Mathematics 401, Spring, 2001

SKIP PAST THE ANNOUNCEMENTS if you so desire.

There are some MAPLE DEMOS at the bottom of the page.

Course procedures and announcements:

• May 8: Final Exam Solutions
• May 4: AT LAST: WEEK 5 HOMEWORK IS FINISHED! ALL homework may now be picked up at, or outside, the respective professor's office. All remaining homework solutions (Week 5 and some miscellaneous holdovers from other weeks) will be at the Bright copy center after sometime on Monday.
• May 4: Recently there have been increasingly obvious instances of students essentially copying the answer key (sometimes including mistakes!) and turning it in "late". Recall that all student solutions are published by Caveat Emptor Press. Also, sometimes we see 5 or 6 identical papers, often containing the same obvious error. The homework system in this course is designed to facilitate your learning from fellow students, present and past. However, it is a self-defeating abuse to fail to put in due individual effort on your two problems per week, and it is a violation of ethics to seek credit for papers that you did not really write at all.
• May 2: Most of the homework is now ready to be picked up outside my office (in particular, Week 10!). Many papers from Week 12 (namely, Problems 1, 4, and 6) have not been returned by the reviewers. [#1 and #4 are now OK - May 4.] If you wrote one of these papers and want some points for it, recall that the course handout states: "You are strongly urged to keep a copy (or at least a rough draft) of your paper when you turn it in." This is the reason!
• May 1: I will be in my office in the afternoons Wednesday, Friday (except 3-4), and Monday (till 4), other business permitting. I can't commit to particular times this far in advance. Homework papers will be available outside my office as soon as I can process them. Solutions for Tests 2 and 3 and numerous homework solutions have gone to the copy center recently.
• Apr. 23: CalcLab accounts will be deleted May 11! Anything you want to save must be backed up to another system by then.
• Apr. 22: Please bring in any homework envelopes in your possession for Weeks < 12 by Monday, Apr. 23 (even if you have not reviewed them!). Please return Homework 12 (relevant to Fulling's section only) by Friday, Apr. 27.
• Apr. 5: All the homework summary reports received to date have been posted below!
• Apr. 1: Reminder: Dr. Wilber's class will meet in CVLB 419 tomorrow (Monday, April 2). If necessary, check back here on Tuesday to learn where to go on Wednesday. Thank you for your cooperation!
• Feb. 25:
  • No office hour (by Fulling) Wednesday, 2/28 (because of graduate oral exam)
  • Office hour on Wednesday, 3/7 will end at 11:30 (because of Math 152 common exam meeting)
• Feb. 12: Results of Homework Set 1 have been posted with extensive grader comments.
• Feb. 12: Relaxations of the schedule around the test:
  • Homework problems due today will be accepted through tomorrow (Tue. 2/13) at the appropriate professor's office (or mailbox). The envelopes will go to the reviewers on Wednesday.
  • The test (Wed. 2/14) will include a take-home question due Mon. 2/19.
  • Reviews of Hwk 4 are due Wed. 2/21.
  • Hwk 5 is due Fri. 2/23.
  • Please get back on schedule: Hwk 6 and Reviews 5 due Wed. 2/28!
  • Similar accommodations may be made around the other two hour tests; await details later.
• Feb. 9: In Problem 2 of Homework 4, you are supposed to study the behavior as omega -> infinity. In other words, set omega = 1/epsilon and expand things as power series in epsilon, as usual.
• Feb. 2: Note change in Wilber office hours (below).
• Feb. 1: Exercise 1 on p. 22 of Bush concerns a projectile falling against a resistance force proportional to the cube of the speed. A more realistic model has the force proportional to the square of the speed:
  • an article by experts (an aerospace engineer and a mathematician) on the validity and physical origin of that model
  • solution for a falling body by regular perturbation theory (Foundation Coalition lecture notes)
  • perturbative solution for a projectile (a Maple lab exercise)
  • numerical (nonperturbative) solution for a projectile (a Maple lab exercise)
• Jan. 20: Office hours:
  • Fulling: M 3:00-3:30, W 11:00-12:00 (also TR 3:10-3:35 in HELD 109)
  • Wilber: M 12:30-1:30, T 1:00-2:00 (changed 2/2)
  Feel free to consult either of us.
• Jan. 17: Group list: PDF or DVI or TEX source (ASCII readable -- including names of Greek letters!)
• Course handout (syllabus): PDF or DVI
• Homework problems: PDF or DVI
• Instructions for the Homework Review Generator
• The first 50 pages of the class notes: (copyright) PDF or DVI (This will disappear after awhile. It is here as a convenience until you buy the notes.)
• Evans Harrell and James Herod, Linear Methods of Applied Mathematics
• TEX and all that: I really want to encourage and help you to put your work on the Web, and to read what others have put there, and also to discuss mathematics with specificity in e-mail and your reviews and reports. I have compiled some links that may be useful. (More useful would be for the state of the technology to advance so that the process becomes easy and natural for all concerned. That is happening slowly.)
  • Information on the Web about putting math on the Web. I urge all of you to read at least the first item (the one from Swarthmore). The later items become increasingly technical, and often refer to "solutions" that are not useful to us now because not every reader has the necessary software. The whole page will be of interest to those who might be interested in helping develop the higher education of the future.
  • Information about DVI viewers. If you are unable to read the excellent homework papers of TeX users such as Andrew Barkley (M. 311, f98) and Gabe Valderrama (M. 311, s00), you should read this!
  • On-line introductions to TeX. If you want to learn to use TeX yourself, here is free documentation!

Homework by weeks:

1. • assignment (Fulling) (Wilber)
   • solutions and reports
2. • assignment (Fulling) (Wilber)
   • solutions and reports
3. • assignment (Fulling) (Wilber)
   • solutions and reports
4. • assignment (Fulling) (Wilber)
   • solutions and reports
   • Test A answer key (DVI) (PDF)
5. • assignment (Fulling) (Wilber)
   • solutions and reports
6. • assignment (Fulling) (Wilber)
   • solutions and reports
7. • assignment (Fulling) (Wilber)
   • solutions and reports
8. • assignment (Fulling) (Wilber)
   • solutions and reports
   • Test B answer key (DVI) (PDF)
9. • assignment (Fulling) (Wilber)
   • solutions and reports
10. • assignment (Fulling) (Wilber)
    • solutions and reports
11. • assignment (Fulling) (Wilber)
    • solutions and reports
12. • assignment (Fulling) (Wilber)
    • solutions and reports
    • Test C answer key (DVI) (PDF)
13. • assignment (Fulling) (Wilber)
    • solutions and reports
14. • assignment (Fulling) (Wilber)
    • solutions and reports
    • Final exam answer key (DVI) (PDF)

Computer demonstrations

These demonstrations were designed to be performed in the classroom "live", but the output is still instructive. If you have Maple, the input files may also be useful. (The graphs show up better on printout or in Maple than in the html files. Also, you can rerun the program with different parameters.)

• Convergence of Fourier series.
  • Square wave ._. Maple input
  • Triangle wave ._. Maple input
• Cesaro means of Fourier series. (This is not part of the M. 401 syllabus, but the commentary is pretty self-explanatory. Roughly speaking, Cesaro told us to average the partial sums so as to smooth out the "wiggles".)
  • Square wave ._. Maple input
  • Triangle wave ._. Maple input
• I have some animations of solutions of the wave equation. Unfortunately, they require to be executed on a computer running Mathematica.

Go to home pages: Fulling ._._. Wilber ._._. Calclab ._._. Math Dept ._._. University

e-mail: fulling@math.tamu.edu

Last modified Fri 7 Nov 03