\subsection{\bf Summary of Newton Cotes Rules}

\begin{slide}

\begin{itemize}

\item Both these are equi-spaced (in $x_i$) rules with $g(x)=1$ and
the generalization to arbitrary $n$ are called Newton-Cotes
formulae (see Abramowitz and Stegun to find them explicitly
written out).  

\item We can relax restrictions:
\begin{description}
\item{$\bullet$} (a) $x_i$ equidistant
\item{$\bullet$} (b) $x_0 = a$ and/or $x_n = b$
\item{$\bullet$} (c) $g(x) = 1$
\end{description}

\item The reader need only solve (NI.5) to find relevant formulae for
any $n$.  

\item You will find in the books, discussions of so called open
formulae where $g(x)=1$ as above, but one omits one or both of the
end-points.  The remaining $n$ or $n-1$ points ($x_1 \ldots x_n$ or
$x_0 \ldots x_{n-1}$ or $x_1 \ldots x_{n-1}$) are still equidistant.
\end{itemize}
\end{slide}

