Syllabus [PDF; updated 1/22/07 4:00 PM]
Lectures: Tue/Thu 11:00 AM--12:15 PM, 301 Snow Hall
Instructor: Jeremy Martin
Office: 541 Snow Hall
Office hours during finals week: Thursday 5/17, 1:00--4:30 PM,
or by appointment
KU course line number: 63722
Textbook: Vector Calculus, 3rd edn., by Susan Jane Colley
Announcements | Schedule | Homework | Tests | Final Exam | Links
The following is an approximate schedule for the topics to be covered in each lecture. Future days are subject to change.
| Date | Topics | Sections of textbook | Assignments due / notes |
|---|---|---|---|
| Tue 1/23 | Administrivia; vectors; equations of lines; dot products | 1.1, 1.2, 1.3 | |
| Thu 1/25 | Cross products; matrices and determinants; equations of planes | 1.4, 1.5 | |
| Tue 1/30 | More on planes; distance; n-dimensional geometry | 1.5, 1.6 | HW 1 (1.1 - 1.4) |
| Thu 2/1 | Polar, cylindrical, and spherical coordinates; functions | 1.7, 2.1 | |
| Tue 2/6 | QUIZ; graphs of surfaces | 2.1 | HW 2 (1.5 - 2.1) |
| Thu 2/8 | Multivariable limits | 2.2 | Last day of Drop Period I |
| Tue 2/13 | Partial derivatives; tangent planes; differentiability | 2.3 | HW 3 (2.1 - 2.2) |
| Thu 2/15 | General properties of the derivative; the Chain Rule | 2.4, 2.5 | |
| Tue 2/20 | Higher partial derivatives; directional derivatives | 2.4, 2.6 | HW #4 (2.3 - 2.5) |
| Thu 2/22 | Directional derivatives and the gradient; the Jacobian; the Inverse and Implicit Function Theorems | 2.6 | |
| Tue 2/27 | Q&A DAY | HW #5 (2.6 - 2.8) | |
| Thu 3/1 | MIDTERM #1 | ||
| Tue 3/6 | Parameterized curves and arclength | 3.1, 3.2 | |
| Thu 3/8 | Vector fields; gradient and divergence | 3.3, 3.4 | |
| Tue 3/13 | Divergence and curl | 3.4 | HW #6 |
| Thu 3/15 | Multivariable Taylor series; the Hessian | 4.1 | |
| Tue 3/27 | Hessian examples; extrema | 4.2 | HW #7 |
| Thu 3/29 | More extrema; Lagrange multipliers | 4.3 | |
| Tue 4/3 | Areas, volumes and double integrals | 5.1, 5.2 | HW #8 |
| Thu 4/5 | Changing the order of integration; triple integrals | 5.3, 5.4 | |
| Tue 4/10 | Q&A DAY | HW #9 | |
| Thu 4/12 | MIDTERM #2 | ||
| Tue 4/17 | More triple integrals; change of variables; integration in other coordinate systems | 5.4, 5.5 | |
| Thu 4/19 | Applications of integration | 5.6 | Last day of Drop Period II |
| Tue 4/24 | Scalar and vector line integrals | 6.1 | HW #10 |
| Thu 4/26 | Reparameterization; contour integrals; Green's Theorem | 6.1 | |
| Tue 5/1 | Green's Theorem: proof and examples | 6.2 | |
| Thu 5/3 | Applications of Green's Theorem; conservative vector fields | 6.3 | HW #11 |
| Tue 5/8 | Parameterized surfaces; surface integrals | 7.1, 7.2 | |
| Thu 5/10 | Stokes and Gauss's Theorems | 7.2, 7.3 | HW #12 |
Homework is due at 5:00 PM every Tuesday (except days after midterm tests), starting January 30. This makes a total of 12 homework assignments; your two lowest scores (including assignments not turned in) will be dropped. Only turn in the required problems. Not every problem will necessarily be graded, but part of your homework score will be for doing all the assigned problems. The homework is worth 20% of your grade. You can turn in homework in class, leave it in my mailbox in the Math Department office, 405 Snow, or bring it to my office, 541 Snow (if I am not around, you can leave it in the wall box or slip it under my door). Your homework should be as neat and legible as if it were typed, and all sheets should be stapled together.
Turn in only the problems marked "Required". The problems marked "Practice" are mostly drill-type problems and/or similar to one of the required problems, and are not to be turned in.
Each week, I'll choose four or five problems from the "Required" list to be graded for correctness and clarity. About three-quarters of your homework grade will be based on those problems; the remaining one-quarter will be based on completeness -- that is, making at least a reasonable attempt to solve each of the required problems.
Homework turned in late will not be accepted.
