Catalog

Multivariable Calculus

Mathematics MIT CC BY-NC-SA 4.0 35 lectures

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.

Syllabus

  1. 1 Lecture 1: Dot Product
  2. 2 Lecture 2: Determinants
  3. 3 Lecture 3: Matrices
  4. 4 Lecture 4: Square Systems
  5. 5 Lecture 5: Parametric Equations
  6. 6 Lecture 6: Kepler's Second Law
  7. 7 Lecture 7: Exam Review
  8. 8 Lecture 8: Partial Derivatives
  9. 9 Lecture 9: Max-Min and Least Squares
  10. 10 Lecture 10: Second Derivative Test
  11. 11 Lecture 11: Chain Rule
  12. 12 Lecture 12: Gradient
  13. 13 Lecture 13: Lagrange Multipliers
  14. 14 Lecture 14: Non-Independent Variables
  15. 15 Lecture 15: Partial Differential Equations
  16. 16 Lecture 16: Double Integrals
  17. 17 Lecture 17: Polar Coordinates
  18. 18 Lecture 18: Change of Variables
  19. 19 Lecture 19: Vector Fields
  20. 20 Lecture 20: Path Independence
  21. 21 Lecture 21: Gradient Fields
  22. 22 Lecture 22: Green's Theorem
  23. 23 Lecture 23: Flux
  24. 24 Lecture 24: Simply Connected Regions
  25. 25 Lecture 25: Triple Integrals
  26. 26 Lecture 26: Spherical Coordinates
  27. 27 Lecture 27: Vector Fields in 3D
  28. 28 Lecture 28: Divergence Theorem
  29. 29 Lecture 29: Divergence Theorem (cont.)
  30. 30 Lecture 30: Line Integrals
  31. 31 Lecture 31: Stokes' Theorem
  32. 32 Lecture 32: Stokes' Theorem (cont.)
  33. 33 Lecture 33: Maxwell's Equations
  34. 34 Lecture 34: Final Review
  35. 35 Lecture 35: Final Review (cont.)

Course materials