• Plot a point in space.
• Distinguish between right and left handed systems.
• Find the distance between two points.
• Write the equation of a sphere given the center and radius.
• Determine the center and radius of a sphere from a quadratic equation.
• Find the projection of a point onto the xy, yz, and xz planes.
• Describe a region in space using inequalities.

• Find linear combinations of vectors graphically and analytically.
• Find the vector from point A to point B.
• Find the magnitude and direction of a given vector.
• Find the vector given its magnitude and direction.
• Verify properties 1-8 of vectors.

• Calculate the dot product of two vectors.
• Find the angle between two vectors.
• Calculate work.
• Determine whether vectors are orthogonal, parallel, or neither.
• Prove a property of the dot product
• Find the scalar projection of b onto a
• Learn the Cauchy-Schwartz inequality

• Calculuate the cross product of two vectors.
• Interpret the cross product as
  • Torque
  • |a||b|sin(t)n.
• Find areas of a parallelograms and triangles.
• Find the triple cross product and interpret as volume.
• Simplify expressions using properties of cross products.

• Given a point on a line and a vector parallel to the line, write the Vector equation, parametric equations, and symmetric equations for the line.
• Given any of the above equations, identify a point on the line and a vector parallel to the line.
• Tell whether two lines are parallel, skew, or find the point of intersection.
• Given a point on a plane and a normal vector, write the vector equation, the scalar equation, and the standard equation of the plane.
• Given any equation of a plane, find a point on the plane and a vector normal to the plane.
• Tell whether two planes are parallel, and if not, write the equation of the line of intersection.
• Tell whether two planes are perpendicular.
• Find the distance from a point to a plane.

• Identify cylinders and graph them.
• Identify a second degree equations with the corresponding quadric surface and its graph.

• Find the domain of a vector function
• Find the limit of a vector function
• Find a vector function representing the intersection of two surfaces
• Find the derivative of a vector function
• Find the integral of a vector function
• Prove a derivative property of a vector function
• Simplify an expression using the derivative properties of a vector function.

• Given the acceleration, initial velocity, and initial position, find the position at any time.
• Given a position function, find the velocity.
• Given the velocity function, find the acceleration.

• Find values of functions of more than one variable given either formulas or graphs or tables.
• Given a function of two variables, graph its domain and find its range.
• Identify surfaces with their equations using traces.
• Describe how the graph of g(x,y) is related to the graphs of g(x,y)+a, g(x-h,y-k), ag(x,y), -g(x,y), g(x/a,y/b).

• Find limits of multivariate functions.
• Show that limits of multivariate functions do not exist.
• Determine the set of points at which a multivariage function is continuous.

Do 11.2 #4, 5, 20, 21, 26, 29

• Given a contour map of a function, estimate partial derivatives
• Given the equation of a multivariate function, calculate the first and second partial derivatives.
• Show that a function satisfies a particular partial derivative equation.

• Given a multivariate function and a point, find the equation of the tangent plane.
• Given a multivariate function f and a point P, find the linearization of the f at P
• Use the linearization to approximate f at a point.
• Tell when a function is differentiable at a particular point.

• Use the chain rule to find dz/dt if z = f(x,y), x=x(t), y=y(t)
• Use the chain rule to find partial derivatives if z = f(x,y), x=x(r,s), y=y(r,s)
• Use the chain rule to do implicit differentation

• Find the directional derivative of a function at a point in a given direction.
• Find the gradient of a multivariate function at a point.
• Find the maximal value and direction of the directional derivative of a function at a given point.

• Translate a word problem into the form given in class:
  Find [variable(s)] to [Maximize|Minimize]
  [Objective function]
  Subject to
  [Constraints]
• Find stationary points of multivariate functions by setting the gradient to zero.
• Classify stationary points as Max, Min, or Saddle points
• Find boundary maxima and minima

• Use the midpoint rule to estimate a double integral.
• Set up a double integral that represents a volume.
• Evaluate a double integral over a rectangular region using an iterated integral.
• Use the properties of double integrals to simplify computations.

• Set up iterated integrals to represent double integrals over general regions.
• Sketch the region represented by an iterated integral.
• Change the order of integration of an iterated integral.

• Set up iterated integrals to represent double integrals in polar coordinates.
• Sketch the region represented by an iterated integral.
• Convert from Cartesian to Polar Coordinates to evaluate an iterated integral.

• Given a density function of two variables, find the total mass of a region.
• Find the First Moment of a plane region about the x and y axes with double integrals.
• Find the center of mass of a plabe region.
• Find the Moment of inertia of a plane region