Lecture Notes

The notes below represent summaries of the lectures as written by Professor Auroux to the recitation instructors.

I. Vectors and matrices
0 Vectors Week 1 summary (PDF)
1 Dot product
2 Determinants; cross product
3 Matrices; inverse matrices Week 2 summary (PDF)
4 Square systems; equations of planes
5 Parametric equations for lines and curves

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

Topological considerations

Maxwell's equations

Week 14 summary (PDF)
34 Final review
35 Final review (cont.)