%Gradients
%If you modify this file, please indicate here and in the footnote
%Math263D

\documentclass[12pt]{article}
\usepackage{times}
\pagestyle{empty}

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\addtolength{\evensidemargin}{-.58in}
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\begin{document}

\begin{center}
{\Large
Gradients
\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(-2:.2:2); &   \\
      \verb&   Z = X.*exp(-X.^2 - Y.^2);&\\
      \verb&   mesh(X, Y, Z)&\\
      Rotate this plot into various positions until you fully understand the shape.


\item Next enter the following:\\
      \verb&   [DX, DY] = gradient(Z);&\\
      \verb&   contour(X,Y,Z) &\\
      \verb&   hold on&\\
      \verb&   quiver(X,Y,DX,DY)&\\
      \verb&   hold off&

\item Repeat the above steps for the functions: 
$f(x, y) = exp(-x^2 - y^2)$ and $f(x, y) = x + y$.

\item What is the relationship between contour (level) curves and gradient vectors?

\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 vector field plot capabilities of
     the program and aid in the understanding of the meaning of the
     gradient.}

\end{document}
