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Date	Title	Summary	Solutions
January 20	Finding parametric equations	Finding parametric equations for an ellipse Finding parametric equations for a straight line Understanding how changing the interval of parameter values can change the curve that is drawn Analyzing the behavior of curves defined by parametric equations Finding parametric equations for more complicated curves	Answers for recitation activity
January 27	Finding parametric equations and arc length in 3D	Finding and modifying parametric equations for a circle Finding parametric equations for a 3D helical curve Setting up and evaluating an integral for arc length in 3D Learning about the size of human DNA molecules	Answers for recitation activity
February 3	Using Contour Plots to Visualize in 3D	Understanding two dimensional representations of three dimensional objects Finding the contour plot for a function of two variables Using a contour plot to sketch a three dimensional surface Sketching three dimensional graphs of functions with two variables	Answers for recitation activity
February 10	Proving Vector Identities	Performing calculations involving the vector dot product Performing calculations involving the vector cross product Proving statements involving two and three dimensional vectors Using geometrical ideas and formulas to prove vector identities	Answers for recitation activity
February 17	Sketching graphs of quadric surfaces	Recognizing when the graph of a function is a quadric surface Sketching the graph of a surface in 3D using a contour plot Using the formula of a quadric surface to anticipate the appearance of the graph of a function Sketching the graphs of quadric surfaces	Answers for recitation activity
February 24	Limits of functions in two dimensions	Techniques for showing when the limit of a function f(x,y) does not exist Graphical tool/strategy for investigating the existence of two dimensional limits Numerical tool/strategy for investigating the existence of two dimensional limits Algebraic tool/strategy for investigating the existence of two dimensional limits	Answers for recitation activity
March 3	Visualizing linear approximations	Adapting tangent line and tangent plane equations to create an equation for the linear approximation Relating the terms of the linear approximation of f(x,y) to volumes Relating the terms of the linear approximation of f(x,y,z) to volumes Visualizing the linear approximation of f(x,y,z) as a volume	Answers for recitation activity
March 17	Locating global maximums and global minimums	Locating the points on a surface z = f(x,y) where the partial derivatives are both equal to zero Locating the points on a surface z = f(x,y) where at least one of the partial derivatives is undefined Finding the points on the boundary of a region R in the xy-plane where extrema (global maximums and global minimums) may occur Finding the global maximum and global minimum value of f(x,y,z) over a region R	Answers for recitation activity
March 24	Introduction to Lagrange Multipliers	Setting up the Lagrange Multiplier system of equations in two and three dimensions Solving the system of equations to find all solutions Testing the value of the function begin optimized to find the global maximum and global minimum (subject to the constraint)	Answers for recitation activity
March 31	Applications of Double Integrals	Finding limits of integration for double integrals over a non-rectangular region Evaluating double integrals over a triangular region Calculating the x and y coordinates of the center of mass for an object with variable density	Answers for recitation activity
April 7	Setting Up Triple Integrals	Finding limits of integration for triple integrals over a rectangular region Finding limits of integration for triple integrals over a triangular region Finding limits of integration for triple integrals over a non-linear region Evaluating triple integrals with constant, linear and non-linear limits of integration	Answers for recitation activity