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 17) 

II. Partial derivatives 
8 
Level curves; partial derivatives; tangent plane approximation 

9 
Maxmin 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 
Nonindependent variables 

15 
Partial differential equations; review 
Problem set 5 due 

Exam 2 (covering lectures 815) 

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 1624) 
Problem set 9 due 
IV. Triple integrals and surface integrals in 3space 
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 2532) 

33 
Topological considerations
Maxwell's equations

Problem set 12 due 
34 
Final review 

35 
Final review (cont.) 

36 
Final exam 
