Mathematics 412 (stacked honors), Sections 200/501, Fall 2012

SKIP PAST THE ANNOUNCEMENTS if you so desire. ._. (or to near the bottom)

Announcements

• 3 Dec: Office hours during dead and exam weeks: (subject to change)
  • Monday 12/3: Regular office hour at 3:00, but I must leave at 3:45.
  • Tuesday 12/4: Regular office hour at 3:00.
  • Wednesday 12/5: I expect to be in the office in the afternoon, except 3:00-4:15.
  • Thursday 12/6: I expect to be in the office in the afternoon, until 3:45.
  • Friday 12/7: Probably in the office 3-5.
  • Monday 12/10: Probably in the office 3-5.
• 2 Dec: Yet another AMUSE seminar (more student presentations, Tuesday).
• 26 Nov: This week's AMUSE seminar (student presentations, Tuesday).
• 20 Nov: You can pick up your test this afternoon at my office. The grades are in eLearning.
• 18 Nov: The last homework will be due on 28 Nov (Wednesday, not Monday as previously announced).
• 12 Nov: This week's AMUSE seminar.
• 2 Nov: Next week's AMUSE seminar.
• 31 Oct: Next week's Math Club meeting.
• 28 Oct: Tuesday office hour (10/30) will end (and start) early -- say 2:30-3:20.
• 25 Oct: Next week's AMUSE seminar.
• 22 Oct: This week's AMUSE seminar [was] especially recommmended.
• 15 Oct: The hearing (below) was cancelled, so I will probably be in my office 2:00-4:30 all this week except for these hours: Mon 2, Wed 3, Thurs 4, Fri 2, Fri 4.
• 11 Oct: Office hour trouble next week (Oct. 15 and 17).
• 7 Oct: Math Club meeting TOMORROW, Monday, Oct. 8, 7:00 p.m., BLOC 117, on "Symmetry and Infinity: The Banach-Tarski Paradox" ._._. and also AMUSE seminar, Tuesday, Oct.9, 5:30 p.m., BLOC 627, on "Representing the Mechanical Behavior of Matter". (Click on the title to see a summary.)
• 19 Sep: Aggie Acturaries Club meeting Thursday, 20 Sept.
• 27 Aug: Talk by astronaut Greg Chamitoff this Thursday, 30 Aug.

Course procedures and resources

• This is a "stacked" section. That means that Honors students (Sec. 200) and regular students (Sec. 501) are in the same class. The full implications of that will be discussed in class on Monday (Aug. 27).
• Classroom: BLOC 164
• Instructor: S. A. Fulling
  Email: fulling@math.tamu.edu
• Required textbooks:
  1. R. Haberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 4th edition, Prentice-Hall, 2004.
  2. S. A. Fulling, Math 412 lecture notes with Appendices B and C and the Nature articles discussed in Appendix C.
• Course handout
• Related information
  • Please see my home page for up-to-date office hours.
  • Instructions for using eLearning to check your homework and test grades.
  • Teams
• Old M. 412 course pages (including exams with solutions)
  • Fall 2007 course page
  • Fall 2006 course page
  • Fall 2005 course page
  • Fall 2004 course page
  • Fall 2000 course page
• Homework solutions (written mostly by David Miller, edited and published by Changchun Wang)
• Fourier series Maple demos:
  1. Triangle wave
     • partial sums ._. Maple code
     • Cesaro means ._. Maple code
  2. Square wave
     • partial sums ._. Maple code
     • Cesaro means ._. Maple code
  3. Sawtooth wave
     • first version ._. Maple code
     • displaced version (murkier formula but clearer graphs) ._. Maple code
  4. Animated version by Dakota Blair. "The code can actually be copied verbatim for each file."
  5. New cosine wave Mathematica session
• More Maple demos:
  1. Eigenvalues of a Robin Sturm-Liouville problem. Maple input and output.
  2. Bessel functions and Fourier-Bessel series. Maple input and output.
  3. Sample associated Legendre functions with either l or m equal to 8. Mathematica output.
• Notes for extra "honors" lectures
  • The three-string problem
  • Mathematical theory of vegetable cellars
  • Asymptotics of Bessel functions
  • Airy's integral
• Miscellaneous extra material
  • Another big rectangle problem
  • Books on distributions (generalized functions)
  • Recommended historical article: L. Challis and F. Sheard, The Green of Green Functions, Physics Today 56 No. 12 (Dec. 2003) 41-46
  • Some review problems worked by the Fall '05 section
  • Green functions for the Schrodinger equation

Homework by weeks:

1. Sept. 5: 12.2.2, 12.2.3, 12.3.5, 12.3.6, 12.4.1, 12.4.4
2. Sept. 12: 12.5.3(a,c), 2.3.1(b,c), 2.3.2(e), 12.5.4 [Relate your answer to 2.3.2(e)], 2.3.3(a,c), 2.3.6, 12.5.1(a,c)
   Read exercise numbers carefully: some are from Chapter TWO, some from Chapter TWELVE.
3. Sept. 21 (Friday, but covered on Wednesday's test): 3.2.2(b,f), 3.3.1(a,b), 3.3.3(b,c), 3.3.14, 3.3.16, 2.2.3, "2.2.3(b)" [Click]

   Solutions for Test A ._. Mathematica graphics for the d'Alembert solution

4. Sept. 26: 2.4.1(a,b), 2.4.2, 2.5.1(a,d), 2.5.2(a,b)
5. Oct. 3: 7.3.1(d), 7.3.4(b), 7.4.1(b,c)
6. Oct. 10: 10.2.2, 10.3.3, 10.3.5, 10.3.6, 10.4.8, 10.5.16, 10.6.13
7. Oct. 17: 10.3.13, 9.3.5(a,c), 9.3.6(a,c) [9.3.6(c) means: Use answer to (a) to solve 9.3.5(c).], 9.3.22 [and use the result to solve y' + y = f(x), y(0) = 0, for arbitrary f], 10.4.3, extra(a) [click], extra(b) [click]

   Solutions for Test B

8. Oct. 24: The exercises this week are not from Haberman, but from a special assignment: 1, 2, 3, 4, 5
9. Nov. 2 (Friday): 5.4.1, 5.4.6 [See p. 195 (5.7.1) for the nonuniform string wave equation.], 5.5.1(c), 5.5.2, 5.5.8, 5.8.8(c,d)
10. Nov. 7: 5.3.3, 5.3.9, 2.5.3, 2.5.6(a), 2.5.8(c), 2.5.4, 7.8.7
11. Nov. 14: 7.8.8, 7.7.1, 7.7.3, 7.7.8, 7.9.1(c), 7.9.3(c), 7.5.1, 7.5.2

    Solutions for Test C

12. Nov. 28: 7.10.1(b), 7.10.2(b), 7.10.3(c), 7.10.9(a), 7.10.10(a), 7.10.12, 5.9.3, 7.8.10

    Solutions for Final Exam

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e-mail: fulling@math.tamu.edu