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 final exam is scheduled for Thursday, December
20, 4:00–7:00 PM, in SEC 203.
- 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.