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{\Large Review for Test 2}

\begin{enumerate}[I.]

\item Material covered: 14.1-15.3, especially 14.6-15.3

\item  Study Hints:
	\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 the -- especially the ones
		I have assigned for homework.
	\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 14.1 - 14.5 (could be on the test, but will not be stressed)
	\begin{enumerate}[1.]
	\item  Cartesian coordinates in three space
	\item  Equations in three space (equation of spheres and planes especially).
	\item  Distances in n-space.
	\item  Vector in n-space.
	\item  Angle in n-space
	\item  Cross product in three space.
	\item  Lines and curves in three space: tangent directions, speed,
	\item  Velocity and acceleration of a curve.
	\item  Curvature
	\end{enumerate}

\item  Material in 14.6 - 15.3 (will be the bulk of the test)
	\begin{enumerate}[1.]
	\item  Surfaces in 3-space, especially quadric surfaces
	\item  Recognizing the equation of a surface.
	\item  Recognizing the equation of a ``cylinder''
	\item  Recognizing a quadric surface
	\item  Getting a decent graph of a surface
	\item  Cylindrical and spherical coordinates.
	\item  Converting back and forth between the different coordinates (including converting equations)
	\item  Equations in Cartesian, cylindrical and spherical coordinates.
	\item  Graphing in cylindrical and spherical coordinates.
	\item  Functions of two or more variables.
	\item  Domain and range of a function
	\item  Graphing a function of two variables.
	\item  Graphing level curves of a function of two variables.
	\item  Putting level curves into a 3-dimensional graph
	\item  Partial derivatives - computing
	\item  Partial derivatives - geometric meaning
	\item  Limits - computing
	\item  Continuous functions
	\item  Open and closed sets in the plane.
	\item  Equality of mixed partials
	\end{enumerate}

\item  Good examples of problems to look at.
	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  Be able to graph some of the easier surfaces.
		Good examples would include: 
		\begin{itemize}
		\item  14.6: 1-7, 11,16-20
		\end{itemize}
	\item  Convert coordinates back and forth
		\begin{itemize}
		\item  14.7: 1-4
		\end{itemize}
	\item  Graph in cylindrical and spherical coordinates
		\begin{itemize}
		\item  14.7: 5-12,
		\end{itemize}
	\item  Convert equations between coordinate systems
		\begin{itemize}
		\item  14.7:15-28
		\end{itemize}
	\item  The concepts test of chapter review is a good review
	\item  Sample test problems
		\begin{itemize}
		\item  Especially: 22-34
		\end{itemize}
	\item  Domains of equations
		\begin{itemize}
		\item  You should be able to find the domain of most functions of two variables.
			For example: 15.1: 1-2
		\end{itemize}
	\item  Graphing level curves, and coming up with a graph in 3-space
		\begin{itemize}
		\item  7-14,17-20
		\end{itemize}
	\item  Computing partial derivatives.  Remember all your 1-variable derivative rules!
		\begin{itemize}
		\item  15.2: 1-7,13-16.
		\end{itemize}
	\item  Mixed partials - be able to compute!
		\begin{itemize}
		\item  15.2: 17,19,39,40
		\end{itemize}
	\item  Geometrical interpretation of partials
		\begin{itemize}
		\item  15.2: 25-28
		\end{itemize}
	\item  Notation - understand the different notation for partial derivatives
		\begin{itemize}
		\item  15.2: 37-38
		\end{itemize}
	\item  Finding limits.
		\begin{itemize}
		\item  15.3: 1-8
		\end{itemize}
	\item  Recognizing continuous functions: be able to tell which points a function is or is not
		continuous.  Be able to explain why!
		\begin{itemize}
		\item  15.3: 9-14
		\end{itemize}
	\item  Finding limits along paths: be able to compute the limit as you approach a point from different paths
		\begin{itemize}
		\item  15.3: 15-17
		\end{itemize}
	\item  Be able to sketch a set in the plane
		\begin{itemize}
		\item  15.3: 19-22
		\end{itemize}
	\item  Chapter review:
		\begin{itemize}
		\item  Concepts test: 1-6
		\item  Sample test problems: 1-16
		\end{itemize}
	\end{enumerate}


\end{enumerate}






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