640:244:17–19
Differential Equations for Engineering and Physics
SPRING 2011
Basic information
Final Exam: Wednesday, May 11, 4:00-7:00, PH 115
- There will be a FINAL EXAM PROBLEM SESSION on Tuesday, May
3, 1:30-3:30, in SEC 209.
- Here is the review problem set for the final
exam. As explained on the problem set, it is not complete,
covering primarily material we have discussed since the second exam. You
should also consult the review problem set for exam
1 and the review problem set for exam 2; it
might be a good idea to review the midterm exams themselves, as well.
- Coverage: The exam will cover all the material of the course,
with the following exceptions:
- Section 2.6: Exact equations will be
covered, but integrating factors will be omitted. But the use of integrating
factors for linear equations (Section 2.1) will be covered.
- Section 3.5: The solution for a double root for the characteristic
equation will be covered, but the general reduction of order method will be
omitted.
- Section 7.7: This section will not be covered on the exam.
- Office hours during reading period and exam week:
- E. Speer, Hill 520: Monday, May 9, 1:30-3:00 PM.
- E. Kupin, Hill 618: Monday, May 2, as usual;
Wednesday, May 4, 1:00-4:00 PM
Thursday May 5, 12:00-3:00 PM
Announcements and supplementary material
- 4/20/2011:
- Here are the phase plane plots for the
predator-prey model which were shown in class today.
- One does in fact observe cyclic behavior of populations in nature, but
it is not clear to what extent a simple model like the predator-prey
equations we have studied can help explain them. If you would like to read
more about this, here are a (very) few references. I displayed pages from
the first and third of these in the lecture.
- An article by C. Elton and M. Nicholson
discussing in some detail the actual records for lynx pelts of the Hudson
Bay Trading Company. There are nice graphs showing the cyclic oscillations
in the lynx population (as indicated by trapping records).
- A survey article by P. J. Wangersky
discussing the general applicability of populations models of the Lotka-Volterra type.
- An article by M. E. Gilpin entitled
"Do Hares Eat Lynx?" Besides its amusing title, this article seems to have
intelligent things to say about the general problem of modeling population
behavior.
- A set of
lecture notes on cycles in populations from a course given by Dr. Bob
Schooley at the University of Illinois. This is a power point
presentation.
- 4/15/2011: Here are the slides showing the phase plane for the
pendulum and the competing species models that I discussed in class
on April 14.
- 3/31/11: Here are the slides showing the
phase plane of two dimensional linear systems of ODEs that I discussed in
class on March 29 and 31.
- 3/23/11: There is an error in the original version of the notes
on linear algebra, posted in the next entry. Equation (5) should be
changed. The version below has been repaced by a corrected one. If you
don't want to download the entire set of notes again, you may obtain the
correction from this erratum.
- 3/9/11: Here are the notes on linear
algebra which we will use to supplement Section 7.3 of the text.
This version was corrected on March 23.
- 3/8/11: Here are the slides showing response of an oscillator to forcing that I showed
in class on March 1.
- 2/18/11: Here is the summary of the
method of undetermined coefficients that I showed
in class on February 17.
- 2/07/11: One of the students in our class, Jing Chai, told me
that he found this website useful. It contains matlab codes for various
numerical methods.
- 2/04/11: Here are two documents that I showed in class on
February 3:
- 2/02/11: Here are two documents that I showed in class on
February 1:
Exam 2
The second exam will be on Tuesday, April 5.
- Coverage: We will cover all the work on the syllabus from the
material covered on Exam 1 through Section 7.5, including material in the
posted lecture notes. Of course, you are also responsible for any material
from Exam 1 which is needed to support this later material.
- Problem Session: A problem session will be held on Sunday,
April 3, from 2:30 to 4:30 P.M. in SEC-209. This is not
a review presented by me but a chance for you to ask questions about any
material in the course.
- Extra office hours: Beth will hold extra office hours on
Friday, from 3:00 to 5:00 P.M., in Hill 618. She will also hold her
usual Monday morning office hours and will devote the recitations on Monday
to exam review.
- Review Problems: here is a set of
problems to help you review for the exam, and to give you something to
ask questions about at the problem session.
Exam 1
The first exam will be on Tuesday, February 22.
- Coverage: We will cover all the work on the syllabus through
Section 3.5.
- Problem Session: We will hold a problem session on Sunday,
February 20, 2:30–4:30, in SEC 210. This is not a review
presented by me but a chance for you to ask questions about any material in
the course.
- Review Problems: here is a set of
problems to help you review for the exam, and to give you something to
ask questions about at the problem session.
- Applications of first-order linear equations: In Section 2.3 and
in the problems for that section our text considers applications of first
order linear equations to a variety of models of real-world situations.
Although our list of suggested homework problems included several of these,
in lecture and on the practice problem set we considered only problems
involving flow of solutions into and out of a tank (or lake). For this
reason I will put only problems of this sort on the exam. Related material
in the text includes Examples 1 and 3, and problems 1–6 and 19, of
Section 2.3.