Lecture topics and homework assignments. Last updated May 7, 2004.
Date |
Section |
Topics |
Notes |
Homework Problems Assigned |
1/21 |
14.1 |
Functions of two or more variables; graphs; level sets. | 23, 27, 29, 35 | |
1/23 |
14.3 |
Meaning of partial derivatives |
Geometric meaning and symbolic meaning | 5,11--16 (all) |
1/26 |
14.3 |
Computing partial derivatives | Examples; higher derivatives; mixed partials. | 21,23,27,36(done in class),45,47,49,51,59 |
1/28 |
14.4 |
Tangent plane to graph of z = f(x,y) | Differentiability at (a,b) means having a good linear approxiamtion at (a, b). Formula for this linear approximation. | 1,3,5; hand in 6. |
1/30 |
14.4 |
More on linear approximation | differentials | 11,13,31,33,35 |
2/2 |
14.5 |
Chain rule | 1,3,5; hand in 6. | |
2/4 |
14.5 |
Chain rule (continued) | Exercise 50 was done in class. | 7,9,11,19,21,41; hand in 42. |
2/6 |
14.6 |
Directional derivative, gradient introduced. | 3,5,7,9,11,13,15; hand in 12 (or 16). | |
2/9 |
14.6 |
Gradient (cont.) | Meaning of of gradient; tanget lines/planes to level sets | 37,39,41,45; hand in 56. Help on 56. |
2/11 |
14.7 |
Finding local maxima and minima | Brief introduction | 3,5,7,9 (find critical points only); hand in 8 from last semester's practice test. |
2/13 |
14.7-8 |
Maxima and minima (cont.) | Local extremes and global extremes. Methods for one variable generalize. Second derivative test. Global extremes on closed bounded sets. | 5,7,9,13,17; hand in 16. |
2/16 |
14.8 |
Lagrange multipliers | 14.7: 29,31,33 (done in class); hand in 32; 14.8: 3,5,7; p963: 57 | |
2/18 |
Review |
Suggestion. Work the practice test without looking at the answers. Attempt to do it all in 50 minutes. If you miss a question, practice on some similar questions. Then attempt the 9/22 test, again allowing yourself only 50 minutes. | ||
2/20 |
ch. 14 |
TEST | Answers: Page1, Page 2, Page 3 | |
2/27 |
15.1-15.2 |
Double integrals and volume. Iterated integrals and Fubini's theorem. Computing iterated integrals using Fundamental Theorem of Calculus. | 15.2: 5,7,9,11 |
|
3/1 |
15.2-15.3 |
More on double integrals over rectangular regions. Integrals over general plane regions | Some solved problems from 15.2. | 15.2: 13,15,17,19,21,25 |
3/3 |
15.3 |
general plane regions (cont.) | 15.3: 3,7,9,11,13,17,33,35,37,39,41 | |
3/5 |
No class. (A make-up class will be scheduled later this semester.) | Complete HW from 3/3!!! | ||
3/8 |
15.3 |
examples |
||
3/10 |
15.4 |
polar coordinates |
15.4:1-17 (odd); hand in 15.4:14 on 3/15 |
|
3/12 |
15.4 |
polar coordinates |
15.4: 19,21,23,25 hand in 15.4:26 on 3/17 |
|
3/15 |
15.7 |
triple integrals |
Express in all 6 orders: the triple integral of f(x,y,z) over the tetrahedron with vertices at (0,0,0), (a,0,0), (0,b,0), (0,0,c) |
|
3/17 |
15.7 |
triple integrals |
15.7: 13,15,29,30 | |
3/19 |
15.8 |
cylindrical and spherical coordinates | hand in 15.7: 32 on 3/22 15.8: 3,5,11,13,17,19,21,35; hand in 15.8: 22, 36 on 3/24 |
|
3/22 |
16.2, 16.6 |
Integrals on parametric curves |
Lecture notes | Do the three exercises in the lecture notes. Solutions |
3/24 |
16.6, 16.7 |
Integrals on parametric surfaces |
See pp. 1083-5, 1093-7. | |
3/26 |
Review 1 | Practice test. Picture for #6. | ||
3/29 |
Review 2 | |||
3/31 |
Integration |
TEST | ||
4/2 |
16.1 |
Vector fields | ||
| 4/5-4/9 | Spring Break | |||
4/12 |
16.2 |
line integrals and work | 16.2: 17,18,19,20 | |
4/14 |
16.3 |
A gradient field is: 1) exact and 2) path independent. | 16.3: 3,5,7,9 | |
4/16 |
16.3 |
Finding potential functions. Path-independent fields are gradient fields | 16.3: 19,21,23,25 | |
4/19 |
16.4 |
Green's Theorem | 16.4: 1,3,7,9; hand in 10 | |
4/21 |
16.5 |
Operations on vector fields | -- | 16.5: 3,5,7 |
4/23 |
16.5 |
Divergence and curl | -- | 16.5: 9,10,11,12,15, 23--29 |
4/26 |
16.7 |
Parametric surfaces (again; see 3/24) |
-- | 16.7:5 |
4/28 |
16.7 |
Flux integrals |
-- | 16.7: 19,21,23,25 |
4/30 |
16.8 |
Stokes Theorem / Take-home exam |
Get a copy of the take-home | -- |
5/3 |
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review/discussion |
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5/5 |
-- |
review/discussion |
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5/7 |
-- |
Take-home exam DUE. |
-- | -- |
5/10 |
FINAL |
In ususal classroom, 3PM--5PM |
To review for final, see review for Fall 2003 |
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