The notes below represent summaries of the lectures as written by Professor Auroux to the recitation instructors.
| LEC # | TOPICS | LECTURE NOTES |
|---|---|---|
| I. Vectors and matrices | ||
| 0 1 2 |
Vectors
Dot product Determinants; cross product |
Week 1 summary (PDF) |
|
3
4
5 |
Matrices; inverse matrices
Square systems; equations of planes Parametric equations for lines and curves |
Week 2 summary (PDF) |
| 6 |
Velocity, acceleration Kepler’s second law |
Week 3 summary (PDF) |
| 7 | Review | |
| II. Partial derivatives | ||
| 8 | Level curves; partial derivatives; tangent plane approximation | Week 4 summary (PDF) |
| 9 | Max-min problems; least squares | |
| 10 | Second derivative test; boundaries and infinity | |
| 11 | Differentials; chain rule | Week 5 summary (PDF) |
| 12 | Gradient; directional derivative; tangent plane | |
| 13 | Lagrange multipliers | |
| 14 | Non-independent variables | Week 6 summary (PDF) |
| 15 | Partial differential equations; review | |
| III. Double integrals and line integrals in the plane | ||
| 16 | Double integrals | Week 7 summary (PDF) |
| 17 | Double integrals in polar coordinates; applications | |
| 18 | Change of variables | Week 8 summary (PDF) |
| 19 | Vector fields and line integrals in the plane | |
| 20 | Path independence and conservative fields | |
| 21 | Gradient fields and potential functions | Week 9 summary (PDF) |
| 22 | Green’s theorem | |
| 23 | Flux; normal form of Green’s theorem | |
| 24 | Simply connected regions; review | Week 10 summary (PDF) |
| IV. Triple integrals and surface integrals in 3-space | ||
| 25 | Triple integrals in rectangular and cylindrical coordinates | Week 10 summary (PDF) |
| 26 | Spherical coordinates; surface area | Week 11 summary (PDF) |
| 27 | Vector fields in 3D; surface integrals and flux | |
| 28 | Divergence theorem | |
| 29 | Divergence theorem (cont.): applications and proof | Week 12 summary (PDF) |
| 30 | Line integrals in space, curl, exactness and potentials | Week 13 summary (PDF) |
| 31 | Stokes’ theorem | |
| 32 | Stokes’ theorem (cont.); review | |
| 33 |
Topological considerations Maxwell’s equations |
Week 14 summary (PDF) |
| 34 | Final review | |
| 35 | Final review (cont.) | |
