Math 433/533, Theory of Ordinary Differential Equations, Spring 2017, Class Announcements Page

Welcome

Welcome to the class. You should expect to find homework assignments and other important class announcements and links to class resources on this page. You should be in the habit of checking this page regularly; I will not necessarily say much about homework assignments in class -- this is the official place to find out about them!

I will generally add new material near the top of the page: a few items may always remain at the top.

Office Hours and other schedule information

My office hours are stated on my office door card (which is also attached to my office door), which also includes the times of my classes and seminars. I am thinking of typically coming in late on Mondays and leaving early Wednesdays and Fridays: at times when I am working at home, e-mail will reach me.

April 19 Homework

This assignment is due on the last day of class. There will be one more assignment due at the final exam period (at which I am currently planning to offer a make-up exercise). Problems 16.3 [the point here is to write it out in system form and verify that the Lipschitz condition they describe causes the Lipschitz condition for systems to hold; you may restrict yourself to doing this for n=2, a system of two equations]; 16.4 [I think the hint works: you do need to do the work leading up to the point where the hint applies then complete the argument using the hint]; 16.6 [the hint gives an answer, but you need to explain clearly why this gives a counterexample to an 11.1 style result]. I may have more to say when I have actually worked these myself; I'm not very satisfied with this as a homework set. I reserve the right to add new problems or change some of these as late as Sunday.

April 7 Homework

On Thursday April 6th we are stalled in the middle of discussing theorem 16.3. Your homework due April 13 is 16.1 (set up and carry out enough steps of the Picard iteration to get the pattern); 16.2 (he really does mean 1.6, 1.8 in chapter 1); doing it for n=3 is enough; you may optionally attempt 16.4 (I may lecture it when I figure it out). Set up spreadsheets to estimate the solutions to the two problems in 16.1: you may turn in the spreadsheets electronically -- do some experiments and discuss the magnitude of the error in your estimates for different step sizes (with actual numbers) on your papers. In response to a request from the class, we consider the equation u1' = x + u2^2; u2' = x + u1^2; u1(0)=1; u2(0) = -1. Show that this system satisfies a Lipschitz condition and determine an interval around 0 on which we are sure that it has a unique solution. You may use b=1. This should involve some fairly evil bookkeeping, and you need to remember what his measure of distance is (taxicab metric). Showing that it has a Lipschitz condition should not be hard.

Week 10

Week 8

Week 7

Week Five

Week Three

Week Two

Week One