Math 226 - Spring 2009

What is multivariable calculus? Multivariable calculus (MVC) differs from single-variable calculus (SVC) mainly in that, while SVC has to do with derivatives and integrals of real-valued functions of one variable, MVC methods allow us to treat functions of several variables. The difference may not seem like much, but in fact it's huge. The real world involves many, many variables, and so MVC methods let us study and model more real-world phenomena, and in more detail, than would be possible with SVC methods alone.

Instructor: Paul Zorn, Old Science 214, phone x3414, e-mail: zorn@stolaf.edu

Office hours, Spring 2009: Monday, Wednesday, Friday 2:00 -- 3:00; Tuesday, Thursday 9:30 -- 10:30 At other times, please make an appointment --- or just look for me in my office, but I might not be there.

Keeping in touch: This is our class web page; please bookmark it. I'll update it often with homework assignments, solutions, hints, etc. Lots of good stuff will also be found in our class folder on the L: drive.

Textbook: James Stewart, Multivariable Calculus, 6e .

What we'll cover: We'll cover most of Chapters 11, 13, 14, 15, 16, and 17

Grades, tests, important dates, etc.: There will be a midterm test (75 pts each), three short quizzes (25 pts each), a final exam (125 points, part take-home and part in-class), and perhaps a project of some kind, worth 25 points. Homework will also contribute heavily to your grade (about 100 points over the semester). Here are some dates; all are tentative except for the final.

Quizzes: February 25 (Wednesday), March 18 (Wednesday), April 24 (Friday)

Midterm: April 3 (Friday)

Final exam: May 18 (Monday), 7:00--9:00 pm.

About learning disabilities : If you have a documented disability for which accommodations may be required in this class, please contact Ruth Bolstad or Connie Ford in the Academic Support Center (x3288) located at the very back of The Village. If you already have documentation on file in the Academic Support Center you are required to present your letters to the professor within the first two weeks of class.

Homework policy: Homework will be assigned at most classes; it's due no later than 4pm on the due date. Late homework is not accepted unless an arrangement has been made with me in advance.

I strongly encourage you to work with classmates on homework. Homework papers may include up to two names.

Course calendar and homework assignments Information for each day includes the section(s) to be discussed that day and the homework due.

Day 1: Monday, 9 February

Discuss: Section 11.1, start 11.2

Assignment 0: Does not exist.

Day 2: Wednesday, 11 February

Discuss: Section 11.2

Due: Assignment 1: 11.1: 2-10(even), 11, 14, 24, 28

Day 3: Friday, 13 February

Discuss: Finish 11.2, 11.3

Due: Assignment 2: 11.1: 37, 38, 41. 11.2: 1-4, 7, 8, 17, 18

Day 4: Monday, 16 February

Discuss: Finish 11.3, 11.4

Due: Assignment 3: 11.2: 22, 26, 39-42, 53. 11.3: 2,4,6

Day 5: Wednesday, 18 February

Discuss: Finish 11.4, 11.5

Due: Assignment 4: 11.3: 8, 10, 12, 16, 18, 20, 22, 24, 25, 56, 57, 58, 63, 64

Note: This looks like a lot of problems, but most are quickies.

Day 6: Friday, 20 February

Discuss: First half of 11.5 (about parabolas and ellipses, 13.1)

Due: Assignment 5: 11.4: 3, 4, 7, 8, 18, 22, 30, 45, 47, 49, 50

Note: You'll need a calculator or Maple on some of these.

Day 7: Monday, 23 February

Discuss: 13.1, start 13.2

Due: Assignment 6: 11.5: 3-6, 9-12, 17, 18, 57. 13.1: 1,2,3

Note: You'll need to read ahead into 13.1, of course.

Day 8: Wednesday, 25 February

Quiz. Then start 13.2

Day 9: Friday, 27 February

Quick check-in on 13.2; discuss 13.3

Due: Assignment 7: 13.1: 4,5,8,9,12,14,16,31,32. 13.2: 6, 24

Day 10: Monday, 2 March

Discuss 13.3, 13.4

Due: Assignment 8: 13.3: 2, 4, 6, 8, 10, 12, 18, 20, 24, 25, 35, 36, 44

Day 11: Wednesday, 4 March

Discuss 13.4, 13.5

Due: Assignment 9: 13.4: 2-8 even, 9, 10, 14, 15, 16

Day 12: Friday, 6 March

Discuss 13.5

Due: Assignment 10: 13.4: 18, 20, 27-30, 33, 34. 13.5: 2, 3, 4, 6, 7, 8

Day 13: Monday, 9 March

Discuss 13.5, 14.1

Due: Assignment 11: 13.5: 10, 12, 15, 16, 24, 26, 28, 30, 44. Optional for two points extra credit>: 76

Day 14: Wednesday, 11 March

Discuss 14.1, 14.2

Due: Assignment 12: 13.5: 44, 46, 55, 56, 63, 64, 66, 69. 70. 14.1: 7-10, 19-24 (no reasons needed)

Here is the solution to one of the problems above.

