| 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.) |