Math 5260 Dynamical Systems
Syllabus
Fall 2001
Prof. Peckham
- Instructor: Bruce Peckham, Assoc. Professor, Dept. of Mathematics and Statistics
- Office: 104 Campus Center, 726-6188, bpeckham@d.umn.edu
- Office Hours: M 1:30-2:30pm, T 1-2pm, WF 10:30-11:30am,
or by appointment
- Meeting times: MWF 12-12:50 in Cina 308
Classes will occasionally be replaced by labs, usually in Montague 209.
- Text: Nonlinear Dynamics and Chaos,
by Steven H. Strogatz
Course Description
Dynamical Systems is currently
one of the most active and rapidly growing areas of
mathematics. Dynamical systems are typically divided into continuous
(differential equations) and discrete (iteration of maps). This course
covers both continuous and discrete dynamical systems.
We focus on nonlinear dynamical systems. Consequently, we
concentrate on
qualitative descriptions of solutions, as
opposed to computing formula solutions.
For example, we study the
long-term behaviors of solutions. There is a surprising amount of
complexity present in the ``orbits" of relatively simple differential equations
and maps. Our goal will be to understand some of these ``simple'' systems,
and in the process, understand what is meant by chaos.
The material is mostly covered in Chapters 1-12 of the Strogatz
text. Not all sections of all chapters will be covered.
Some supplemental material, not included in the text, will occasionally
be presented in lecture.
Course Prerequisites
Differential Equations with Linear Algebra (Math 3280) or equivalent or
permission of the instructor.
Grading (Topics and dates are tentative)
Exam 1: seventh week Ch's 1,2,3,5,10 15%
Exam 2: fourteenth week cumulative 20%
HW sets, Labs, ...: 65%
-------------------------- ---
Total: 100%
HW Corrections: Correcting incomplete or incorrect homework is strongly
encouraged. Half credit will be assigned for corrections.
General policy statement
Lectures, material in the text, homework sets, and tests are
all intended to complement each other. No one is a replacement for any of the
others. You are, in general, expected to learn material which is covered via
any of these sources.
Homework Sets and Ground Rules
Homework/labs will be turned in roughly every week or two.
All work should be neatly written,
well-organized, and complete.
For regular homework sets, you are encouraged to exchange
ideas with each other, but each person should write up his/her
solutions completely
in his/her own words. It is never appropriate to give a written version of a
problem/proof to another classmate, except to have the classmate read and
evaluate your work with you present.
It is OK to verbally explain your ideas to another classmate, as long as the
classmate then writes up his/her work on his/her own.
One person copying a classmate’s solutions is expressly forbidden
and will result in both students receiving zeroes for that complete
homework set and facing academic disciplinary action.
It is often instructive to read the problems at the end of
each section and think about how you would solve them, even if you don't actually
attempt to solve them.
Assignments will be confirmed by email, and all past and
current assignments will be posted on the web
at `www.d.umn.edu/~bpeckham/Math5260F2001.html'.
Computer Lab Policy
Labs will be assigned as part of homework sets.
Some time
to do labs will be provided during regularly scheduled times. Other time
must be arranged on your own.
You are encouraged to any formal labs in the course
with a lab partner. When you do, you may turn in one lab writeup for the
pair. It is expected, however, that both partners participate in
all parts
of the lab. For example, it is unacceptable for one person to do the computer
part of a lab and another to do the writeup. In particular, both partners
should have proofread the final version before handing the lab in. You
should not have the same lab partner for more than two labs.
Computational expectations. Most labs will be performed with Macintosh
software packages: notably Differential Systems for differential
equations and Chaos and Dynamics for discrete dynamical systems.
Both packages are available on the "Lab Server" from any of the ITSS "Full
Access" labs on campus with Macintosh machines.
No computer programming will be required,
but writing your own programs to do your own investigations, or to
duplicate tasks performed by the course software, is encouraged.
Missed Exams or Quizzes
Missed quizzes
or exams will
be assigned a zero score unless you provide a valid written, signed
(by a Doctor, for example) excuse for
your absence; unless it is not possible to do so, you must provide verbal
notice ahead of time to your
instructor for an absence. Arrangements
for a makeup should be made as soon as you know you will miss.
Do not wait for the next
class. You can leave the instructor
a message 24 hours a day by phone or email.
Oversleeping,
poor preparation, slight colds, and cold weather are not valid excuses.
Disabilities
Please inform me of any disabilities of
which I should be aware
in order to provide for equitable participation.
Other References
- Lower level and Popular:
- Differential Equations, by Blanchard, Devaney and Hall, 1995.
Emphasizes the qualitative and numerical as well as analytical approach.
- Fundamentals of Differential Equations, by
Nagle and Saff. UMD's Differential Equations I
(Math Q3380, S3280 through S2000) text.
- Differential Equations and Linear Algebra, by Stephen W. Goode, 2nd
edition, 2000. UMD's text for Math 3280,
Differential Equations and Linear Algebra.
- Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics, by
R. L. Devaney, Addison-Wesley, 1990. Introduction to discrete dynamical systems,
aimed at high school level (but containing much more).
- Chaos: Making a New Science, by J. Gleick, Viking, 1987. History
of some of the ``players" in Chaos theory.
- Comparable level
- A First Course in Chaotic Dynamical Systems: Theory and Experiment by
R. L. Devaney, Addison-Wesley, 1992. Text used for the old quarter course:
Discrete Dynamical Systems (Math Q5695).
Excellent introductory text for discrete dynamical systems, including
complex dynamics (Mandelbrot set, Julia Sets). Material from this text will
be used to supplement Chapter 10 material in Strogatz.
- Chaos: An introduction to dynamical systems by Alligood,
Sauer, and Yorke, Springer-Verlag, 1996. Second choice for text for
Math 5260. Includes both differential equations and discrete dynamical
sytems.
- Differential Equations and Dynamical Systems, by L. Perko,
Springer-Verlag, 1991.
- Differential Equations: A Dynamical Systems Approach, by Hubbard and
West, Springer-Verlag, 1991.
- Differential Equations, Dynamical Systems,
and Linear Algebra, by Hirsch and Smale, 1974. Major emphasis on linear algebra,
including Jordan Canonical Form.
- Dynamics and Bifurcations, by Hale and Kocak, Springer-Verlag, 1991.
Text used for the old quarter course Differential Equations II (Math Q5385).
Differential equations and discrete dynamical systems.
- Higher level
- Nonlinear Oscillations,
Dynamical Systems, and Bifurcations of Vector Fields, by Guckenheimer and
Holmes, Springer-Verlag, 1982. Classic introductory graduate differential
equations text.
- An Introduction to Chaotic Dynamical Systems, second edition,
by R. L. Devaney, Addison-Wesley, 1989. (Discrete dynamical systems. Intro
graduate level text.)
This page (http://www.d.umn.edu/~bpeckham/www) is maintained by
Bruce Peckham (bpeckham@d.umn.edu)
and was last modified on
Tuesday, 02-Sep-2003 16:23:34 CDT.