642:527

METHODS OF APPLIED MATHEMATICS

FALL 2007

Basic information

• Instructor: Professor E. Speer, Hill Center 520, 732-445-1313
• Office hours: Note added office hour on Tuesday afternoon.
  • Tuesday, 9:00--9:40 AM, Murray 115
  • Friday, 9:00--9:40 AM, Murray 111
  • Tuesday 12:30--1:30 PM, Hill 520
  • Tuesday 3:20--4:40 PM, Hill 520
• Detailed course information and policies: As web page and as a PDF file.
• Tentative syllabus: As web page and as a PDF file.
• Homework assignments and solutions: Click here for assignments and solutions.

Final exam

• The exam is cumulative, but will probably emphasize Chapters 17, 18, and 19, in particular, material that we have covered since the last exam.
• Here is the formula sheet for the final exam. It consists of the formula sheets for exams 1 and 2, plus the standard form of a Sturm-Liouville problem and formulas for the Fourier transform and for d'Alembert's solution. You will also be given the tables in the appendices of our text for the Laplace and Fourier transforms.
• We will hold a problem session Wednesday, December 19, 2:00–4:00 PM, in ARC 206.
• I will hold office hours Tuesday, December 18, 3:30–5:00 PM and Thursday, December 20, 10:00–12:00 AM.
• Here is last year's final exam for your amusement. Bear in mind, however, that I did not construct this and it does not necessarily reflect the nature of our exam.

Announcements

• Here is a Maple worksheet showing animated solutions of the wave equation. (I intended to show this in class on Thursday 12/13, the day the projector system was unavailable.)
• Remember that we have an extra class Thursday, December 13, 5:00–6:20 PM, SEC 117 to make up for the class we lost to the football game.
• I regret that I must cancel my office hour on Tuesday afternoon, December 11, 3:20–4:40.
• Here is the Maple worksheet for the Fourier transform that I showed in class on 12/6.
• Here are some notes on the problem of solving the heat equation in a disk, as discussed in class November 15 and November 27. Your comments on these notes, and on any errors they contain, are welcome.
• Since Assignment 12 is due Thursday, December 6, I will hold special office hours on December 6: 11:00–12:00 AM and 3:20–4:40 PM.
• Exam 2 has been rescheduled: it is now scheduled for November 20.
  • The exam will cover all our work from the previous exam through Thursday, November 8. In terms of the text, this is roughly:
  • Sections 7.1 through 7.5,
  • Sections 9.6, 9.9, 9.10,
  • Sections 17.1 through 17.4 and Section 17.6,
  • Part of 18.3, specifically, solving the heat equation in one dimension, on a finite interval, with homogeneous boundary conditions.
  • Here is a set of review problems, most taken from last year's second exam. This was prepared by Professor Dan Ocone, the instructor for this course last year, so these problems may not be a good guide to this year's exam. You might just view it as another chance to practice.
  • Here is the formula sheet that will be given out with the exam.
  • I will hold special office hours next week, all in Hill 520:
    • Monday, November 19, 2:00 to 3:30 PM;
    • Tuesday, November 20, 10:30 to 11:30 AM;
    • Tuesday, November 20, 3:20 to 4:40 AM;
  • Here are the solutions to exam 2.
• Here is a pdf file showing more details of the Sturm Liouville problem that we solved on 11/13, including plots of some of the eigenfunctions.
• Here is the pdf file of the Maple worksheet showing Fourier series that I showed in class on 11/1 and 11/6. Shown are the Fourier series for the step function and for the steady-state response of a damped oscillator driven by a that square wave.
• Here are the phase plane portraits for competing species models that were shown in class on Tuesday, October 23.
• Here are some notes on the geometry of the orbits for centers and foci. Your comments on these notes, and on any errors they contain, are welcome.
• We will not hold class on Thursday, October 18. That class will be made up on Thursday, December 13.
• Here is a file with some plots of the phase plane of the pendulum
• Exam 1 is scheduled for October 11. It will cover all work on series solutions and Laplace transforms.
• Here is the formula sheet that will be given out with Exam 1. You will also be given the table of Laplace transforms from Appendix C of the text.
• Here is a copy of last year's first exam. This was prepared by Professor Dan Ocone, the instructor for this course last year, so it may not be a good guide to this year's exam. You might just view it as another chance to practice.
• I will hold special office hours on Thursday, October 11, from 2:00 to 3:00 in Hill 520.
• Here are the solutions to exam 1.
• 9/13/2007: Here is a summary of the Frobenius method in PDF form.
• 9/11/2007: Here are the solutions to the placement quiz in PDF form.