ME 494 Mathematics

UIC
ME 494 Mathematics
Fall Term, 2002
MW 11:00 - 12:15 pm
306 AH

Instructor:
Michael J. Scott
3057 ERF
(312) 996-4354
mjscott@uic.edu

Office Hours: open, except Thursday afternoons. Week-to-week availability is posted outside the office door.

Announcements

The final exam will be held Thursday, Dec. 12, 10:30am-12:30pm in room 1003ERF. There will be a closed-book portion and a section on which you may use your few sheets of handwritten notes.

Handouts

The course syllabus (PDF).
A sheet on grading policies (PDF).

Assignments

Assignment 0 is to register for the class.
Homework 1: p. 1113: 5(b)(d)(f), 6(e), and p. 1124: 2(e), 4. (PDF of relevant pages)
Issued 28 August, due 4 September.
(Solutions.)
(Solutions, uncropped. Try this if the other file doesn't work.)
Homework 2: p. 1134: 4(c), 5(c), 6(c), p. 1135: 10, and p. 1136: 16. (PDF of relevant pages)
Issued 4 September, due 11 September.
(Solutions.)
(Solutions, uncropped. Try this if the other file doesn't work.)
Homework 3: pp. 1146-7: 8, 9, 11(c), 12, and 14. (PDF of relevant pages)
Issued 11 September, due 18 September.
(Solutions.)
(Solutions, uncropped. Try this if the other file doesn't work.)
Homework 4: pp. 1194-5: 4(e)(i), 7, 9(f), and p. 1206: 2, 3. (PDF of relevant pages)
Issued 18 September, due 25 September.
(Solutions.)
(Solutions, uncropped. Try this if the other file doesn't work.)
Homework 5: pp. 1233-4: 4(b)(c), 7, p. 1239: 3(b)(l), and pp. 1255-6: 1(b), 3(b), 4. (PDF of relevant pages)
Issued 7 October, due 14 October.
(Solutions.)
Homework 6: p. 438: 1(b-e), 7, 10, 13, and pp. 448: 5. Issued 23 October, due 30 October.
(Solutions.)
Homework 7 (PDF).
Issued 30 October, due 6 November.
(Solutions.)
Homework 8: This homework is in two parts:
The first part of the homework must be brought to class on Monday, Nov. 11:
Suppose you apply Gram-Schmidt orthogonalization two separate times to an arbitrary set of linearly independent vectors, starting the process with a different vector each time. Do you expect the two sets of orthogonal vectors to be the same, or different? Explain/justify.
Be prepared to discuss your answer and convince someone else that it is correct.
The second part of the homework is due on Wednesday, Nov.13:
Reading: Greenberg, Sections 10.1 - 10.2
Problems: p. 480: 15, 16.
Issued 6 November, due 11 and 13 November.
(Solutions.)
Homework 9 (PDF).
Issued 13 November, due 20 November.
(Solutions.)
Homework 10: pp. 552-3: 12, 18, 20, 26 (it may be helpful to compare the properties of the determinant), and p. 566: 10 (do the relevant reading, and you are encouraged to use a computer).
Issued 22 November, due 27 November.
(Solutions.)

Bonus Problems
From time to time, I will post problems that I think may be useful or interesting. They are not worth any points in the grade calculus, except that they may offer you a chance to demonstrate deep understanding and thus may influence the 5% of the grade reserved for participation and exceptional work.
I hope that you will attempt these problems when YOU think they may be useful or interesting.

(Aug. 26) We discussed the difficulties of displaying visually the behavior of a function that maps the complex numbers to itself. One proposed method was to create two surface plots, one for u(x,y) and one for v(x,y). The problem to attempt here is to implement this for general functions using any software you like. The answer would be a package that I could run and enter the function I would like to display.
You may also propose and implement your own, different, method for visualizing complex functions.
Mandar Deshpande found a MATLAB program at http://math.rice.edu/~polking/holo.html.
(Sep. 23) We saw in the homework that a function could be cooked up to satisfy the Cauchy-Riemann equations without being differentiable; the particular function was well-defined away from z=0, and defined explicitly to be 0 at z=0. The problem is to find a function that has a nice representation in a neighborhood of some z=a but requires explicit definition at z=a (probably z=0, but we don't want to be restrictive) and is differentiable at z=a, or to show that it can't be done.
(Oct. 28) We saw in class that the relative magnitudes of x and y can change and even reverse for different norms. This is true even in a vector space as simple as R^2. What can you say about the calculation of the angle theta using the inner product? Is theta always the same? If not, do the angles theta_1 between x and y and theta_2 between w and z keep their relative magnitudes? (Obviously, we don't care if our scale changes: we can use radians, or 17 times radians, or degrees for our units.)

Last updated: Mon Aug 26 15:51:55 CDT 2002
Send questions and comments to mjscott@uic.edu

UIC ME 494 Mathematics Fall Term, 2002 MW 11:00 - 12:15 pm 306 AH

UIC
ME 494 Mathematics
Fall Term, 2002
MW 11:00 - 12:15 pm
306 AH