Additional problems may be added up to one week before the due date.
| Assignment # | Due date | Sections | Required problems | Practice problems |
|---|---|---|---|---|
| 1 | 1/30 |
1.1 (p. 7) 1.2 (p. 16) 1.3 (p. 25) 1.4 (p. 37) |
2, 4, 6, 11, 16, 24 9, 10, 14, 24, 35, 37(a), 38 2, 6, 8, 10, 14, 17, 24, 28(a) 6, 9, 10, 12, 25, 38 |
3, 5, 12, 14, 23 1, 3, 4, 6, 13, 15, 19, 25, 31, 39 1, 5, 9, 13, 15, 26 1, 3, 4, 7, 11, 19, 26, 39 |
| 2 | 2/6 |
1.5 (p. 46) 1.6 (p. 57) 1.7 (p. 71) |
2, 8, 10, 16, 20, 24, 28, 34 6, 9, 11, 21, 28, 30 10, 14, 23, 24, 25, 26, 32, 37 |
1, 5, 9, 17, 23, 31 1, 5, 7, 8, 22, 23, 25, 26, 31 1, 5, 17, 19, 20 (try doing this without a calculator) |
| 3 | 2/13 |
2.1 (p. 92) 2.2 (p. 107) |
4, 14, 16, 28, 33 12, 14, 18, 22, 28, 40, 46 |
1, 2, 3, 5, 7, 9, 11, 17, 18, 27, 30 3, 4, 5, 8, 11, 13, 15, 31, 41, 43, 48 |
| 4 | 2/20 |
2.3 (p. 124) 2.4 (p. 137) 2.5 (p. 150) |
4, 10, 14, 20, 24, 30, 34, 50 2, 6, 18, 20 2, 6, 10, 16, 22, 28 |
1, 2, 3, 7, 9, 12, 13, 15, 17, 21, 23, 25, 29, 33 1, 3, 5, 10, 11, 13, 17 1, 5, 9, 15, 17, 19, 26, 27, 29 |
| 5 | 2/27 |
2.6 (p. 167) 2.7 (p. 170) 2.8 (p. 171) |
2, 8, 10(a,b) (and optionally (c)), 12, 18, 20, 34 28, 30 6, 8, 18, 26, 30 |
3, 5, 7, 13, 19, 21, 41 1--4, 7--27, 29 1--4, 7, 9, 19--25, 28, 29, 31 |
| 6 | 3/13 |
3.1 (p. 188) 3.2 (p. 206) 3.3 (p. 213) |
2, 4, 8, 10, 16, 26 2, 6, 10 2, 8, 10, 18, 20, 24, 26 |
1, 5, 9, 11, 13, 15, 17, 27 1, 5, 7, 8, 13 1, 11, 12, 17, 21, 23, 25, 17 |
| 7 | 3/27 |
3.4 (p. 221) 4.1 (p. 244) |
1, 2, 4, 6, 8, 12, 23, 28 4, 8, 12, 14, 16, 18 |
3, 5, 7, 9, 13, 14, 15, 24, 25, 29 1, 3, 5, 9, 13, 13, 17, 19 |
| 8 | 4/3 |
4.2 (p. 257) 4.3 (p. 270) |
2, 4, 6, 10, 18, 20, 22, 28, 36 2, 4, 6, 18, 24, 34 |
1, 3, 7, 9, 15, 19 3, 5, 7, 17, 19, 21, 27, 33 |
| 9 | 4/10 |
5.1 (p. 291) 5.2 (p. 308) 5.3 (p. 311) 5.4 (p. 321) |
2, 4, 8, 10, 14 4, 6, 10, 12, 16, 20, 22 4, 8, 14, 16 2, 6, 10 |
1, 3, 5, 7, 11 1, 3, 7, 9, 13, 15, 23, 27 1, 3, 9, 13, 17 3, 7, 9 |
| 10 | 4/24 |
5.4 (p. 321) 5.5 (p. 341) |
12, 20, 24 1, 2, 4, 6, 8, 16, 20, 24, 26 |
11, 15, 23 3, 5, 7, 10, 11, 13, 18, 27 |
| 11 | 5/3 (Changed from 5/1) |
6.1 (p. 379) 6.2 (p. 388) |
1, 2, 4, 6, 8, 14, 20, 24 1, 2, 4, 6, 8, 16, 20 |
3, 5, 7, 9, 15, 21, 23, 27 5, 7, 13, 14, 19 |
| 12 | 5/10 (Changed from 5/8) |
6.3 (p. 399) 7.1 (p. 417) |
1, 2, 4, 8, 12, 18, 20, 22 2, 4, 8, 22, 24 | 5, 7, 9, 11, 13, 19, 21 1, 3, 5, 13, 21, 26 |
There will be a 30-minute quiz in class on Tuesday, February 6, worth 10% of your grade. The quiz will cover material from Chapter 1 of the textbook. This is intended partly as a diagnostic, to give you some idea of how you're doing before the first drop date.
There will be two in-class tests on Thursday, March 1 and Thursday, April 12. Each test is worth 20% of your final grade. Some or all of the Tuesday before each test will be devoted to a review session.
Test #1
Test #2
The final exam is scheduled for Friday, May 18, 10:30 AM--1:00 PM, Snow 301. The exam will cover the entire semester's worth of material, with emphasis on the material not covered on the two midterm tests (starting approximately with Section 5.4). The exam is worth 30% of your final grade.
Here is a review handout, including lists of practice problems.
Review sessions:
The average score on the final exam was 209/300 (70%) and the median was 213/300 (71%). Contact the instructor for more information.