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\centerline{Mathematics 371 -- Numerical Analysis}
\centerline{Problem Set 3}
\centerline{\it October 10, 2001}
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From the text:
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$\bullet$ Section 3.1: 1a,c, 3a,c, 3a, 7a, 10, 17, 25, 29.
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{\it However}, change the directions for problem 25 as follows:  Instead
of using the Lagrange form of the interpolating polynomial by hand,
use the following Maple commands to do this problem.  Begin by loading
the {\tt CurveFitting} package with:
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\centerline{\tt with(CurveFitting);}
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The command we want in this package is called {\tt PolynomialInterpolation}
(note the capitalization -- you will need to enter it exactly like 
this).  This function will compute the interpolating of degree $\le n$
for a list of $n+1$ points.  To use it, you can begin by creating 
a list of the $x$-values you want, for instance:
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\centerline{\tt xlist := [0.2,0.35,0.4,0.55];}
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Then do the same for the $y$- or $f(x)$-values you want.  These
should be listed {\it in the same order} as the $x$-values.
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\centerline{\tt ylist := [12.3,13.3,14.5,17.9];}
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Then the command
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\centerline{\tt IP := PolynomialInterpolation(xlist,ylist,x);}
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will compute the interpolating polynomial as a function of the variable
$x$, and assign it to the variable {\tt IP}.  You can then perform any 
other computations you want with this (plotting, differentiating, root-finding,
etc.) 
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Do parts a and b of the problem from the text.  Then add the following part:
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\item{c)}  Plot your interpolating polynomials to visualize where the 
maxima are located.  Do you think these interpolating polynomials
approximate the true weight curves very well?  Explain.
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$\bullet$ Section 3.2/1a, 2a, 5a, 7, 14, 17.
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{\it Assignment}
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Individual writeups due Wednesday, October 17.
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