# 21-260: Differential Equations

### 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.