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MIT 18.02 Multivariable Calculus

By MIT OpenCourseWare

Course audio
Course audio: English
Level
Advanced
Length
15 lessons

What you'll be able to do

  • Use vectors, planes and the cross product in 3D
  • Compute partial derivatives, gradients and constrained extrema
  • Evaluate multiple and line integrals

About this course

MIT's second-semester calculus course with Professor Denis Auroux, recorded in 2007. The lectures begin with the dot product, determinants and the cross product, matrices and inverse matrices, and equations of planes, then cover parametric curves, partial derivatives, gradients, Lagrange multipliers, double and triple integrals, line integrals and the theorems of Green, Gauss and Stokes. It suits engineering and physics students after a first calculus course. Follow with MIT 18.03 Differential Equations.

Before you start: Single-variable calculus (e.g. MIT 18.01)

Syllabus

Sabaq lists the first 15 videos of this playlist; the rest continue on YouTube. Full playlist on YouTube

  1. 1Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007
  2. 2Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007
  3. 3Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007
  4. 4Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007
  5. 5Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007
  6. 6Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007
  7. 7Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007
  8. 8Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07
  9. 9Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007
  10. 10Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007
  11. 11Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007
  12. 12Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07
  13. 13Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007
  14. 14Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007
  15. 15Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007

What to take next

Related courses

Videos by MIT OpenCourseWare, played from their official YouTube channel. Subscribe on YouTube

Licence: CC BY-NC-SA 4.0, MIT OpenCourseWare, ocw.mit.edu. Free for everyone, never sold.

Sabaq lists the first 15 videos of this playlist; the rest continue on YouTube. Full playlist on YouTube

Lessons last checked Oct 2026. Course summary and lesson structure by Sabaq.

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