## 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 two-dimensional 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, 21-28, 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, 53-38; p. 919: 7, 8, 44, 68a-d; 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: 1-8, 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 2-D. 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 3-D. 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: 11-16, 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 Catch-up. None. None. Wednesday is last day of classes. The final is on Dec. 22 (Friday) from 8-11am, in the usual classroom.