| I. | Vectors and matrices |
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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
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| 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.) |
