I. Vectors and matrices
0-Vectors (Note: Video is not available for this topic.)

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

II. Partial derivatives

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

III. Double integrals and line integrals in the plane

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

IV. Triple integrals and surface integrals in 3-space

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 (cont.): applications and proof

30-Line integrals in space, curl, exactness and potentials

31-Stokes' theorem

32-Stokes' theorem (cont.); review

33-Topological considerations - Maxwell's equations

34-Final review

35-Final review (cont.)