\documentclass[12pt,a4paper]{article}

% Set the page dimensions... there are lots of other ways to 
% do this by specifying marginwidths etc...

\textheight=24cm
\textwidth=17cm
\voffset=-20mm
\hoffset=-0.95in

\title{Another Sample Document showing some maths}
\author{Diki Porter}

\begin{document}

\maketitle

To get maths in line with your normal text, you do something
like this $x+y=1$, where $x < 1$ and $y \geq 1$.\\
\\
Here's something more complicated: Define polar coordinates
$(r,\theta)$ where $x = r \cos \theta$ and $y = r \sin \theta$.\\
\\
There are loads of other standard functions, such as 
$\exp$, $\log$, $\tan$, $\arccos$.\\
\\
\\
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How do we get maths to appear in the display:
\[
 x^{2}+y^{2} = 1
\]
Here we have used superscripts. Also, we can have
\begin{displaymath}
 f_{i}^{2} \approx a_{0} + (x-x_{i}) a_{1} 
\end{displaymath}
\\
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These equations are not labelled. To get labelling of equations use
this environment:
\begin{equation} \label{eqn:1}
 a_{ij} = x_{i} - y_{j}, \qquad i,j=0,1
\end{equation}
I can then reference this equation by saying in equation (\ref{eqn:1})
we showed...
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What about other ~~~~~~ more complicated constructs ?
\begin{equation} \label{sum}
 \lim_{N \to \infty} \sum_{n=0}^{N} \frac{1}{n^{2}} = \frac{\pi^2}{6}
\end{equation}
or
\begin{equation}
 \int_{\alpha}^{\beta} \log(x) \mathrm{d} x = \left[ x \log(x) - x
 \right]_{\alpha}^{\beta}
\end{equation}


\end{document}
