| LEC # | TOPICS | KEY DATES |
|---|---|---|
| I. Vectors and matrices | ||
| 0 | Vectors | |
| 1 | Dot product | |
| 2 | Determinants; cross product | |
| 3 | Matrices; inverse matrices | |
| 4 | Square systems; equations of planes | Problem set 1 due |
| 5 | Parametric equations for lines and curves | |
| 6 |
Velocity, acceleration Kepler’s second law |
|
| 7 | Review | Problem set 2 due |
| Exam 1 (covering lectures 1-7) | ||
| II. Partial derivatives | ||
| 8 | Level curves; partial derivatives; tangent plane approximation | |
| 9 | Max-min problems; least squares | Problem set 3 due |
| 10 | Second derivative test; boundaries and infinity | |
| 11 | Differentials; chain rule | |
| 12 | Gradient; directional derivative; tangent plane | Problem set 4 due |
| 13 | Lagrange multipliers | |
| 14 | Non-independent variables | |
| 15 | Partial differential equations; review | Problem set 5 due |
| Exam 2 (covering lectures 8-15) | ||
| III. Double integrals and line integrals in the plane | ||
| 16 | Double integrals | Problem set 6 due |
| 17 | Double integrals in polar coordinates; applications | |
| 18 | Change of variables | |
| 19 | Vector fields and line integrals in the plane | Problem set 7 due |
| 20 | Path independence and conservative fields | |
| 21 | Gradient fields and potential functions | |
| 22 | Green’s theorem | Problem set 8 due |
| 23 | Flux; normal form of Green’s theorem | |
| 24 | Simply connected regions; review | |
| Exam 3 (covering lectures 16-24) | Problem set 9 due | |
| 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 | Problem set 10 due |
| 28 | Divergence theorem | |
| 29 | Divergence theorem (cont.): applications and proof | |
| 30 | Line integrals in space, curl, exactness and potentials | |
| 31 | Stokes’ theorem | Problem set 11 due |
| 32 | Stokes’ theorem (cont.); review | |
| Exam 4 (covering lectures 25-32) | ||
| 33 |
Topological considerations Maxwell’s equations |
Problem set 12 due |
| 34 | Final review | |
| 35 | Final review (cont.) | |
| 36 | Final exam | |
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