Day 15: Friday, 13 March

Discuss 14.2, 14.3

Due: Assignment 13: 14.1: 41, 42. 14.2: 1-10

Day 16: Monday, 16 March

Discuss 14.3 (only stuff on arclength), 14.4 (first half)

Due: Assignment 14: 14.2: 23, 24, 32, 33, 34, 45, 46. 14.3: 1,2, 10

Note: In 14.3 we'll do only the material on arclength, not on curvature. In 14.4 we'll work only through the middle of page 878.

Day 17: Wednesday, 18 March

Quiz; through section 14.3. Then start 15.1.

Day 18: Friday, 20 March

Discuss 15.1

Due: Assignment 15: 14.4: 3, 4, 8, 15, 16, 19. 15.1: 2, 5

Optional for two points extra credit: 14.4: 22. (If you do it, hand it in separately.)

Day 19: Monday, 30 March

Discuss: 15.1, 15.2

Day 20: Wednesday, 1 April

Discuss: 15.2, 15.3

Due: Assignment 16: 15.1: 7, 8, 12, 13, 23, 24, 30, 31. 15.2: 5, 7, 9 (no long-winded reasons necessary---just give the answers).

Day 21: Friday, 3 April

Midterm.

Day 22: Monday, 6 April

Discuss: 15.3, 15.4

Due: Assignment 17: 15.3: 15-22, 35, 36, 41, 42

Note: These are very simple---indeed, your calculator can probably do all of them, or at least check your work. But know how to do these by hand, too.

Day 23: Wednesday, 8 April

Discuss: 15.4, 15.5

Due: Assignment 18: 15.3: 3-10. 15.4: 1-4

Note: Problem 9 in Section 15.3 is fun. The answer is in the back of the book, but don't peek until you've really tried.

Day 24: Monday, 13 April

Discuss: 15.5, 15.6

Due: Assignment 19: 15.4: 11, 12, 13, 17, 18, 21, 22. 15.5: 1-3, 7-9

Day 25: Wednesday, 15 April

Discuss: 15.6, 15.7

Due: Assignment 20: 15.5: 13, 14, 21, 22, 23. 15.6: 1, 2, 7-10

Day 26: Friday, 17 April

Discuss: 15.7

Due: Assignment 21: 15.6: 11-14, 18-20, 38-40. 15.7: 1-3

Note: For the problems in 15.7 you'll need the second derivative test on page 960. We'll discuss it in class, of course, but for the problems you can just use it.

Day 27: Monday, 20 April

Discuss: 15.7, 16.1

Due: Assignment 22: 15.7: 4-8, 11-13, 19

Note: You can hand this in on Wednesday, 22 April.

Day 28: Wednesday, 22 April

Discuss: 16.1, 16.2

Due: Assignment 23: 15.7: 31, 32. 16.1: 1, 2, 5, 6

Day 29: Friday, 24 April

Quiz on Chapter 15 (sections 1-7)

Day 30: Monday, 27 April

Due: Assignment 24: 16.1: 8-12, 16.2: 3-7

Discuss: 16.3, 16.4

Day 31: Wednesday, 29 April

Discuss: 16.4, 16.5

Due: Assignment 25: 16.2: 27, 28. 16.3: 7-10, 19, 20, 39, 40, 45, 46

Note: You can calculate a lot of the integrals in this assignment using technology. The main point is to set them up.

Day 32: Friday, 1 May

Due: Assignment 26: 16.4: 3-10, 22, 23. 16.5: 3, 4

Discuss: 16.5, 16.9 (2d stuff only) Optional for two points extra credit>: 16.4: 36

Day 33: Monday, 4 May

Due: Assignment 27: 16.9: 1-4, 7-10, 11-13, 16

Discuss: 17.1, 17.2

Day 34: Wednesday, 6 May

Discuss: 17.2

Due: Assignment 28: 17.1: 5, 6, 11-14, 27, 29-32. 17,2: 1, 2

Note: For the last two problems, just ferret out the appropriate formulas in 17.2. This makes the problems easy.

Day 35: Friday, 8 May

Discuss: 17.2, 17.3

Due: Assignment 29: 17.2: 3-10, 17-22.

Notes: (i) For 17-22, use the first part of Definition 13 on the top of page 1078 or (it's the same thing) the boxed formula on page 1079. See also Example 7, page 1078. (ii) Feel free to use technology to calculate the integrals. The main point is to set them up correctly.

Day 36: Monday, 11 May

Discuss: 17.3, 17.4

Due: Assignment 30: 17.2: 23-28, 29a, 30a, 46, 47. 17.3: 1, 2

Notes: The last two problems take no calculation; find the appropriate theorem.

Day 37: Wednesday, 13 May

Due: Assignment 31: 17.3: 3-7, 11-15, 19, 20, 23, 33

Overview of integration; review of semester

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