MA 226: Ordinary Differential Equations

Fall 2017

Tu-Th 9:30-11:00 AM in Stone B50

Robert L. Devaney
Department of Mathematics

Office: Room 274 MCS
Tel. (617)-353-4560
e-mail: bob <-at->
Office hours: M Tu W 12-1 and by appointment

General Course Information

A Little Philosophy and a Warning: This is a course in ordinary differential equations. However, the course is by no means "ordinary." In years past, before we had widespread access to computers and computer graphics, courses in ordinary differential equations consisted mainly in a series of special tricks to solve special differential equations. Unfortunately, most differential equations (and in particular most differential equations that arise in applications) cannot be solved explicitly by these or any other methods.

Today we all have access to high-speed computers and computer graphics. Like humans, computers cannot solve most differential equations that arise. However, they can give us an APPROXIMATE or NUMERICAL solution. For many purposes, this is good enough.

Unfortunately, computers make mistakes (sometimes because of round-off errors or sometimes because the differential equation is not suited to numerical approximation). So we always have to be careful when we solve differential equations this way. More importantly, the output of the computer is not a formula that we can use to compute values of our solutions. Rather, the output from the computer is a rather lengthy list of numbers. Most often, it is best to view this list geometrically as a phase line or plane or other geometric object.

All of this means that this will be a very different type of mathematics course. In this course you will rarely be asked to generate specific formulas for solutions of differential equations. Rather, you will be asked to understand the algorithms that lead to numerical solutions, to interpret the resulting pictures produced by the computer, and to relate these images back to the original application.

You will also be required to perform lengthy labs and submit written lab reports. Your homework problems and questions on exams will often involve essays rather than simple routine computations. And you will often have to use technology to come up with answers to questions that are posed. Most of the labs will use the software that comes with the text. Be sure you have this software on your computer. Most students in the past have found this kind of course quite challenging, but lots of fun. If you are used to the old style of mathematics courses, be prepared for something quite different and perhaps much more relevant to whatever your use for differential equations is.

Warning: In the past, I have had problems with students submitting duplicate lab reports or copying portions of other students' reports. This is strictly forbidden. If you copy any portion of another student's lab report and submit it as your own, I consider this a serious infraction of University rules and will forward the lab reports to the appropriate disciplinary committee. Click here to see the University policy on academic conduct.

Grading Policy:

Your grade will be determined as follows

There will be three midterm exams in this course. However, we will drop your lowest score. Important: There are NO makeup exams in this course. If you miss an exam you will receive a zero for that exam and, presumably, you will wish to drop that score. Also, late lab assignments will not be accepted. All labs must be handed in during (or before) the class on the day they are due. The grader usually picks up the labs right after class and I cannot ask the grader to return to pick up labs that were not handed in on time. Also, I cannot accept email versions of the labs; you must have a friend drop your lab off in class if you cannot attend on the day that the lab is due. Finally, I allow the TF for this course to make arguments for raising the final grade a notch or two for students who have made exceptional contributions either in discussion section or in the main lecture.

The midterm exams will be held on

The Final Exam is scheduled for Tuesday, 12/19, 9-11 AM, in Stone B50.

All grades for this course will be posted on the Blackboard website for this course. Please check from time to time that all of your grades have been recorded properly. Notify me immediately if there are discrepancies. Important: You have one week from the time that midterm exams or labs are returned to challenge any grading discrepancies. After one week, your grade on that exam/lab is final. So please look over the grading right away.

Attendance, Class Participation, and Other Rules:

At each lecture, I will post the names of twenty or so randomly chosen students. Sometimes this will occur at the beginning of class; other times at the end of class. If your name is posted, I ask that you speak to me so that I can verify your attendance. Please bring your student ID. This helps me to match names with faces. I do this so that I can get to know the names of students who participate actively in the course as well as those who spend the time sleeping or not paying attention. This then helps me to decide whether or not to raise the final grade for students who are active participants. If you are not present (or arrive late) on the day that your name is posted, you will lose one of the four percentage points allocated in your final grade for attendance. You can expect to be selected for this honor approximately four times during the term, possibly more. By the way, all universities now have a strict policy regarding texting or using cellphones during class. Here is a wonderful video that explains this policy!


The text for the course will be that great! little book called Differential Equations, Fourth Edition, by Blanchard, Devaney, and Hall. Published by Brooks-Cole/Cengage Learning, 2012. ISBN 978-0-495-82674. I recommend buying several copies and giving them as presents to your favorite people! Incidentally, the Third Edition is no longer suitable for this course. Also, you should download the software that is available with the text. Several of the labs due in this course will make extensive use of this software.

Other information:

Homework is assigned at each lecture but not picked up or graded. Please note that there are review problems posted just before each midterm exam. Many of the exam questions will resemble the review and homework problems.

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