% This is the source file "example.tex" Note that Latex does not
% read lines preeceded by the symbol %, which we can thus use
% to make comments in the source file. The source file is created
% with an editor. 
% To compile (in Unix) the source file "example.tex" type
%                  latex example
% which will produce the binary file "example.dvi" and some
% accessory files "example.aux" and "example.log". If there are
% error messages, go back to the source file and fix the mistakes.
% Note that to make the internal references to work (eg the numbered
% equationsa nd the bibliograpy) you need to type "latex example"
% twice. 
% The file "example.dvi" can be viewed for example by typing
%                  xdvi example
% The best way to use Latex is to keep two windows, one to edit
% the source file and the other to view it. To produce an output
% postscript file type
%                  dvips example
% which will produce the file "example.ps". This file can be then
% printed, or viewed by means of Ghostview
%                  gv example.ps
% pr converted to pdf
%                  ps2pdf example.ps example.pdf


% The following line must be at the beginning of a Latex source file:
\documentclass{article}

% The following line is necessary if you want to include pictures:
\usepackage{graphicx}

% This is where you can define your own symbols if you want, somthing
% which is useful if you use a particular difficult symbol many times:
\newcommand{\rhos}{\rho_s}
\newcommand{\vn}{{\bf {v}}_n}
\newcommand{\bom}{{\mbox{\boldmath $\omega$}}}

% The following must be here to start the document 
\begin{document}

% after which you enter your document.

{\centerline{\bf THIS IS THE TITLE}}
\bigskip

This file shows the basics of Latex.
Using Latex is simple. The text is simply typed in,
no matter
if
you break the lines in the source file. Lines are automatically
indented, like this:

It is possible to force Latex not to indent a new line. To do this
you need to type the right command in the source file, and the result
is the following:
\bigskip

\noindent
Note that latex commands are typically denoted with a backslash.


This is how to quote a book\cite{Poole} or paper\cite{Auton} from
your bibliography.

Here are few examples of symbols: lower and upper case greek 
letters are $\alpha$, $\gamma$, $\Gamma$,
$\lambda$, $\Lambda$; superscripts and subscripts are
$a^2=b_0$, $S_{ijk}$ and $\rho_p$; boldface symbols for vectors are
${\bf A}$, ${\bf r}_p$, ${\bf {\hat a}}$, ${\bf {\widehat {A}}}$. We have also 
$dy/dx=x^3-1$,  $d{\bf r}_p/dt$,
$\infty$, $t \to \infty$,
$\forall$, $\exists$, $\hbar$, $\leftarrow$, $\rightarrow$, $\Leftarrow$,
$\vert$, $\iff$,
$\ell$, $\Re$, $\Im$, $\triangle$, $\circ$, $\bullet$, $\star$,
$\nabla$ $\nabla^2$, $\sum$, $\int$, $\oint$, $\prod$,  $\pm$, $\mp$, $\cdot$,
$\times$, $\wedge$, $\approx$, $\equiv$, $\sim$, $\simeq$, $\not=$, 
$\ll$, $\gg$, $\perp$, $\sqrt{2}$, $\sqrt[3]{2}$,
$\in$, $\ni$, $\leq$, $\geq$, 
Other symbols are $\#$, $\$ $, $\&$, $\{$. Examples of functions are
$\sin{\theta}$, $\cos{(\theta)}$, $\exp{(x)}$.
Examples of accents are: math\'{e}matique, alg\`{e}bre and Schr\"{o}dinger.

Examples of numbered equations are:

\begin{equation}
\frac{du}{dt}=-u,
\label{population}
\end{equation}

\noindent
and

\begin{equation}
\frac{d{\bf u}_p}{dt}=\frac{1}{\tau}({\bf v}_n-{{\bf u}_p}),
\label{motion}
\end{equation}

\noindent 
We can refer to a numbered equation
in the following way: Eq.~(\ref{motion}).

To avoid numbering an equation do the following:

\begin{displaymath}
\frac{D {\bf v}}{Dt}=\frac{\partial {\bf v}}{\partial t}
+({\bf v}\cdot\nabla){\bf v},
\end{displaymath}

Here are more symbols:
$C_k= \sum_{i=0}^{\infty}A_{ki} B_i$.
You can force a big space between one line and the next in this way:
\bigskip

\noindent
or a medium space
\medskip

\noindent
or a small space
\smallskip

\noindent
A very big space is done like this:
\vskip 1truecm


More formulae:  $f_3\approx f_1\gg f_2$ and

\begin{equation}
\int_a^b f(x)dx=\oint_C f(x)dx=K,
\end{equation}

Here are the symbols which I defined before the begin document command:
$\rhos$, $\bom$ and $\vn$.

The following are multi-line formulae; the first is numbered and the
second is not:
\begin{eqnarray}
\left| \frac{1}{\zeta -1} \right |
=\left( \frac{f(x)}{g(x)}\right ),\\
c=d,
\end{eqnarray}

\begin{eqnarray*}
a=b,\\
c=d,
\end{eqnarray*}

Note also the size of the brackets in the first expression.

\noindent
We can have {\it italics} and {\rm roman} characters.
Compare $L\approx 10^4~\rm cm^{-2}$ with
$L\approx 10^4~cm^{-2}$. 

Now force a page break.
\vfill
\eject

Here is how to insert a figure:

\begin{figure}
\centering \includegraphics[height=4.0in,angle=-90]{fig1.epsi}
\caption{Vortex line density $L$  vs time $t$.}
\label{length}
\end{figure}

This is how to make a list:
\begin{enumerate}
\item{} apples
\item{} oranges
\end{enumerate}

Another way is the following:
\begin{itemize}
\item{} banans
\item{} cherries
\end{itemize}


% This is how one does the bibliography:
\begin{thebibliography}{9}

\bibitem{Poole}
D.R. Poole, C.F. Barenghi, Y.A. Sergeev and W.F. Vinen,
{\it Instability of particle paths}, Elsdon University Press (2004).

\bibitem{Auton}
T. R. Auton, J. C. R. Hunt and M. Prud'homme, J. Fluid Mech. {\bf
{197}}, 241 (1988).

\end{thebibliography}

% Finally, the following line must be there to close the document:
\end{document}
