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{\Large {Calculus III, Spring 2000}}\\
\large Review for Final Exam
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\begin{enumerate}

\item Vector Calculus: Know all of the formulas on p.~962.  (None of
them will be given to you on the exam!)  Be able to explain all the
symbols used, particularly the definition of the line and surface
integrals.

\item Be able to derive identities of vector calculus. Examples:
p.~963 no.~28--31, related problems from the Chapter 14 homework
assignments, and Theorem~3 on p.~924 or Theorem~11 on p.~927.

\item Typical Divergence Theorem problems: Use the Divergence Theorem
to convert a surface integral into a triple integral; see p.~964
no.~42 and Section 14.9 exercises.

\item Typical Stokes' and Green's Theorem problems:  Convert line
integrals to surface integrals, and vice versa.  See the homework
problems from Section~14.4 and~14.8.

\item Conservative (Gradient) Vector Fields: How do you check if a
  vector field is conservative?  What does this test have to do with
  Stokes' Theorem?  How do you find the potential?

\item Total Mass, Center of Mass, Moment of Inertia:  Pay attention to
p.~923 no.~24, 25 when you revise.

\item Be able to graph a Vector Field. (Section 14.1 exercises.)

\item Multiple Integrals:  All topics from the second Midterm.  Pay
particular attention to the change of order of integration in double
integrals (p.~888 no.~16), triple integrals in spherical coordinates
(p.~889 no.~55), and integration in polar coordinates (p.~856 no.~32).

\item Minimax Problems (with or without constraints): These will be a
substantial portion of the exam!  Problems like p.~829 no.~63, 71.

\item Chain rule: See p.~829 no.~49.

\item Gradients and directional derivatives: p.~829 no.~52, 55.

\item Find equation for a tangent plane: p.~829 no.~39.

\item Differentials: p.~828 no.~44.
  
\item Check you knowledge of Chapter 11 material.  Most of it is
  working knowledge for the later Chapters anyway, but do expect a
  direct question on some Chapter 11 topic.

\end{enumerate}

\subsubsection*{Office hour schedule for Finals week:}
\begin{tabular}{@{}lll}
Friday, April 28 & 12:00 noon--1:00 p.m. & Royce, DRB 213 (!) \\
Monday, May 1 & 12:00 noon--1:00 p.m. & Royce, DRB 213 \\
              & 7:00--8:00 p.m. & M.O., DRB 230 \\
Tuesday, May 2 &2:00--4:00 p.m. & M.O., DRB 230 \\
or by appointment.
\end{tabular}

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