Math 4791/5791 - Problem Set 6
Fall 1998

Due October 15

1. We will now return to Chapter 3 and study the important topic of bifurcations in first order ODEs. We will cover sections 3.1, 3.2, 3.4, and 3.5 thoroughly. We will also have a look at catastrophes as discussed in section 3.6.
2. Bifurcations. Please do problems 3.1.1, 3.2.3, 3.4.3, 3.4.5 from the text.
3. A classical epidemic model. Problem 3.7.6 and 6.5.6 from the text.
4. Period of the Pendulum.* Problem 6.7.4 of the text.

* means required of graduate students.

Just For Fun

(Use your imagination) One hot day a mile-long railroad rail expands by one foot and bows upward along the arc of a circle. How high off the ground is the center of the rail? Find an approximate solution first and then an exact solution.