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{\Large {Calculus III, Spring 2000}}\\
\large Review for Midterm II
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\begin{enumerate}

\item Gradients: Definition, geometric interpretation, tangent plane
to level surface, relation with directional derivative.

\item \textbf{Minimum and Maximum Values}: Problems like p.~819,
no.~7, p.~820 no.~25.  Try to avoid the second derivative test.

\item \textbf{Lagrange Multipliers}:  Problems like p.~826 no.~17,
p.~827 no.~23, 29.

\item Simple Double Integrals: See Section 13.2 exercises.

\item Double integrals when the region of integration is not a
rectangle: Problems like p.~850 no.~9.

\item \textbf{Change of Order of Integration}: Problems like p.~850
no.~39.  Always sketch the domain of integration.

\item \textbf{Volume and Area Integrals}:  Problems like p.~850 no.~19.

\item \textbf{Integration in Polar Coordinates}: Problems like p.~856
no.~25.

\item Area and Volume Integrals in Polar Coordinates.  Problems like
p.~856 no.~11, 17.

\item Center of Mass, Moment of Inertia: See Section 13.5 exercises.

\item Surface Area: See Section 13.6 exercises.

\item \textbf{Change of Variables in Double Integrals}: Problems like
p.~887 no.~11, 19.  (Double integrals only.)

\item Triple integrals and integration in cylindrical and spherical
coordinates: Sections 13.7 and 13.8 exercises.

\end{enumerate}

\noindent General notes:

\begin{itemize}

\item No calculators.  A list of infrequently used formulae will be
supplied, if necessary.

\item Paper will be supplied.

\item Remember the \emph{Give Up} option.

\end{itemize}

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