Skip Navigation

Multivariable Calculus

Apply Now Enroll in this Course

Prerequisites: Qualifying math score and completion of Calculus BC

Course Format: Individually Paced

Course Length: Typically 6 months

Recommended School Credit: One full year of high school credit equal to or greater than an AP class or one semester of college credit

Course Code: MVC

Course Description


Multivariable Calculus is an online and individually-paced course that covers all topics in JHU's undergraduate Calculus III: Calculus of Several Variables course. In this course, students will extend what was learned in AB & BC Calculus and learn about the subtleties, applications, and beauty of limits, continuity, differentiation, and integration in higher dimensions. Computer-based interactives, homework and quizzes help to reinforce concepts taught in the class. Online course materials supplement the required textbook.

Each student is assigned to a CTY instructor to help them during their course. Students can contact their instructor via email with any questions or concerns at any time. Live one-on-one online review sessions can be scheduled as well to prepare for the graded assessments, which include quizzes, homework, midterm exams, and a cumulative final. Instructors use virtual classroom software allowing video, voice, text, screen sharing and whiteboard interaction.

Topics include:

  • Vectors in Euclidean space
  • Vector analysis
  • Analytic geometry of three dimensions
  • Curves in space
  • Partial derivatives
  • Optimization techniques
  • Multiple integrals
  • Vector fields
  • Green's theorem
  • Divergence theorem
  • Stokes' theorem
  • Differential forms

For a detailed list of topics, click the List of Topics tab.

Image of Multivariable Calculus banner.

Materials Needed

A textbook purchase is required for this course:

Multivariable Calculus, 7th edition, by James Stewart

  • ISBN10: 0-538-49787-4
  • ISBN13: 978-0-538-49787-9

mvc text

List of Topics

Upon successful completion of the course, students will be able to demonstrate mastery over the following topics:

Vectors and the Geometry of Space

  • Three-Dimensional Coordinate Systems
  • Vectors
  • The Dot Product
  • The Cross Product
  • Equations of Lines and Planes
  • Cylinders and Quadric Surfaces

Vector Functions

  • Vector Functions and Space Curves
  • Derivatives and Integrals of Vector Functions
  • Arc Length and Curvature
  • Motion in Space:  Velocity and Acceleration

Partial Derivatives

  • Functions of Several Variables
  • Limits and Continuity
  • Partial Derivatives
  • Tangent Planes and Linear Approximations
  • The Chain Rule
  • Directional Derivatives and the Gradient Vector
  • Maximum and Minimum Values
  • Lagrange Multipliers

Multiple Integrals

  • Double Integrals over Rectangles
  • Iterated Integrals
  • Double Integrals over General Regions
  • Double Integrals in Polar Coordinates
  • Applications of Double Integrals
  • Surface Area
  • Triple Integrals
  • Triple Integrals in Cylindrical Coordinates
  • Triple Integrals in Spherical Coordinates
  • Change of Variables in Multiple Integrals

Vector Calculus

  • Vector Fields
  • Line Integrals
  • The Fundamental Theorem for Line Integrals
  • Green's Theorem
  • Curl and Divergence
  • Parametric Surfaces and Their Areas
  • Surface Integrals
  • Stokes' Theorem
  • The Divergence Theorem
  • Differential Forms and the General Stokes' Theorem

Back to top

Sample Video Lecture

Sample Video

Vector projection video sample

Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.