Ordinary Differential Equations 2920

ODEs and Dynamical Systems by Gerald Teschl

Theory of ODES by Chris Grant

Grades

Schedule

• 8/29,8/31, 9/6: Read Chapter 1 of Teschl. Do the following homework problems in Teschl: 1.1 p5;1.3,1.4,1.5,1.8 p8;1.13 p12;1.19,1.21 p 18. DUE Thursday 9/15
• 9/8 Start Chapter 2.
• 9/15 2.4,2.5 HOMEWORK DUE SEPT 29
• 9/20-9/22 2.5,2.6,2.7 HOMEWORK DUE OCT 6
• 9/17-9/29 2.7 (if we dont finish) and 3.1,3,2
• 10/4: 3.3 HOMEWORK 4 DUE OCT 13
• 10/11-10/13 3.4-3.6 Floquet theory!!! HOMEWORK 5 DUE Oct 27
• No class 10/19
• Section 3.7, intro to 5.1 HW No. 6 Due Nov 3 - it is a short one!!
• 10/25-10/27 5.2-5.3
• 11/1-11/3 : Sturm Lioville and eigenvalues HOMEWORK 7 Due Nov 17
• 11/8-11/10 6.1-6.4 Teschl
• 11/15-11/17 Liapunov functions
• 11/22 Newtons equations in 1 D and some planar ODE stuff
• HOMEWORK 8 DUE THURSDAY DEC 8
• 11/29 -12/1 Predator prey, Lienard equations
• 12/6-12/8 Poincare Bendixson Theory
• Last Homework DUE 12/15 Do exercises 7.2,7.8,7.11 in Teschl and 1,2,4 in the pdf here: Click me Do the following:
  Recall a heteroclinic orbit is a nonconstant trajectory whose omega (+infinity) and alpha (-infinity) limit sets consist of distinct fixed points and a homoclinic is a heteroclinic where the fixed points are the same. A limit orbit is a periodic orbit, a heteroclinic, or homoclinic orbit. Sketch a separate phase portrait for each of these cases as well as representative phase portraits showing it is valid. Kepp Lemma 7.17 / 7.18 in mind!
  • A trajectory T with alpha(T)=omega(T)={x0} but T is not {x0}
  • A trajectroy T such that omega(T) has one limit orbit and one fixed point
  • A trajectory T such that omega(T) has two limit orbits and two fixed points
  • A trajectory T such that omega(T) is a periodic orbit and alpha(T) is different periodic orbit.
  • A trajectory T such that omega(T) consistes of five limit orbits and three fixed points.
• 12/15-12/17 Probabaly some stuff on the lorenz equations??