Change of Variables, Jacobians

Lecture Description

Course Description

Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.

Course Index

1. Areas and Lengths in Polar Coordinates
2. Vectors, Dot Product
3. Cross Product, Determinant
4. Lines and Planes
5. Cylinders and Quadric Surfaces
6. Vector-Valued Functions and Space Curves
7. Functions of Several Variables
8. Limits and Continuity
9. Partial Derivatives
10. Tangent Planes and Linear Approximations
11. The Chain Rule
12. Directional Derivatives and the Gradient Vector
13. Maxima and Minima
14. More Maxima and Minima; Lagrange Multipliers
15. Midterm Review
16. More Lagrange Multipliers
17. Double Integrals Over Rectangles
18. Double Integrals over General Regions
19. Double Integrals in Polar Coordinates
20. Applications of Double Integrals
21. Triple Integrals
22. Triple Integrals in Cylindrical Coordinates
23. Triple Integrals in Spherical Coordinates
24. Change of Variables, Jacobians
25. More change of variables and Jacobians
26. Vector Fields
27. Line Integrals
28. Green's Theorem I
29. Green's Theorem II
30. Curl and Divergence
31. Parametric Surfaces
32. More Parametric Surfaces; Surface Integrals, part I
33. Surface Integrals, part II
34. Surface Integrals, part III
35. Stokes' Theorem I
36. Stokes' theorem II
37. Divergence Theorem I
38. Divergence theorem II
39. Review I
40. Review II