Calendar

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