The following list shows a summary of the topics covered in this course. To see all of the course pages, visit the Table of Contents.

Module 1: Parametric Equations and Polar Coordinates

• Parametric Equations
• Calculus of Parametric Curves
• Polar Coordinates
• Area and Arc Length in Polar Coordinates
• Conic Sections

Module 2: Vectors in Space

• Vectors in the Plane
• Vectors in Three Dimensions
• The Dot Product
• The Cross Product
• Equations of Lines and Planes in Space
• Quadric Surfaces
• Cylindrical and Spherical Coordinates

Module 3: Vector-Valued Functions

• Vector-Valued Functions and Space Curves
• Calculus of Vector-Valued Functions
• Arc Length and Curvature
• Motion in Space

Module 4: Differentiation of Functions of Several Variables

• Functions of Several Variables
• Limits and Continuity
• Partial Derivatives
• Tangent Planes and Linear Approximations
• The Chain Rule
• Directional Derivatives and the Gradient
• Maxima/Minima Problems
• Lagrange Multipliers

Module 5: Multiple Integration

• Double Integrals over Rectangular Regions
• Double Integrals over General Regions
• Double Integrals in Polar Coordinates
• Triple Integrals
• Triple Integrals in Cylindrical and Spherical Coordinates
• Calculating Centers of Mass and Moments of Inertia
• Change of Variables in Multiple Integrals

Module 6: Vector Calculus

• Vector Fields
• Line Integrals
• Conservative Vector Fields
• Green’s Theorem
• Divergence and Curl
• Surface Integrals
• Stokes’ Theorem
• The Divergence Theorem

Module 7: Second-Order Differential Equations

• Second-Order Linear Equations
• Nonhomogeneous Linear Equations
• Applications
• Series Solutions of Differential Equations