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Homework 5 \\
MA/CS 375, Spring 2000 \\
Due May 2 \\
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This homework will count as part of your grade so you must work independently.
It is permissible to discuss it with your instructor, fellow students,
and friends. However, the programs/scripts and report must be done only
by the student doing the project. TURN IN TESTS OF ALL FUNCTIONS YOU WRITE!

\begin{description}
\item[i.] Use $4$, $8$, $16$ and $32$ equispaced points (+1!) and
the Matlab function spline to compute 
interpolants to the following functions:
\begin{enumerate}
\item $e^{-x^2}$, $-2 \leq x \leq 2$.
\item $\frac {1}{1+x^2}$, $-5 \leq x \leq 5$.
\item $\sqrt{x}$, $0 \leq x \leq 4$.
\end{enumerate}
Plot the function together with the four interpolants on one graph. Compute
the maximum error on one hundred equispaced points. (Do NOT interpolate on 
these.) Comment on the convergence.
\item[ii.] 3.3.10
\item[iii.] 4.2.3 
\item[iv.] 4.3.1
\item[v.] 4.4.2
\end{description} 

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