640:252:01 Fall 2013 Home

640:252:01

Elementary Differential Equations

FALL 2013

Basic information

Instructor: Professor Eugene Speer
- Hill Center 520
- 848–445–7974
- speer at math.rutgers.edu
Office hours:
- Tuesday, 3:20–4:40 PM, Hill Center 520
- Thursday, 10:20–11:40 AM, Hill Center 520
- Or by appointment or chance in Hill Center 520
Detailed course information and policies: As web page and as a PDF file.

Class Diary: A record of our progress through the material

Course web page: The general web page for Math 252 includes links to a suggested syllabus and to several sets of supplementary notes.

Homework assignments and solutions: Click here for assignments.

Final Exam

The exam will be held on Thursday, December 19, from 12:00 to 3:00 P.M., in SEC 217. The exam will be cumulative, although some emphasis will be placed on topics from the end of the course, which were not covered on either of the two earlier exams.

Coverage: The exam will cover:
- All material from the first two exams. Details of that coverage are still available below on this web page.
- All material covered since the second exam. More specifically: this includes material from Sections 5.1 through 5.4, 3.6, 4.1 though 4.4, 1.4, 7.1, and 7.2. We did not cover the idea of "Hamiltonian systems"" from 5.3, although we did of course discuss conserved quantities, also covered there.
Last assignment: Assignment 11 (not to be collected) has been posted, and solutions will soon be posted on Sakai.
Review: There will be a review/problem session on Friday, December 13, from 1:00 to 3:00 PM, in Hill Center 124. Here is a set of review problems, now including some short answers.
Office hour: I will hold an office hour on Thursday December 19, from 9:30 to 11:00 AM, in Hill 520.

Announcements and supplementary material

12/10/2013: Here is a Maple worksheet with some plots for driven harmonic oscillators that I showed in class, and here are the slides on results of Euler's method and comparison of different methods, also from class.
12/02/2013: Here are the notes on One Dimensional Motion in a Potential. We discussed related material in class on November 15, 19, and 22.
11/25/2013: Here are the slides that I showed in class on November 22, showing phase portraits for the pendulum.
11/16/2013: Here are the slides that I showed in class on November 8, showing various views of the phase plane for competing species (both weak and strong competition).
11/15/2013: Here are the notes Some Remarks on Phase Planes, which talk about finding conserved quantities.
11/04/2013: Our treatment of matrix exponentials was not completely parallel to the treatment in the notes posted on October 29 (below). Here are some Supplementary Notes on Matrix Exponentials which should fill in any gaps.
10/29/2013: Here are the notes Introduction to Matrix Exponentials which I referred to in class today.
10/24/2013: Here is a Maple file showing phase portraits for several types of linear systems; these are examples which were discussed in class over the last week.
10/11/2013: Here are some review notes on linear algebra, as well as some notes on linear systems of ODEs which cover the material we discussed on October 1 and October 4.
9/29/2013: Here is the Maple work sheet of phase-plane plots that I showed in class on September 24 and 27.
And here are some supplementary notes on bifurcations from the course web page.
9/17/2013: Here are some notes on linearization. Only a small part of this material is covered in the text, but you are responsible for it. today.
9/10/2013: Here is the Maple file , with sketches of several slope fields and some solution curves for each, that I showed in class today.
9/3/2013: As we work through the first chapter of the text you should also read the supplementary notes available here and also on the course web page.

Exam 2

The second exam will be on Tuesday, November 12. The exam is closed book and closed notes, and no calculators are permitted. You will be given a small formula sheet; see the review problems (soon to posted below).

Coverage: The exam will cover our work in the course through Friday, November 1; material which was on the first exam will not be covered explicitly but of course some of it might be relevant for questions on later material. The material covered since the first exam includes:
- Material on general properties of systems of linear ODEs, covered in class and summarized in the posted notes on linear systems of ODEs . I will not include any specific questions on linear algebra but some of the material in the posted review notes on linear algebra might be relevant.
- Material from Sections 3.1–3.5, 3.7, and part of 3.8 of the text.
- Material on matrix exponentials covered in class and in the two sets of posted notes: Introduction to Matrix Exponentials and Supplementary Notes on Matrix Exponentials

Problem Session: We will hold a problem session on Friday, November 8, 3:00-4:30 PM, in Hill 124.. This is not a review presented by me but a chance for you to ask questions about any material in the course. In particular, I suggest that you work on the review problems before the review session.

Review Problems: Here is a set of review problems to help you review for the exam, and to give you something to ask questions about at the problem session. Here are some short answers to help you check your work.
Extra office hours: I will hold extra office hours on Monday, November 11, 10:30–11:30 AM and 2:00–3:00 PM in Hill 520.

Exam solutions: Now posted on Sakai.

Exam 1

The first exam will be on Tuesday, October 8. The exam is closed book and closed notes, and no calculators are permitted. I do not plan to give out any formula sheet.

Coverage: We will cover all our work in the course through Friday, September 27; this means all the work on Chapters 1 and 2 of the text. Specifically, in Chapter 1 we have covered everything except Section 1.4 on Euler's method, and the "guessing" method for linear equations discussed in Section 1.8. In Chapter 2 we have covered essentially all of Sections 1 through 4 except the exact solutions of the mass-spring problems. Finally, the exam will cover the posted notes on linearization of ODEs

Problem Session: We will hold a problem session on Friday, October 4, 3:00–4:30 PM, in Hill Center 124. This is not a review presented by me but a chance for you to ask questions about any material in the course. In particular, I suggest that you work on the review problems before the review session.

Review Problems: here is a set of review problems to help you review for the exam, and to give you something to ask questions about at the problem session. Short answers are included for most of the problems, to help you check your work.
Extra office hours: I will hold extra office hours on Monday, October 7, 1:30–3:00 in Hill 520.

Exam solutions: Now posted on Sakai.