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 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 
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