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Calculus Revisited: Multivariable Calculus

Mathematics MIT CC BY-NC-SA 4.0 26 lectures

Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. _Multivariable Calculus_ is the second course in the series, consisting of 26 videos, 4 Study Guides, and a set of Supplementary Notes. The series was first released in 1971 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time. **About the Instructor** Herb Gross has taught math as senior lecturer at MIT and was the founding math department chair at Bunker Hill Community College. He is the developer of the {{% resource_link "93e1d797-1cc4-4a98-bf28-77b52ec250f3" "Mathematics As A Second Language" %}} website, providing arithmetic and algebra materials to elementary and middle school teachers. **Acknowledgements** Funding for this resource was provided by the {{% resource_link "0baa3cb0-2dbd-4550-9ce3-64edb8a3d204" "Gabriella and Paul Rosenbaum Foundation" %}}. ### Other Resources by Herb Gross [Calculus Revisited: Single Variable Calculus](/courses/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/) [Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra](/courses/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/)

Syllabus

  1. 1 Lecture 1: The "Game" of Mathematics
  2. 2 Lecture 2: "Arrow" Arithmetic
  3. 3 Lecture 3: Three-Dimensional Vectors
  4. 4 Lecture 4: The Dot Product
  5. 5 Lecture 5: The Cross Product
  6. 6 Lecture 6: Equations of Lines & Planes
  7. 7 Lecture 1: Vector Functions of a Scalar Variable
  8. 8 Lecture 2: Tangential & Normal Vectors
  9. 9 Lecture 3: Polar Coordinates
  10. 10 Lecture 4: Vectors in Polar Coordinates
  11. 11 Lecture 1: n-Dimensional Vector Spaces
  12. 12 Lecture 2: Calculus of Several Variables
  13. 13 Lecture 3: Directional Derivatives
  14. 14 Lecture 4: The Chain Rule
  15. 15 Lecture 5: Integrals Involving Parameters
  16. 16 Lecture 6: Exact Differentials
  17. 17 Lecture 1: Linearity Revisited
  18. 18 Lecture 2: The "Game" of Matrices
  19. 19 Lecture 3: Inverting a Matrix
  20. 20 Lecture 4: Inverting More General Systems of Equations
  21. 21 Lecture 5: Maxima and Minima in Several Variables
  22. 22 Lecture 1: Double Multiple Sums
  23. 23 Lecture 2: The Fundamental Theorem
  24. 24 Lecture 3: Multiple Integration and the Jacobian
  25. 25 Lecture 4: Introduction to Line Integrals
  26. 26 Lecture 5: Green's Theorem

Course materials