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\title{A Part III Essay}
\author{A. PartIIIStudent}

\begin{document}

\maketitle

\section{Introduction}

This is LaTeX template constructed very quickly by Peter Haynes from John
Rudge's Part III essay submitted in 2003.

\section{Approach}

Here is a second section and some equations (taken at random from the Rudge
Part III essay). 

Non-dimensionalise all lengths on the gap thickness. Let $h(\theta)=1+\epsilon
\cos \theta$, where $\epsilon$ gives the eccentricity of the annulus.

Introduce the dynamic pressure $p_{dyn}=p-\rho g z$. Henceforth drop the dyn
suffix and work with dynamic pressure.  The thin layer approximations give

\begin{equation*}
\mu \frac{\partial^{2}u_{\theta}}{\partial r^{2}} = \frac{1}{a} \frac{\partial
p}{\partial \theta}
\end{equation*}

\begin{equation*}
\mu \frac{\partial^{2}u_{z}}{\partial r^{2}} = \frac{\partial p}{\partial z}
\end{equation*}

That's enough equations.

\section{Results and Conclusions}

Not every Part III essay will have a Results or Conclusions section.

Here is an example of the use of a Figure. \ref{figure} shows a picture of
something. The figure is taken from the file {\tt picture.eps}.

\begin{figure}
\includegraphics{picture.eps}
\caption{Figure showing a graph of something.}
\label{figure}
\end{figure}

Here is an example of how to cite a book \cite{batchelor} or a paper
\cite{kraichnan} using BibTeX. The relevant information is stored in the file
{\tt bibfile.bib}. Note use of {\tt bibliographystyle} and {\tt bibliography}
commands below. To make this work you need to run {\tt latex}, then {\tt
bibtex}, then {\tt latex} twice more.

A more straightforward option is simply to insert a list of
references directly into the .tex file.

\bibliographystyle{plain}
\bibliography{bibfile}
\end{document}
