1. Surface
sketching
2. Distance
formula and the equation of a sphere
3. Basic vector
operations
4. Dot product
5. Cross product
6. The plane
7. The line
8. Vector-valued
functions
9, Velocity and
acceleration
10. Integrals of
vector-valued functions. Arc length
11. Introduction
to partial derivatives
12. Partial
derivatives - examples
13. The
tangent plane and the differential
14. Chain Rule - Part
1
15. Chain Rule - Part
2
16. Directional
derivatives
17. Gradient - Part 1
18. Gradient - Part 2
19. The potential
function
20. Introduction
to double integrals
21. Double
integrals over rectangular regions
22. Double
integrals over nonrectangular regions
23. Reversing
the order of integration
24. Polar
coordinates - 1
25. Polar
coordinates - 2
26. Area
as a double integral
27. Center of mass
and centroids
28. Triple
integrals - introduction
29. Triple
Integrals in rectangular and cylindrical coordinates
30. More
triple integral practice
31. Spherical
coordinates
32. Change of
variables for multiple integrals
33. Surface
area where z = f(x,y)
34. Surface
area - parametric
35. The torus
problem
36. Critical points
37. Applied max-min
problems
38. More applied
max-min problems