Perform basic vector computations, as well as dot and cross products of two vectors and projection of one vector onto another vector.
Convert between cylindrical, rectangular and spherical coordinates. Understand when it’s prudent to switch to one coordinate system over another in computing an integral.
Determine the equation of a plane in 3-d, including a tangent plane to a surface in 3-d.
Find the parametric equations of a line in 3-d.
Perform calculus operations on functions of several variables, including limits, partial derivatives, directional derivatives, and gradients; understand what the gradient means geometrically.
Find maxima and minima of a function of two variables; use Lagrange Multipliers for constrained optimization problems.
Understand divergence and curl of a vector field.
Compute double and triple integrals in rectangular, spherical and cylindrical coordinates; proper use of double or triple integrals for finding surface area or volume of a 3-d region.
Compute line and surface integrals.
Determine if a vector field is conservative and if so, find the corresponding potential function.
Use and understand when to apply Green’s Theorem, Gauss’ Divergence Theorem and Stokes Theorem.