Ordinary Differential Equations 2920
Fall 2016
Tue/Th 4-5:15 PM
THACKERAY 524
Bard Ermentrout
Thackeray 502
EMAIL: bard_at_pitt_dot_edu
Office hours: by appointment
Textbooks
ODEs and Dynamical Systems by Gerald Teschl
Theory of ODES by Chris Grant
Grades
Grades will be based on the weekly homework. There will be no exams.
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??