Change of Variables

Lecture Description

Course Description

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.

Related Resources

Summary of Lectures 18, 19 & 20   |  Problem Set 7

Course Index

1. Dot Product
2. Determinants; Cross Product
3. Matrices; Inverse Matrices
4. Square Systems; Equations of Planes
5. Parametric Equations for Lines and Curves
6. Velocity, Acceleration - Kepler's Second Law
7. Review: Vectors and Matrices
8. Level Curves; Partial Derivatives; Tangent Plane Approximation
9. Max-Min Problems; Least Squares
10. Second Derivative Test; Boundaries and Infinity
11. Differentials; Chain Rule
12. Gradient; Directional Derivative; Tangent Plane
13. Lagrange Multipliers
14. Non-Independent Variables
15. Partial Differential Equations; Review
16. Double Integrals
17. Double Integrals in Polar Coordinates; Applications
18. Change of Variables
19. Vector Fields and Line Integrals in the Plane
20. Path Independence and Conservative Fields
21. Gradient Fields and Potential Functions
22. Green's Theorem
23. Flux; Normal Form of Green's Theorem
24. Simply Connected Regions; Review
25. Triple Integrals in Rectangular and Cylindrical Coordinates
26. Spherical Coordinates; Surface Area
27. Vector Fields in 3D; Surface Integrals and Flux
28. Divergence Theorem
29. Divergence Theorem (continued): Applications and Proof
30. Line Integrals in Space, Curl, Exactness and Potentials
31. Stokes' Theorem
32. Stokes' Theorem (continued); Review
33. Topological Considerations - Maxwell's Equations
34. Multivariable Calculus Final Review
35. Multivariable Calculus Final Review (continued)