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

\item Vectors: Know the basic concepts (length, dot product, cross
product, projection) and typical applications thereof.

\item Equations for lines and planes: Know how to convert between
different forms of these equations, questions similar to the Section
11.5 exercises, equation for tangent plane (Section 12.4).

\item (Quadratic) Surfaces: Sketch the graph of a given equation, and
convert from and to cylinder and spherical coordinates (emphasis on
Section 11.10 exercises).

\item Parametric curves: What are they? How can you eliminate the
parameter?  How can you get some idea about how the graph looks like?

\item Arclength, curvature: Know definitions; what is the arclength
parameterization? Review questions like p.~739 no.~19, 28.

\item Velocity, acceleration: p.~748 no.~19, 20.

\item Functions of several variables: Be able to visualize (describe
and sketch) the graphs (e.g., p.~768 no.~43--52, 59--64).

\item Limits and continuity: Section 12.2 exercises (in particular the
use of polar coordinates to compute limits).

\item Partial derivatives: Know definition, the chain rule needs a lot
of practice. (Section 12.5 exercises!)

\item Differentials: Review, in particular, p.~793 no.~25, 29, 31, 35.

\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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