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