Ordinary Dierential
Equations and
Dynamical Systems
Gerald Teschl
Note: The AMS has granted the permission to post this online edition!
This version is for personal online use only! If you like this book and want
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Series solutions
1
Regular series
We will study the solutions to certain second order linear dierential equations. We will start with equations
that are analytic at t = 0 and then turn to those that have singularities. Recall that a function is analytic
a
HOMEWORK 3 - Math 2920 - ODE I
RUBIN & ERMENTROUT - Fall 2012
This assignment is due in class on Thursday, October 25th, 2012.
1. Express etA as a polynomial in A for
1 1 4
A = 1 1 4
4 4 2
2. Sketch all the possible phase portaits of the system
x = ax 2y
ERMENTROUT & RUBIN - Fall 2012
HOMEWORK 2 - Math 2920 - ODE I
This assignment is due in class on Tuesday, October 9, 2012.
Let f be a function from U , an open subset of I n , to I n , throughout this assignment.
R
R
1. Problem 2.6 (Teschl), pg. 39, parts
HOMEWORK 2
Due Sept 13
1. It is possible to prove existence directly using nothing more than calculus.
Suppose that f (t, x) is dened in [t0 , t0 + ] B (a, ) and bounded
with bound, M . Let b = min(, /M ). f has a Lipschitz constant L. Let
t
yn+1 = a +
f
FINAL EXAM 2920: Due Friday December 12th in my oce before 5:00 PM
1. (20 pts) Find both Lyapunov & asymptotic stability where relevant. If
the system if Hamiltonian, nd the Hamiltonian. If linear stability doesnt
help and the system is non-Hamiltonian, t
MATH 2920 Ordinary Dierential Equations I - Fall 2012 (2131)
CLASS MEETINGS: TuTh, 4:00-5:15 PM, Thackeray 524
INSTRUCTORS: Dr. Bard Ermentrout and Dr. Jonathan Rubin;
oces: Thackeray Hall rooms 502 (Ermentrout) and 501 (Rubin);
phone: 412-624-8324 (Ermen
ERMENTROUT & RUBIN - Fall 2012
HOMEWORK 2 - Math 2920 - ODE I
This assignment is due in class on Tuesday, October 9, 2012.
Let f be a function from U , an open subset of I n , to I n , throughout this assignment.
R
R
1. Problem 2.6 (Teschl), pg. 39, parts
Ordinary Dierential
Equations and
Dynamical Systems
Gerald Teschl
Note: The AMS has granted the permission to post this online edition!
This version is for personal online use only! If you like this book and want
to support the idea of online versions, pl