Math 2920
*** ORDINARY DIFFERENTIAL EQUATIONS I *** Fall 2017
Instructor: David
Swigon
Office: Thackeray 511, 4126244689, swigon@pitt.edu
Lectures:
TuTh 4:005:15pm, Thackeray
524
Office
Hours: TuTh
2:003:00pm or by appointment.
Course
Web Page: (check frequently for changes and updates) http://www.math.pitt.edu/~swigon/math2920.html
Course
Description
The course
will develop a basic theory of ordinary differential equations including the
existence & uniqueness of solutions of the initial value problem,
dependence on initial conditions, theory of linear differential equations and
systems, dynamical systems approach to autonomous differential equations local
& global behavior, HartmanGrobman theorem,
analysis of planar dynamical systems, etc.
Prerequisites
Linear
algebra, advanced calculus. Undergraduate ODE course is welcome but not
necessary.
Textbook
Gerald Teschl, Ordinary Differential Equations and Dynamical Systems,
AMS 2012, ISBN13: 9780821883280
downloadable from http://www.mat.univie.ac.at/~gerald/ftp/bookode/index.html
(we will not be using the Mathematica codes)
Other recommended books
Jack K.
Hale, Ordinary Differential equations,
Dover, 2009
Philip
Hartman, Ordinary Differential equations,
SIAM, 2002
Lawrence Perko, Differential
equations and dynamical systems, Springer, 2001
M. W.
Hirsch, S. Smale, and R. L. Devaney, Differential Equations, Dynamical Systems,
and an Introduction to Chaos, Elsevier/Academic Press, 2004
Grading
Scheme
Homework: 30%
Midterm
Exam: 30%
Final
Exam (cumulative): 40%
Schedule
Tentative
syllabus is given below. Homework assignments will be posted online and are due
one week after they are assigned.
Disability Resource Services
If
you have a disability for which you are or may be requesting an accommodation,
you are encouraged to contact both your instructor and Disability Resources and
Services, 140 William Pitt Union, 4126487890 or 4123837355 (TTY) as early
as possible in the term. DRS will verify your disability and determine
reasonable accommodations for this course.
Academic Integrity
Cheating/plagiarism will not be tolerated. Students
suspected of violating the University of Pittsburgh Policy on Academic
Integrity will incur a minimum sanction of a zero score for the quiz, exam or
paper in question. Additional sanctions may be imposed, depending on the
severity of the infraction. On homework,
you may work with other students or use library resources, but each student
must write up his or her solutions independently. Copying solutions from other
students will be considered cheating, and handled accordingly.
Syllabus
Week 
Reading 
Topics 
HW 
Aug
29, Aug 31 
Teschl,
§1.21.5, 2.1 
Review:
Classification of ODEs,Methods
for solving first order equations, Preliminaries 

Sep
5, Sep 7 
Teschl,
§2.22.3, 2.7 
Initial Value Problems Existence
& uniqueness of solutions, Peano’s theorem 
Problems
2.3, 2.4, 2.5, 2.6 (ii) and (iii), 2.8, 2.10 Due
Sep 14 
Sep
12, Sep 14 
Teschl,
§2.4, 2.6 
Dependence
on initial conditions, Extensibility of solutions 
Problems
2.14, 2.15, 2.19, 2.20 Due
Sep 21 
Sep
19, Sep 21 
Teschl,
§3.13.2 
Linear Systems Matrix
exponential, autonomous systems and equations Nineteen Dubious Ways to Compute
the Exponential of a Matrix, 25 years later 

Sep
26, Sep 28 
Teschl,
§3.33.4, 3.6 
Wronskian,
Variation of parameters, Periodic linear systems 
Problems
3.5, 3.16, 3.27, 3.28, 3.40 + Prove Corollary 3.16 Due
Oct 5 
Oct
3, Oct 5 
Teschl,
§6.16.3 
Dynamical Systems Flow,
vector field, integral curves 

Oct
10 Oct
12 
Teschl,
§6.46.5 
FALL
BREAK (Monday schedule) Orbits,
Poincare map, Liapunov and asymptotic stability 
Problems
6.1, 6.4, 6.5, 6.7, 6.9 Due
Oct 19 
Oct
17, Oct 19 
Teschl,
§6.6 
Liapunov’s
method, La Salle principle 

Oct 24 
MIDTERM EXAM 


Oct
26 
Teschl,
§6.6 
Liapunov’s
method, La Salle principle 

Oct
31, Nov 2 
Teschl,
§7.17.2 
Planar dynamical systems LotkaVolterra
systems, Lienard’s equation, Van der Pol’s equation 
Due
Nov 7 
Nov
7, Nov 9 
Teschl,
§7.27.3 
Jordan
curve theorem, PoincareBendixson theorem 

Nov
14, Nov 16 
Teschl,
§8.18.3 
Higherdimensional dynamical systems Attracting
sets, Lorentz equation 
Due Nov 21 
Nov
21 
Teschl,
§9.19.2 
Local Behavior Stable
& unstable manifolds, Stable manifold theorem 

Nov
28, Nov 30 
Teschl,
§9.3 
Hartman
Grobman theorem 
Due
Dec 11 
Dec
5, Dec 7 
Teschl,
§9.3 
topological
conjugacy 


