Geometry in Space, Vectors
 Use the parallelogram law to add geometric vectors.
Resolve geometric vectors into components parallel to
coordinate axes.
 Perform the operations of vector addition and scalar multiplication,
and interpret them geometrically.
 Use the dot product to calculate magnitude of a vector, angle
between vectors,
and projection of one vector on another.
 Find and use direction angles and direction cosines of a vector.
 Use parametric equations for plane curves and space curves.
 Use and convert between parametric and symmetric equations for a
straight line.
 Find a tangent line at a point on a parametric curve; compute the
length of a parametric curve.
 Compute velocity, unit tangent and acceleration vectors along a
parametric curve;
resolve acceleration into tangential and normal components and
compute curvature.
 Use and interpret geometrically the standard equation for a plane.
 Use the cross product; interpret the cross product geometrically and
as area of a parallelogram;
interpret the vector triple product as volume of a parallelopiped.
 Recognize cylinders and quadric surfaces from their Cartesian
equations.
 Use cylindrical and spherical coordinates, and convert among these
two and rectangular coordinates.

Derivatives for Functions of Two or More Variables
 Represent a function of two variables as the graph of a surface;
sketch level curves.
 Calculate partial derivatives and the gradient.
 Use the gradient to find tangent planes, directional derivatives and
linear approximations.
Interpret the gradient geometrically.
 Use the Chain Rule.
 Find and classify critical points of functions, using the second
derivative test.
 Find maximum and minimum values for a function defined on a closed,
bounded, planar set.

Multiple Integrals
 State the definition of the integral of a function over a rectangle.
 Use iterated integrals to evaluate integrals over planar regions, and
to calculate volume.
 Build on elementary integration techniques to evaluate multiple
integrals efficiently.
 Set up and evaluate double integrals in polar coordinates.
 Set up and evaluate integrals to compute surface area.
 Set up and evaluate triple integrals in Cartesian coordinates.
 Use double and triple integrals to compute moments, center of mass,
and moments of inertia.
 Use cylindrical and spherical coordinates; change coordinates from
rectangular to cylindrical or spherical or the reverse.
 Set up and evaluate triple integrals in cylindrical and spherical
coordinates.
 Change the order of variables in multiple integrals.
 Carry out change of variables in multiple integrals.

Vector Calculus
 Calculate the curl and divergence of a vector field.
 Set up and evaluate line integrals of scalar functions or vector
fields along curves.
 Recognize conservative vector fields, and apply the fundamental
theorem for line integrals of conservative vector fields.
 State and apply Green's Theorem.
 Set up and evaluate surface integrals; compute surface area and
the flux of a vector field through a surface.
 Set up and evaluate integrals over parametric surfaces.
 State and apply the Divergence Theorem.
 State and apply Stokes' Theorem.
