Math 251, Section H1: Multivariable Calculus
Fall 2006

Schedule
Week 
Date of Monday 
Topic 
Workshop 
Homework 
Comments 
1 
Sept. 4 
Points and vectors. Distance between a point and a line. 
Workshop 1. No problem
due. 
p. 797: 5, 9, 28, 30, 32; p. 805: 13, 15, 37, 44 (Hint: do the
twodimensional case first.); Due 9/13. 
No class Monday. 
2 
Sept. 11 
Dot and cross product. Area of a parallelogram. Distance
between skew lines. 
Workshop 2. Problem 2.2
due 9/20. 
p. 797: 4, 7, 18, 42; p. 805: 24, 27, 40; p. 812: 6, 51, 58;
p. 820: 10, 16, 32; Due 9/20. 

3 
Sept. 18 
Equations of surfaces. Cylindrical and spherical
coordinates. 
Workshop 3. Problem 3.4
due 9/27. 
p. 829: 12, 31, 55, 62, 67, 69, 74; p. 837: 9, 2128, 43,
45; p. 843: 19, 27, 48, 49, 55, 68 (Hint: find the angle between
two vectors.); Due 9/27. 
Substitute on Monday and Tuesday. 
4 
Sept. 25 
Plane and space curves. Curvature. 
Workshop 4. Problem 4.2
due 10/4. 
p. 838: 44; p. 855: 6, 13, 26, 36;
p. 861: 3, 15, 18, 48; p. 868: 10, 15, 20, 21, 39, 47, 49, 50
(We'll discuss these last few in class, as well.); Due 10/4. 
Interesting looking space curves of constant curvature
and torsion.
The history of
the subject is worth reading. 
5 
Oct. 2 
Arclength and torsion. Multivariate functions. 
None. 
p. 897: 27, 28, 29, 30, 34, 5338; p. 919: 7, 8, 44, 68ad;
p. 930: 2, 4, 6, 32; Due 10/11. 
Midterm on Wednesday covers material up to section 13.3. Ask
questions on Tuesday! 
6 
Oct. 9 
Partial derivatives. Chain rule. Gradient. Matrices. 
Workshop 5 (updated). Do
both parts of Problem 5.2 concerning the determinant (the last two
bullets). Due 10/18. 
p. 938: 6, 21, 24, 42, 50, 51, 56;
p. 950: 12, 28, 34, 52, 54; p. 961: 5, 8, 32, 39, 46,
51; Due 10/18. 

7 
Oct. 16 
Optimization. Lagrange multipliers. 
Workshop 6. Problem 6.2
due 10/25. 
(Give as many sketches as you can.) p. 970: 3, 6, 14, 18, 23,
40, 43; p. 977: 63; p. 989: 14; p. 994: 9, 10, 16, 23; p. 1002: 7,
13, 23, 24, 37; Due 10/25. 

8 
Oct. 23 
Double integrals. Change of variables. 
Workshop 7. Problem 7.3
due 11/1. 
p. 1022: 6, 7, 10, 13, 22 (We cheated a little in class when
we did this!); p. 1030: 4, 6, 17, 18, 25; p. 1048: 18, 13, 20,
21, 23; Due 11/1. 

9 
Oct. 30 
Surface area. Triple integrals. 
Workshop 8. All problems
due 11/15. 
p. 1048: 9, 10, 15, 17,
22, 24; Due 11/8. 
If you want another viewpoint on the volume of the donut,
perhaps Archimedes
could assist us. What would he say about the surface
area, I wonder? 
10 
Nov. 6 
Vector fields. Line integrals. 
None. 
p. 1060: 5, 21, 23, 25, 26, 33; p. 1071: 1, 3, 4, 10, 20, 22,
24; Due 11/15. 
Midterm on Wednesday. 
11 
Nov. 13 
Div and curl in 2D. Line integrals and Green's
theorem. Rotation of vector fields. 
Workshop 9. Do problem 3
or 4. Due 11/29. 
p. 1081: 4, 5, 7, 16, 20, 33; p. 1089: 1, 2, 4, 10, 12, 21, 27;
Due 11/29. 

12 
Nov. 20 
Divergence form of Green's theorem. 
None. 
None. 
Thanksgiving  no class Tuesday or Wednesday. 
13 
Nov. 27 
Div and curl in 3D. Flux. 
Workshop 10. Do problem
5. Due 12/06. 
p, 1096: 13 (use the fundamental theorem of line integrals),
15, 19, 27, 30, 31, 32; p. 1107: 1116, 21, 24, 32, 41, 44; Due
12/06. 

14 
Dec. 4 
Stokes' Theorem. 
Workshop 11. Do problem
3. Due 12/13. 
p. 1119: 5, 9, 23, 27; p. 1125: 5, 7, 9, 11(a), 19;
p. 1132: 3, 5, 11, 22, 24, 25; Due 12/13. 

15 
Dec. 11 
Catchup. 
None. 
None. 
Wednesday is last day of classes. The final is on Dec. 22
(Friday) from 811am, in the usual classroom. 


