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{\Large Review for Test 3}

\begin{enumerate}[I.]

\item Material covered: 15.3-16.5, especially 15.9-16.5

\item  Study Hints (same as in review~2):
	\begin{enumerate}[1.]
	\item  Understand the concepts reviews in the sections
	\item  Doing all the problems would, of course, be ideal (I know its not practical)
	\item  Look at EVERY computational problem in EVERY section and do the following
		\begin{enumerate}[a)]
		\item  Determine the concepts needed to solve the problem
		\item  Determine the method involved for solving the problem
		\item  You should have done at least one similar problem (and understood it)
		\item  If you have not done a similar problem, do this one
		\end{enumerate}
		This really should not take too long once you get used to studying this way.
	\item  Look at the ``theoretical'' problems and think about some of them -- especially the ones
		I have assigned for homework and talked about in class.
	\item  Think about the type of problems I did at the board in class.
		If I thought they were important enough to do in class, they are probably 
		important enough to put on test.
	\end{enumerate}

\item Material in 15.3-15.8 (could be on the test, but will not be stressed)
	\begin{enumerate}[1.]
	\item  Limits and continuity.
	\item  Differentiablity, gradiants
	\item  Directional derivatives and gradiants
	\item  Chain rule (several forms of this)
	\item  Tangent planes
	\item  Maxima and minima
	\end{enumerate}

\item  Material in 15.9 - 16.5 (will be the bulk of the test)
	\begin{enumerate}[1.]
	\item  Lagrange's method (what is it and how do we use it?)
	\item  Integrals over rectangles
	\item  Definition of integrals
	\item  Integrability theorem
	\item  Properties of integrals
	\item  Iterated integrals (or how to actually compute integrals)
	\item  Nonrectangular regions
	\item  Polar coordinates - these can be tricky getting the limits of integration right when the 
		region is not a polar rectangle.
	\item  Applications of double integrals - total mass and center of mass
	\end{enumerate}

\item  Good examples of problems to look at in sections 15.9-16.5
	Remember: do not be surprised if the test has problems different from this!
	\begin{enumerate}[1.]
	\item  All of the home work problems (of course!)
	\item  Use Lagrange's method.
		Good examples would include: 
		\begin{itemize}
		\item  15.9: 3,10,17
		\end{itemize}
	\item  Properties of integrals
		\begin{itemize}
		\item  16.1: 5-8
		\end{itemize}
	\item  Computing integrals over rectangles
		\begin{itemize}
		\item  16.1: 1-4
		\item  16.2: 13,21
		\end{itemize}
 	\item  Integrals over nonrectangular regions, be able to sketch the region of integration.
		\begin{itemize}
		\item  16.3: 10,15
		\end{itemize}
	\item  How do you switch order of integration?
		\begin{itemize}
		\item  16.3: 33
		\end{itemize}
 	\item  Integration over non simple regions
		\begin{itemize}
		\item  16.3: 38
		\end{itemize}
 	\item  Integration in polar coordinates
		\begin{itemize}
		\item  16.4: 15
		\end{itemize}
 	\item  Applications (mass)
		\begin{itemize}
		\item  16.5: 5,7
		\end{itemize}
 	\item  Chapter 16 review
		\begin{itemize}
		\item  Concepts test: 1-10
		\item  Sample test: 1-3,5-6,10,12-13,16
		\end{itemize}
	\end{enumerate}


\end{enumerate}






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