Date 
Content 
Comments 
M 620 
15.115.3: Review of double integrals in cartesian coordinates 

W 622 
15.415.5: Polar coordinates; applications 

F 624 
15.515.6: Applications continued; surface area. 
Took Quiz 1; solution. 
M 627 
15.7: Triple integration in cartesian coordinates 
Extra practice: Worksheet from Dr. Andy Loveless; worksheet from Dr. Judith Arms. Here are the graphics we looked at today (you need the CDF player to view this). 
W 629 
15.8: Triple integration in cylindrical coordinates 

F 71 
15.9: Triple integration in spherical coordinates 
Graphics for visualizing spherical coordinates. We took Quiz 2; solution. 
M 74 
No class, Independence Day 

W 76 
15.10: Change of variables 

F 78 
Midterm 1; solutions 

M 711 
14.5: The chain rule 

W 713 
14.6: Directional derivatives and the gradient 
Lecture pages 
F 715 
16.1: Vector fields 
Lecture pages. Took Quiz 3; solution. 
M 718 
16.2: Line integrals 
Lecture pages 
W 720 
16.3: Fundamental theorem for line integrals 
Lecture pages 
F 722 
16.4: Green's Theorem 
Lecture pages 
M 725 
16.5: How can we differentiate vector fields? 
Lecture pages 
W 727 
Review day for midterm 2 

F 729 
Midterm 2; solutions; scores. The median was 31.5/50. 
Covers 15.10 (change of variables), 14.56 (derivatives of scalar fields), and 16.116.5. Homework on 16.4 and 16.5 due. First page of the midterm. 
M 81 
16.6: Parametric surfaces 

W 83 
16.6: Parametric surfaces, continued. Begin 16.7: Surface integrals 

F 85 
16.7: Surface integrals, continued. 
16.6 HW parts 1 and 2, due. Lecture pages. Took Quiz 4; solutions. 
M 88 
16.7: Surface integrals, continued (examples of flux integrals). 
16.7 HW part 1 due 
W 810 
16.9: Divergence Theorem 
16.7 HW part 2 due 
F 812 
16.8: Stokes' Theorem 
16.9 HW due 
M 815 
16.8: Stokes' Theorem, continued. Review. 

W 817 
Review for final (16.10) 
16.8 HW due 
F 819 
Final exam. Scores; the median was 32.5/50. 
Emphasizes chapter 16 material, but will also include changeofvariables and the chain rule. You may have one side of one page of handwritten notes. 