This course contains problem sets that accompany each section and module. In these problem sets, students are given an opportunity to apply the quantitative-reasoning skills they learned throughout the module.

Answers are only available to the problems with “Show Solution” links below the question prompt.

Module 1: Parametric Equations and Polar Coordinates

• Problem Set: Parametric Equations
• Problem Set: Calculus of Parametric Curves
• Problem Set: Polar Coordinates
• Problem Set: Area and Arc Length in Polar Coordinates
• Problem Set: Conic Sections
• Module 1 Review Problems

Module 2: Vectors in Space

• Problem Set: Vectors in the Planes
• Problem Set: Vectors in Three Dimensions
• Problem Set: The Dot Product
• Problem Set: The Cross Product
• Problem Set: Equations of Lines and Planes in Space
• Problem Set: Quadric Surfaces
• Problem Set: Cylindrical and Spherical Coordinates
• Module 2 Review Problems

Module 3: Vector-Valued Functions

• Problem Set: Vector-Valued Functions and Space Curves
• Problem Set: Calculus of Vector-Valued Functions
• Problem Set: Arc Length and Curvature
• Problem Set: Motion in Space
• Module 3 Review Problems

Module 4: Differentiation of Functions of Several Variables

• Problem Set: Functions of Several Variables
• Problem Set: Limits and Continuity
• Problem Set: Partial Derivatives
• Problem Set: Tangent Planes and Linear Approximations
• Problem Set: The Chain Rule
• Problem Set: Directional Derivatives and the Gradient
• Problem Set: Maxima/Minima Problems
• Problem Set: Lagrange Multipliers
• Module 4 Review Problems

Module 5: Multiple Integration

• Problem Set: Double Integrals over Rectangular Regions
• Problem Set: Double Integrals over General Regions
• Problem Set: Double Integrals in Polar Coordinates
• Problem Set: Triple Integrals
• Problem Set: Triple Integrals in Cylindrical and Spherical Coordinates
• Problem Set: Calculating Centers of Mass and Moments of Inertia
• Problem Set: Change of Variables in Multiple Integrals
• Module 5 Review Problems

Module 6: Vector Calculus

• Problem Set: Vector Fields
• Problem Set: Line Integrals
• Problem Set: Conservative Vector Fields
• Problem Set: Green’s Theorem
• Problem Set: Divergence and Curl
• Problem Set: Surface Integrals
• Problem Set: Stokes’ Theorem
• Problem Set: The Divergence Theorem
• Module 6 Review Problems

Module 7: Second-Order Differential Equations

• Problem Set: Second-Order Linear Equations
• Problem Set: Nonhomogeneous Linear Equations
• Problem Set: Applications
• Problem Set: Series Solutions of Differential Equations
• Module 7 Review Problems