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Course18.0235 lectures28 h 22 min

Multivariable Calculus

Prof. Denis Auroux · Massachusetts Institute of Technology

Start with lecture 1 At MIT OpenCourseWare

About

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.

Lectures

Video Lectures

  1. Lecture 1: Dot Product 39 min · Video
  2. Lecture 2: Determinants 53 min · Video
  3. Lecture 3: Matrices 52 min · Video
  4. Lecture 4: Square Systems 50 min · Video
  5. Lecture 5: Parametric Equations 51 min · Video
  6. Lecture 6: Kepler's Second Law 49 min · Video
  7. Lecture 7: Exam Review 50 min · Video
  8. Lecture 8: Partial Derivatives 47 min · Video
  9. Lecture 9: Max-Min and Least Squares 50 min · Video
  10. Lecture 10: Second Derivative Test 53 min · Video
  11. Lecture 11: Chain Rule 51 min · Video
  12. Lecture 12: Gradient 51 min · Video
  13. Lecture 13: Lagrange Multipliers 51 min · Video
  14. Lecture 14: Non-Independent Variables 50 min · Video
  15. Lecture 15: Partial Differential Equations 46 min · Video
  16. Lecture 16: Double Integrals 48 min · Video
  17. Lecture 17: Polar Coordinates 52 min · Video
  18. Lecture 18: Change of Variables 50 min · Video
  19. Lecture 19: Vector Fields 52 min · Video
  20. Lecture 20: Path Independence 51 min · Video
  21. Lecture 21: Gradient Fields 51 min · Video
  22. Lecture 22: Green's Theorem 47 min · Video
  23. Lecture 23: Flux 51 min · Video
  24. Lecture 24: Simply Connected Regions 50 min · Video
  25. Lecture 25: Triple Integrals 49 min · Video
  26. Lecture 26: Spherical Coordinates 52 min · Video
  27. Lecture 27: Vector Fields in 3D 51 min · Video
  28. Lecture 28: Divergence Theorem 50 min · Video
  29. Lecture 29: Divergence Theorem (cont.) 51 min · Video
  30. Lecture 30: Line Integrals 50 min · Video
  31. Lecture 31: Stokes' Theorem 49 min · Video
  32. Lecture 32: Stokes' Theorem (cont.) 51 min · Video
  33. Lecture 33: Maxwell's Equations 29 min · Video
  34. Lecture 34: Final Review 44 min · Video
  35. Lecture 35: Final Review (cont.) 49 min · Video

Syllabus and materials

At MIT OpenCourseWare, as the course publishes them.

Credits and licence

Institution
Massachusetts Institute of Technology
Department
Mathematics
Teacher
Prof. Denis Auroux
Term
Fall 2007
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
MIT OpenCourseWare
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
Attribution
Prof. Denis Auroux. Multivariable Calculus. Fall 2007. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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