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Lecture Notes



Lecture Notes

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


LEC #TOPICSLECTURE NOTES
I. Vectors and matrices
0VectorsWeek 1 summary (PDF)
1Dot product
2Determinants; cross product
3Matrices; inverse matricesWeek 2 summary (PDF)
4Square systems; equations of planes
5Parametric equations for lines and curves
6

Velocity, acceleration

Kepler's second law

Week 3 summary (PDF)
7Review
II. Partial derivatives
8Level curves; partial derivatives; tangent plane approximationWeek 4 summary (PDF)
9Max-min problems; least squares
10Second derivative test; boundaries and infinity
11Differentials; chain ruleWeek 5 summary (PDF)
12Gradient; directional derivative; tangent plane
13Lagrange multipliers
14Non-independent variablesWeek 6 summary (PDF)
15Partial differential equations; review
III. Double integrals and line integrals in the plane
16Double integralsWeek 7 summary (PDF)
17Double integrals in polar coordinates; applications
18Change of variablesWeek 8 summary (PDF)
19Vector fields and line integrals in the plane
20Path independence and conservative fields
21Gradient fields and potential functionsWeek 9 summary (PDF)
22Green's theorem
23Flux; normal form of Green's theorem
24Simply connected regions; reviewWeek 10 summary (PDF)
IV. Triple integrals and surface integrals in 3-space
25Triple integrals in rectangular and cylindrical coordinatesWeek 10 summary (PDF)
26Spherical coordinates; surface areaWeek 11 summary (PDF)
27Vector fields in 3D; surface integrals and flux
28Divergence theorem
29Divergence theorem (cont.): applications and proofWeek 12 summary (PDF)
30Line integrals in space, curl, exactness and potentialsWeek 13 summary (PDF)
31Stokes' theorem
32Stokes' theorem (cont.); review
33

Topological considerations

Maxwell's equations

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

 








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