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{\Large Review for Final}

\begin{enumerate}[I.]

\item Material covered: 13.1-17.4

\item  Format: Same format as other in class exams.
	The test will slightly stress the material in chapter 17 more then other sections.

\item  Cheat-sheet: One hand written cheat sheet will be allowed.
	After starting to write up a formula sheet, I decided that this would be easier for everyone.


\item Chapter 13: Plane curves, vectors, vector valued functions, curvature, acceleration.
	\begin{enumerate}[1.]
	\item  Graphing plane curves.
	\item  Manipulating vectors
	\item  Vector valued functions
	\item  Computing curvature of plane curves (lots of formulas!)
	\item  Normal and tangential components of acceleration (several formulas)
	\end{enumerate}


\item  Chapter 14:  Vectors, cross product, curvature, acceleration, surfaces, cylindrical and spherical coordinates.
	\begin{enumerate}[1.]
	\item  Vectors in three space
	\item  Computing cross product and dot product (and what it means)
	\item  Working with curves in 3-space
	\item  Velocity, acceleration and curvature of curves in 3-space.
	\item  Normal and tangential components of acceleration.
	\item  Graphing surfaces in $\R^3$.
	\item  Working with cylindrical and spherical coordinates.
	\end{enumerate}


\item  Chapter 15:  Function of several variables, partial derivatives, differentiability, gradiants, 
	directional derivatives, chain rule, tangent planes, max and mins, Lagrange.
	\begin{enumerate}[1.]
	\item  Working with real valued funtions of several variables.
	\item  Taking partial derivatives
	\item  Derivative of functions of several variables.
	\item  Finding the gradiant and directional derivatives
	\item  Using the chain rule for functions of several variables.
	\item  Finding tangent planes
	\item  Finding maxima and minima (critical points and second derivative test)
	\item  Using Lagrange's method to find maxima and minima with constraints.
	\end{enumerate}


\item  Chapter 16:  Double integrals (rectangles and other), polar coordinates, applications, surface area, 
	triple integrals, change of coordinates.
	\begin{enumerate}[1.]
	\item  Definition of integration
	\item  Integrability theorem
	\item  Iterated integrals
	\item  Finding the limits of integration for iterated integrals
	\item  Change of variables (polar, cylindrical, spherical and in general)
	\item  Applications (Mass)
	\item  Surface area - finding
	\item  Triple integrals (volumes, finding limits of integration)
	\end{enumerate}


\item  Chapter 17:  Vector fields, line integrals, independance of path, Greens theorem.
	\begin{enumerate}[1.]
	\item  Vector fields - graphing
	\item  Line integrals - computing
	\item  Independance of path - finding potential functions and using to compute line integrals
	\item  Greens theorem: applying it to problems (all forms of Green's theorem)
	\end{enumerate}


\end{enumerate}






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