MA 226: Ordinary Differential Equations

Fall 2008

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

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Robert L. Devaney Department of Mathematics Office: Room 164 MCS Tel. (617)-353-4560 e-mail: bob <-at-> bu.edu Office hours: M W 12-1, TU 11-12 and by appointment

General Course Information

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 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.

Grading Policy:

Your grade will be determined as follows

• 40% two midterm exams
  
• 16% lab reports
  
• 40% final exam
  
• 4% class attendance
  

All grades for this course will be posted on the CourseInfo 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 and Class Participation:

At each lecture, I will post the names of a dozen 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. This helps me to match names with faces. If you are not present (or arrive late) on the day that your name is posted, you will lose two of the four points allocated in your final grade for attendance. You can expect to be selected for this honor approximately three times during the term, possibly more.

Text:

The text for the course will be that great! little book called Differential Equations, Third Edition, by Blanchard, Devaney, and Hall. Published by Thomson/Brooks-Cole, 2006. ISBN 0-495-01265-3. I recommend buying several copies and giving them as presents to your favorite people! By the way, the Second Edition is not suitable for this course. Also, this edition does not come with the software necessary for the lab projects.

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.

For homework assignments click here.
For information about lab reports, click here.
For information about sample exams, click here.

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