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{\bf Math 366, Winter `03 \\ Homework 4}
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\noindent{{\bf From Rudin.} pp 239-241: 15, 19, 21, 23

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\noindent{{\bf Profs Personal Problems:}}
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\noindent{\bf 1.} Consider the mapping $f:\R^4\to\R^2$ given by
$$
f(x,y,z,w) = (x^2 - y + z, y^2 - x + w).
$$
Note that $f(1,1,0,0) = (0,0)$. 
\begin{itemize}
\item Show that the equation(s) $f(x,y,z,w) = (0,0)$ can be solved locally
near $(1,1,0,0)$ for $x$ and $y$ in terms of $z$ and $w$.
\item Use linear approximation of $f$ to find a good
approximation $(x_1,y_1)$ of a point $(x,y)$ such that $f(x,y,.1,-.2) =
(0,0)$.
\item Use linear approximation of $f$ (about a slightly different point)
to further improve your first approximation.
\end{itemize}
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