%Contour Plots
%If you modify this file, please indicate here and in the footnote
%Math263C

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\begin{center}
{\Large
Contour Plots\footnote{Copyright \copyright 2002 Steve Chapin, and Todd Young.
All rights reserved. Please address comments to young@math.ohiou.edu.}}
\end{center}

\begin{enumerate}
\item Enter the following commands:\\
      \verb&   [X,Y] = meshgrid(-1:.2:1); &   \\
      \verb&   Z = X.^2 - Y.^2;&\\
      \verb&   contour(Z)&\\
Notice the labeling of the axes. In order to fix this enter instead:
      \verb& contour(X, Y, Z)&

\item Also try the following variations and report what happens:\\
     \verb& contourf(X, Y, Z)&\\
     \verb& contour(X, Y, Z, 10)&\\
     \verb& contour(X, Y, Z, 20)&\\
     \verb& contourf(X, Y, Z, 20)&\\
What is the problem with the last couple of plots?

\item Now try the following alternative way to make contour plots:\\
     \verb& syms x y &\\
     \verb& ezcontour(x^2 - y^2) &

\item Try both commands above to plot the level curves of 
  $z = \sqrt{1 - x^2} - y^2$.

         Notice the squiggles in the curves near the edge. Should those be there?
        Can you find a way to improve this?


\item Write a brief report, using complete sentences and standard mathematical notation.


\end{enumerate}

\vfill
\noindent
\textsf{ The goal of this project is to familiarize the user
     with the contour plot capabilities of
     the program. They should notice that the methods the program uses
     to produce the plots have limitations.}

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