Module 1:
Vectors and Three-Space

Includes:

• Introduction to Vectors

• Component Description of Vectors

• The Dot Product

• The Cross Product

• Lines and Planes in Three-Space

• Vector-Valued Functions and Space Curves

• Motion in Space

• Cylinders and Quadric Surfaces

Module 2:
Derivatives of Multi-Variable Functions

Includes:

• Functions of More than One Variable

• Limits and Continuity

• Partial Derivatives

• Linear Approximation, Tangent Planes, and Differentiability

• The Gradient and Directional Derivatives

• The Chain Rule

• Optimization

• LaGrange Multipliers

Module 3:
Integrals of Multi-Variable Functions

Includes:

• Double Integrals Over Rectangles

• Double Integrals Over More General Regions

• Introduction to Polar Coordinates

• Double Integrals Over Polar Regions

• Applications of the Double Integral

• The Triple Integral

• Introduction to Cylindrical and Spherical Coordinates

• Integrals in Cylindrical and Spherical Coordinates