Math 4791/5791 - Problem Set 10
Fall 1998

Due December 1

  1. Please read sections 7.0 - 7.3 of the text. The rest of Chapter 7 is certainly interesting, but is best left for optional reading.
  2. Limit cycles. Problem 7.1.1.
  3. Coordinate transformations. Problem 7.1.5.
  4. Gradient systems. Problems 7.2.5 and 7.2.7.
  5. Using the Poincare-Bendixson Theorem. Problem 7.3.3
  6. *Using the Poincare-Bendixson Theorem. Problem 7.3.1

Circular pursuit (10 points extra credit for everyone ) (see Problem 7.1.9).

A duck swims at unit speed around the edge of a circular pond of unit radius. Starting at the center of the pond, a dog swims at speed tex2html_wrap_inline18 , at all times moving directly toward the duck. Find the ODEs that describe the path of the dog. Solve these equations, if possible, for various values of s.

tex2html_wrap_inline22 means required of graduate students.


Wed Nov 18 06:00:59 MST 1998