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\begin{center}{\large\bf Math 325, Quiz 3}\\
{\bf 27 November 1991}\end{center}


1.  Find the solution of the heat conduction problem $u_{xx} = u_t$ with
boundary conditions \newline $$u(0, t) = 0, \   u(1,t) = 0 \;{\rm for \; all}\; t
> 0$$ \newline
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and $$u(x,0) = \sin 3x \ \ \ 0 < x < 1.$$

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2.  The point $(0,\; 0)$ is a critical point of $$\begin{array}{clcr} x' & = & -
\sin x + y \\ y' & = & x^2 - 2ye^y \end{array}$$ 
Find the type and stability of this critical point.
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