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Description
The subject of differential equations can be described as the study of
equations involving derivatives. It can also be described as the study of
anything that changes. The reason for this goes back to differential calculus,
where one learns that the derivative of a function describes the rate of
change of the function. Thus any quantity that varies can be described by an
equation involving its derivative, whether the quantity is a
position, velocity, temperature, population or volume.
There are three main ways to study differential equations. There are analytic
methods, wherein a mathematical formula for a solution of a differential
equation is obtained. There are Numerical techniques, which provide an
approximate solution, generally using a computer or programmable calculator.
Differential Equations can also be studied qualitatively, determining
general properties of solution without concern for exact behavior.
In this course, we will emphasize analytic methods, though qualitative and
numerical techniques will make brief appearances.
News
Sunday 7 December: I've posted the table of Laplace Transforms
you will be given on the final exam. Follow the link fromthe final
exam review page.
Saturday 6 December: I've also added some problems from Section
10.1, even though we didn't cover that section in complete detail.
Saturday 6 December: It has come to my attention that Section
7.8 did not appear on any of the review pages. Section 7.8 will be
covered on the exam, and I have added this material to the most recent
review page.
Friday 5 December: Today's class demonstration is available here.
It shows the signal produced by an amplifier with a maximum output
amplitude of 1, when it is fed a signal with amplitude A. The stars
along the bottom represent the energy contributed by the first 10 harmonics.
Thursday 4 December: I have added some previous exam problems
to the review page. The review session is scheduled for Saturday 6
December, 6:00-7:30 in DH 1212.
Wednesday 3 December: A review page has been posted for the
final exam. Note that the final exam will be cumulative. The
review page covers only that information not covered by the other
review pages. You should review the entirity of the course material
for the final exam.
More items will be added to the page over the next few days. In
particular, I will be posting some old exam problems.
Wednesday 26 November: The reading and homework for Week #15
have been posted. Follow the link from the Schedule page.
Monday 24 November: Here is an updated page of course statistics.
Friday 21 November: I have made a slight change to Monday's
homework assignment. You may skip part (d) in problems 9.1.2, 9.1.6
and 9.1.9.
Thursday 20 November: The reading and homework assignment for
Week #14 have been posted. Follow the link from the Schedule page.
Tuesday 18 November: The reading and homework assignments for
Week #13 have been posted. (The homework is not due until the Monday
of Week #14.) Follow the link from the Schedule page.
Monday 17 November: Rather than have a homework assignment due this
Friday, I will postpone the duedate until next Monday. I guess a lot
of you have a hectic week coming up, and there will be no other assignment
next week, because of the Thanksgiving holiday. I'll get the assignment
posted tomorrow.
Friday 14 November: Here is today's classroom demonstration. Note -- In this
demo, the variable k represents the damping coefficient, rather than
the spring constant. Why? Because I wasn't thinking clearly when I
chose a Latin alphabet replacement for gamma.
Thursday 6 November: My office hours will not begin until 2:30 today.
Thursday 6 November: The Java applet we have peen using in
class to draw phase plane diagrams is called "pplane". It is
available here.
Thursday 6 November: The reading and homework assignments for
Week #12 have been posted. Follow the link from the Schedule page.
Friday 31 October: I would like to remind about the matrix
algebra notes
I have made available. It may be a good idea to look them over once
more. Especially the section on determinants.
Thursday 30 October: The reading and exercises for Week #11
have been posted. Follow the link from the Schedule page.
Wednesday 29 October: Here are all the statistics about the course
(and about Exam #2 in particular) that you could ever hope to
have. Anyone want to set up a fantasy differential equations league?
Tuesday 28 October: I have added a note to the homework page
regarding problem 10.2.29. You may want to take a look at it, as it
will save you a bit of trouble in working the problem.
Friday 24 October: The reading and homework assignments for
Week #10 have been posted. Follow the link from the schedule page.
Tuesday 21 October: I will hold office hours today from 3:45-5:30.
Monday 20 October: There had been some discussion of moving the
review session to Tuesday evening. It seemed that there was just as
much conflict with that time, and so the day of the review session
will remain unchanged --- Monday, 7:00-8:30, in DH 1212.
Sunday 19 October: I have posted a Table of Laplace
transforms on the review page.
Sunday 19 October: A review session will be held on Monday 20
October from 7:00-8:30 in DH 1212.
Saturday 18 October: I have posted some previous exam problems
on the review page for Exam #2. Tomorrow I'll write up the table of
Laplace transforms. In the mean-time, don't feel like you need to
memorize a bunch of Laplace transforms.
Wednesday 15 October: I have posted a review page for Exam #2.
It is not yet complete, but it will give you something to get started
on. I will update it this weekend with some old exam problems, and
the table of Laplace Transforms you will have available during the exam.
