
\documentclass[twocolumn,11pt]{article}
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\setlength{\topmargin}{-0.8truein}
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\setlength{\parskip}{10pt}
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\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}

\begin{document}

LaTeX is very flexible and very powerful.
This little example shows you just a tiny bit of 
what it can do.

You create a new paragraph by leaving a blank 
line between sections of text.
In order to change the font from 
regular to {\bf bold} or {\it italic},
you place the desired text inside
``curly brackets'' to isolate it,
and precede it by a LaTeX command;
commands start with a back-slash character.
\{ \textbackslash bf bold \} will make the text {\bf bold}

There are also ways to modify the alignment of 
text, both horizontal and vertical.
For example, one can put a chunk of text

\vskip 12pt
\centerline{\bf into the middle of the page}


Let's go through many examples of creating equations in
LaTeX.  In order to display equations in LaTeX, we 
put the equation stuff between a pair of 
``begin\{equation\}'' and ``end\{equation\}'' statements.

\begin{equation}
y = x^{2x-34}
\end{equation}

Note the number to the right of the equations; that comes
by default.  It's possible to make equations
without the number if you really want to do so.

How about an equation with a square root sign?
We use curly brackets to collect symbols into groups.
Note the difference between the following two examples:

\begin{equation}
v = \sqrt{2gH}
\end{equation}

\begin{equation}
v = \sqrt{2} gH
\end{equation}

You can add your own parentheses if you want to
make it very clear to the reader how the symbols 
ought to be grouped:

% Look, a comment which is NOT included in the formatted output
\begin{equation}
v = \sqrt{2} (gH)
\end{equation}

If you want to express quantities as fractions,
you can use the ``over'' command inside the equation
text to separate the stuff on the top from the stuff
on the bottom.
Note how important it is to place symbols
into the proper groups:
the first example looks okay in the LaTeX source, 
but turns into a big mistake when it is formatted.
The second example uses an extra set of curly brackets
to make sure that all the stuff on the right-hand-side
of the equation actually does remain to the right-hand
side of the equals sign.

% This is not going to work properly
\begin{equation}
x = {-b \pm \sqrt{b^2 - 4ac}}\over{2a}
\end{equation}

% But this will, thanks to an extra set of curly brackets.
\begin{equation}
x = { {-b \pm \sqrt{b^2 - 4ac}}\over{2a} }
\end{equation}

% Mr. Howson asks about subscripts
%    How could I make A-sub-2, for example?
%
\begin{equation}
y = A_2 x
\end{equation}




Superscripts and subscripts are pretty easy to create:
use the carat symbol for superscripts, and the underscore
symbol for subscripts.
If you want to put several symbols together in the superscript
or subscript, use curly brackets to mark them as a group.


% This is not going to work properly
\begin{equation}
V(t) = V_0  e^-t/\tau
\end{equation}

% But this will, thanks to an extra set of curly brackets.
\begin{equation}
V(t) = V_0  e^{-t/\tau}
\end{equation}


% extra equation
\begin{equation}
{ {d^2{x}}\over{{dt}^2} } = A \cos{ \omega t + \phi}
\end{equation}














\end{document}
