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
