\documentclass[12pt]{article} % BB Jan 11 2013.
\textheight 9.0in
\textwidth  6.0in
\topmargin -1.0in  
\headsep    0.4in  
\oddsidemargin  0.25in  
\evensidemargin 0.25in  

\def\sqr#1#2{{\vcenter{\hrule height.#2pt
   \hbox{\vrule width.#2pt height#1pt \kern#1pt
      \vrule width.#2pt}
   \hrule height.#2pt}}}
\def\square{{\mathchoice\sqr64\sqr64\sqr{4.2}3\sqr{3.0}3}}
\def\undertext#1{$\underline{\smash{\hbox{#1}}}$}
% \pagestyle{empty}

\begin{document} \huge

\begin{center}
{Mathematical Physics --- PHZ 3113}\\\vspace {2mm} 
{Curl Classwork (February 1, 2013)}  % \\
\end{center}
\setcounter{equation}{0}

\centerline{------------------------------------------------------}

\bigskip

\begin{enumerate}

\item Use the Levi-Civita tensor to calculate $\nabla\times\vec{r}$,
where $\vec{r}$ is the position vector.

\item Calculate $\nabla\times\vec{r}\,f(r)$, where $\vec{r}$ is 
the position vector and $r=|\vec{r}|$.

\item Use the Levi-Civita tensor to calculate $\nabla\times\nabla f$, 
where $f$ is an arbitrary scalar function.

\item Derive the wave equation for the magnetic field $\vec{B}$
from Maxwell's equations in vacuum
\begin{eqnarray} \nonumber
  \nabla\cdot\vec{B}=0\,, &~& \nabla\cdot\vec{E}=0\,,\\ \nonumber
  \nabla\times\vec{B}=\epsilon_0\mu_0\frac{\partial\vec{E}}{\partial\,t}
  \,, &~& \nabla\times\vec{E}=-\frac{\partial\vec{B}}{\partial\,t}\,.
\end{eqnarray} 

\item Calculate $\nabla\times\vec{F}$ for 
$\vec{F}=-\hat{x}_1x_2+\hat{x}_2x_1$.

\end{enumerate}

\end{document}

