Math 550 (Vector Analysis) Section 001 Fall 2010

Lectures in LeConte 405

MWF 12:20 -- 1:10 PM

Professor: Peter J. Nyikos
Prof. Nyikos's Office: LeConte 406. Phone: 7-5134

Special office hours will be held on the week of exams: Monday, Dec. 6, 1:30 - 4:30; Tuesday, Dec. 7, 2:30 - 4:30; Wednesday, Dec. 8, 2:00-5:30; Thursday, Dec. 9, 12:00 - 4:15: later days Tba.

Usual Office Hours: 11:00 - 12:00 MWF, 2:30 - 3:20 Tuesdays, and 3:30 - 4:30 MW or by appointment (or any time I am in). Exceptions posted on door and announced in advance whenever possible.

The first hour test was on Wednesday, September 29. It covered Chapter 1 and Sections 2.3, 2.4, 2.7 and 2.8.

The second hour test was on Wednesday, October 27. It covered 2.6, 3.3, 4.3, 4.6, 6.2, and 6.3.

The third hour test was postponed from Friday, November 19 to Monday, November 22. It covered reconstructing a function from its gradient (4.6 exercises) 5.1, 5.2, 5.3, and 6.5.

Email: nyikos @ math.sc.edu

Prerequisite: C or better in Math 241.

Last day to withdraw with a "W": October 7.

The textbook for this course is Vector Calculus, , by Miroslav Lovric. ISBN-13 978-0-471-72569-5; ISBN-10 0-471-72569-2.

Approximately one half of this course will cover 241 material in greater depth, emphasizing vector fields; the other half will be essentially new material, including differentiation of vector fields (Section 2.4), change of variables in multiple integrals (Sections 6.4 and 6.5), and surface integrals (Chapters 7 and 8). There will be material covered from all eight chapters, but some will be emphasized much more than others.

Only simple calculators (in other words, those that may be used in taking SAT tests) are needed for this course, and they will be needed only a small fraction of the time, outside of class. Neither the quizzes, nor the hour tests, nor the final exam will require their use, although they may save some time on a few problems. Programmable calculators are not permitted for quizzes, hour tests, or the final exam.

The course grade will be based on quizzes, homework, 3 one-hour tests, a final exam, and attendance. Details on this and on various policies can be found here in pdf format.

Learning Outcomes: Students will master concepts and solve problems based upon the topics covered in the course, including the following: vector fields, line and path integrals, orientation and parametrization of lines and surfaces, differentiation of vector fields, change of variables in double and triple integrals, Jacobians, oriented surface integrals, theorems of Green, Gauss, and Stokes.

Practice problems from the first four lessons (August 20, 23, 25, 27):

1.1 numbers 5, 11, 19
1.2 numbers 1, 3, 13
1.3 numbers 17, 21
1.4 numbers 17, 19, 21
1.5 numbers 1, 19, 21

Homework to be handed in on Friday, August 27:

1.1 numbers 6, 14, 22

1.2 number 4: parametrize the line and the segment with the two points as endpoints.

1.3 numbers 8, 12

Homework handed in from on Wednesday, September 8:

2.3 number 4
2.4 numbers 10, 28

Practice problems from 2.4, not to be handed in:

numbers 9, 11, 27, 37, 41, 47, 53

Homework handed in from 2.4 on Wednesday, September 15:

numbers 32, 38, 48.

There was a quiz on Monday, September 20, with a problem on directional derivatives.

Practice problems from 2.5 and 2.7, not to be handed in:

2.5 numbers 37, 41
2.7 numbers 7, 13, 17, 39, 43, 47

Homework handed in on Wednesday, September 22:

2.5 number 38
2.7 numbers 18, 24, 44

Homework handed in on Monday, September 27:
Re-do Problem 48 on p. 110 in two ways:
(a) with z = 0 and x = 4 and y = 15 (b) with z = -0.1 and x = 4 and y = 15

Homework handed in on Wednesday, October 6:

2.4 number 64
2.8 number 14 (see Example 2.100)
3.3 numbers 8, 22

Practice problems from 2.6 and 2.7, not to be handed in:

2.6 numbers 5, 9, 21, 27
4.6 numbers 13, 15, 23

Homework handed in on Monday, October 11:

2.6 numbers 6, 16, 18, 22, 24
4.6 numbers 14, 22

Practice problems from 4.3, 6.2 and 6.3, not to be handed in:

4.3 numbers 7, 13
6.2 numbers 15, 17
6.3 numbers 1, 13, 15, 19

Homework handed in on Monday, October 18:

4.3 numbers 14, 16
6.2 numbers 12, 20

There was a quiz on Friday, October 22, on Section 6.3.

Practice problems in 6.5:
numbers 1, finish 5, 7 and 9, 11, 13, finish 21, 31

Homework handed in on Friday, October 29:

6.4 numbers 2, 6
Homework handed in on Monday, November 15:
- 5.2 number 16 (b) and (e), first part of 26
- 5.3 Finish number 12
Practice problems in Chapter 7:
- 7.1 numbers 13 and 15 (compare Example 7.7)
- 7.3 number 11
- 7.4 number 9 (compare Example 7.4, p. 437 and Example 7.41, p. 477)
Homework to be handed in Wednesday, December 1:
- 7.1 number 16
- 7.3 number 12 [see Example 7.38 on page 475 for the calculation of the normal vector]
- 7.4 number 12
Extra Credit Problems
Extra credit problems are to be done strictly on your own, except that I am willing to give you advice. You are not to discuss them with anyone else.
There is no due date for extra credit, but once a fully correct solution is handed back, the problem is no longer eligible for extra credit. This is true of any problem crossed out below. If you can't quite get the solution but have some ideas, hand them in for partial credit. I will keep adding to your score as you improve your work on it.

1. [10 points altogether] Number 34 on page 62

2. [8 points] Number 16 on page 416, using squares of the form [0, a]^2
3. [8 points] Number 22a in Section 5.1.
4. [12 points] Number 24 in Section 6.5.
5. [8 points] Number 8 in Section 7.3.
6. [12 points] originally 10 points Number 14 in Section 7.4.

Math 550 (Vector Analysis) Section 001 Fall 2010

Professor: Peter J. Nyikos Prof. Nyikos's Office: LeConte 406. Phone: 7-5134

Extra Credit Problems

Professor: Peter J. Nyikos
Prof. Nyikos's Office: LeConte 406. Phone: 7-5134