Vectors - Addition, Dot Product, Direction Cosines

Vector Product, Scalar Triple Product

Equations of a line in space
Equations of a plane in space

Motion of a particle in Space, normal-tangential components, curvature

Quadric Surfaces - Rectangular, Cylindrical, and Spherical Coordinates

Level Curves and Visualization of Surfaces

Partial derivatives of a function of more than one independent variable
Linear approximation of a function with two independent variables

The chain rule for functions of several variables.

The directional derivative, its definition and physical interpretation

Local Maxiima and Minima of Functions
Absolute Maxima and Minima of Functions

Lagrange Multipliers and constrained optimization

Basics of Multiple Integrals and Applications - Double Integrals

Basics of Triple Integrals and Applications
Approximate Volumes using Double Riemann Sums

Uses of Rectangular, Cylindrical, and Spherical Coordinates

Changing the Order of Integration for Multiple Integrals

Change of Variables in Integrals

Vector Fields

Line Integrals

Surface Integrals

Green's theorem

Divergence theorem (Gauss's Theorem)

Stokes' Theorem

Summary of the Calculus of Vector Fields