Ordinary Differential Equations 2920
Fall 2012
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.
Rough Schedule
- Weeks 1-2 = Tu 9/1 - Tu 9/8: Teschl Chapter 1 (Newton's equations, Classification of differential equations, First order autonomous equations, Finding explicit solutions, Qualitative analysis of first order equations).
- Weeks 2-4 = Th 9/10 - Th 9/24: Teschl Chapter 2 (Theorems of existence, uniqueness, dependence of solutions on initial conditions, maximal intervals of existence; skip Section 2.3).
- Weeks 5-8 = Tu 9/29 - Th 10/22 Teschl Chapter 3 (Linear systems).
- Weeks 9-12 = Tu 10/27 - Tu 11/17: Teschl Chapter 5 (Boundary value problems).
- Weeks 13-16 = Th 11/19 - Th 12/17: Teschl Chapters 6-8 (Dynamical Systems). NOTE: There is no class on November 26 due to Thanksgiving Recess.
Finer schedule
- 9/1,9/3, 9/8: 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 9/17
- 9/10 Start Chapter 2. NOTE: No class on 9/15
- 9/17 2.4,2.5 HOMEWORK DUE SEPT 24
- 9/22-9/24 2.5,2.6,2.7 HOMEWORK DUE OCT 6
- 9/19-10/1 2.7 (if we dont finish) and 3.1,3,2
- 10/6: 3.3 HOMEWORK 4 DUE OCT 15 No class Oct 8.
- 10/13-10/15 3.4-3.6 Floquet theory!!! HOMEWORK 5 DUE Oct 22
- 10/22 Section 3.7, intro to 5.1 HW No. 6 Due Oct 29 - it is a short one!!
- 10/27-10/29 5.2-5.3
- 11/3-11/5 : Sturm Lioville and eigenvalues HOMEWORK 7 Due Nov 16
- 11/10-11/9 6.1-6.4 Teschl
- 11/17-11/19 Liapunov functions
- 11/24 Newtons equations in 1 D and some planar ODE stuff
- HOMEWORK 8 DUE THURSDAY DEC 3
- 12/1-12/3 Predator prey, Lienard equations
- 12/8-12/10 Poincare Bendixson Theory
- Last Homework 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 7.18 / 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??