Monday 13 October: IMPORTANT: The date for Midterm #2 has been
moved from Monday 20 October (The day after mid-semester break) to
Wednesday 22 October.
Wednesday 1 October: The reading and Homework assignments for
Week #8 have been posted. Follow the link from the Schedule page.
Thursday 2 October: The Final Exam schedule has been released.
The exam for this course is scheduled for 8:30-11:30 on December 8.
Thursday 2 October: I've made some corrections to Exercises for
Week #7. All the problems from Section 3.7 in the original posting
were meant to be in Section 3.6. The posted assignmnet is now (I
believe) correct.
Wednesday 1 October: The reading and Homework assignments for
Week #7 have been posted. Follow the link from the Schedule page.
Wednesday 1 October: The Matrix Algebra Review sessions will
continue on Thursday 1 October. Sections
3.4 through Section 4 or 5 of the notes
will be covered. There are three options available --- the times and
places are
| 11:30-12:20 |
PH 125B |
| 12:30-1:20 |
PH A22 |
| 1:30-2:20 |
OSC 206 |
You should not feel obliged to attend the session with the same time as your
regular recitation, go to which ever is convenient.
Wednesday 1 October: Welcome to October!
Tuesday 30 September: I will have to move my office hours to
10:00-11:30 for this Thursday only. Next week, my office hours will
return to their usual time: 2:00-4:00 Thursday.
Sunday 28 September: I have written up a short review of
partial fractions. It may help remind
you how to choose the form for the RHS, when computing partial fractions.
Saturday 27 September: The Reading and Homework assignments for
Week #6 have been posted. Follow the link from the Schedule page.
Friday 26 September: The Reading and Homework assignments for
Week #6 will be posted soon. Probably not today, but definitely by
tomorrow afternoon.
Tuesday 23 September: The Matrix Algebra Review sessions will
be resume on Thursday 25 September, after a week's hiatus. Section
3.3 through Section 4 of the notes
will be covered. There are three options available --- the times and
places are
| 11:30-12:20 |
PH 125B |
| 12:30-1:20 |
DH 1117 |
| 1:30-2:20 |
OSC 206 |
You should not feel obliged to attend the session with the same time as your
regular recitation, go to which ever is convenient.
Monday 22 September: There will be a short homework assignment
due this Friday, 26 September. The problems have been posted, the
reading assignments for the week will be posted later today or tomorrow.
Thursday 18 September: A Review Session for Exam #1 will be
held on Sunday 21 September, from 6:00-7:30pm in DH 1112.
Thursday 18 September: Due to a scheduling error, the matrix
algebra review sessions will be canceled for today. They will
recommence next week. I apologize for the inconvenience.
Wednesday 17 September: The Matrix Algebra Review sessions will
be held again tomorrow, covering Section 3.3 through Section 4 of the notes. There are three options available the times and places
are
| 11:30-12:20 |
PH 125B |
| 12:30-1:20 |
PH A22 |
| 1:30-2:20 |
OSC 206 |
You should not feel obliged to attend the session with the same time as your
regular recitation, go to which ever is convenient.
Sunday 14 September: I've corrected a misprint in the homework
assignment. Problem 2.7.19(abd) has been corrected to 2.7.1(abd).
Thursday 11 September: The reading assignments and exercises for Week #4
have been posted. Follow the link from the Schedule page.
Wednesday 10 September: The matrix Algebra Review sessions continue
tomorrow, 11 September. This week Sections 2.3-3.1 of the notes will be covered. There are three options available the times and places
are
| 11:30-12:20 |
PH 125B |
| 12:30-1:20 |
PH A22 |
| 1:30-2:20 |
OSC 206 |
You should not feel obliged to attend the session with the same time as your
regular recitation, go to which ever is convenient.
Thursday 4 September: The assignments for Week #3 have been posted.
Follow the link from the Schedule page.
Wednesday 3 September: The matrix Algebra Review sessions will begin
tomorrow, 4 September. There are three options available the times and places
are
| 11:30-12:20 |
TBA |
| 12:30-1:20 |
PH A22 |
| 1:30-2:20 |
OSC 206 |
You should not feel obliged to attend the session with the same time as your
regular recitation, go to which ever is convenient. These review sessions will
follow a set of notes
that you might want to print out for yourself.
Monday 1 September: The Week #2 Assignments page has been updated. I
have added some comments about a few problems, and some matrix algebra review
problems. The matrix algebra problems are not required, and should not be
turned in, but if you are unsure whether you want to attend the matrix algebra
review sessions, you can use these problems to help you decide. More
information about the matrix algebra review sessions will be forthcoming.
Wednesday 27 August: The Staff page has been updated with some of the
TA's Office Hours.
Sunday 17 August: Welcome to 21-260 Differential Equations.
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