y)=(0,0) 
\end{array} \right.
$$
%  LATEX NOTE:  The command "\displaystyle" on line 37 makes the fraction big.  
%     To see what that means, you might try deleting it.
%
% Example figure:
%\begin{figure}  
%\begin{center}  
%\includegraphics[height=7in,width=5in,angle=90]{file.eps}  
%\caption{This is a caption}
%\label{FigWhatever}  %A label is used in case you need to refer to it in the text  
%\end{center}  
%\end{figure}  


\section*{Another Section?}

\section*{Conclusions}

\end{document}
