MATH 20750, Ordinary Differential Equations, Spring 08

This web page will be modified during the course of the semester.

Quick Links: Homework, Course E-List Server Archives, Class Grades, and Mathematica Demos.

Course Information

Instructor:

Peter.Cholak.1@nd.edu

Office Hours: See my home page.

Office: Hayes Healy Center 204. 631-6507.

Text: Differential Equations by Polking, Bogges, and Aronld, IBSN: 0-12-143738-0

Class Time: MWF, 12:50--1:40am, Fitz 356. You are expected to attend every class. Excessive absences may result in lowering your grade and even failing the course.

Tutorial: Th, 3:30-4:20, Hayes Healy Center 231 (The instructor is also Cholak).

Problem Sessions: W, 7:30-9:30, Hayes Healy Center 117. These will be ran by Yao McCormick.

What this course is about: When math is applied in other subjects--e.g. physics, biology, economics, chemistry, and electrical engineering-- it is often via differential equations. A derivative tells us how a function is changing and a differential equation tells us how a function is related to it's derivative. My hope in this course is to provide you with a thorough introduction to ordinary differential equations. While I will certainly cover various techniques for finding explicit solutions to differential equations, I also plan to stress `qualitative' and `numerical' aspects of the subject---i.e. understanding the behavior of solutions to a differential equation even when explicit formulae for such solutions cannot be found. In real applications, it is rather rare to encounter a differential equation whose solution can be written down explicitly, so it is important to have techniques that go beyond finding explicit solutions. The equations that do admit explicit solutions end up serving as idealized `models' that shed light on the more complicated equations that one actually encounters.

What This Course Will Cover: We will go through parts of Chapters 1,2,3,4,6,8,9, and 10 of the above textbook. The topics of the course and the time we will allot to each are (roughly) as follows: first order equations (3 weeks); second and higher order linear equations (3 weeks); numerical methods (2 weeks); linear systems of differential equations (3 weeks); non-linear systems of differential equations (2 weeks).

Exams Dates

Exam I: Friday, February 15. Practice Exam 1

Exam II: Wednesday, March 19. Practice Exam 2

Exam III: Friday, April 18. System's Exam from 30560 Problem 5 is from 9.9. Skip this for now. Perhaps on the final. Problem 6, 8 are from Chapter 10, you will see problems like this on the final. Perhaps this is about the right length. But it does not cover all the material. Solutions are available. Some more good problems from past exams. The one things these problems miss are good problems from the end of 9.2 and 9.6. Exam 3 solutions.

Final: Thursday, May 8, 4:15--6:15, 256 Fitz. Look at problems 6,8 from System's Exam from 30560. Some more good problems from past finals. Final solutions.

The exams are in class. Exams may be made up only with an excused absence from the Assistant Vice President for Residence Life.

Homework

Homework is be assigned daily but collected weekly on Friday. I will only answer questions about the homework the class period after the homework is assigned. Be sure check the assignment after class as it might change. While you can work together on the homework, you must note on the homework who worked on the problems with you. You must write up the homework separately. Homework for the proceeding Friday, Wednesday, and Monday will be collected on each Friday starting with the second Friday of class. I hope to use concousre to keep track of your hw grades.

Honor Code

The Honor Code is in effect for all exams and assignments. You are encouraged to work together on assignments, but copying in any form or submitting work done by others as your own is a violation of the Honor Code.

Grades

The exams are worth 100 points each, the final is worth 150 points and the homework is worth 150 points for a total of 550 points. Each exam and the final will be curved. I will use concourse to announce grades.

Computer Programs and Demos

When necessary we will be using Mathematica and Mathlab for demonstrations. We will also use the following java programs: DFIELD and PPLANE. For some of the assigned problems the use of mathematica, mathlab, or the above java programs will be required. Mathematica 6 is available for download. Mathlab is on all the cluster machines. Demos will be posted a day or so before their presentation.

Mathematica Demos

Mathlab:
DFields.
PPlane.
To get several graphs on one page.