Nonlinear Dynamical Systems, Chaos and Fractals - Math 4560

Instructor:  Professor Stephen Montgomery-Smith
Text Book:   Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering, Strogatz.

Office: 222 Math Science Building
E-mail: (this is an effective way to communicate with me).
Telephone:  882-4540.  If you get my answering machine, please state your telephone number slowly and clearly.
Office Hours:  Mon 11a.m., Wed 11a.m. or by appointment, or if I am not busy when you turn up.  Please take advantage of office hours.  If these hours are not convenient for you, please see me after class, or email me, and I can see you at a time that is convenient.

There will be a midterm exam that will take place shortly before the last day to drop without a grade (

The second midterm and the final will be projects, in effect, a 'take home' exam.  There will also be homework.  For homework, I will allow that students help each other, (but don't hand in identical answers.)  But for the take home exams, I am going to ask that you do not work in teams.  If you get stuck, come and ask me.  The third midterm, close to the end of the semester, will test you on knowledge of the theory.  Midterms be preceded by reviews which will tell you what to focus on in studying.

Total 500 points (100 each midterm, 100 points given to homework, 100 points for the final.)  All students (undergraduate and graduate) will be graded on a plus minus grading scale.

A free alternative to Matlab is Octave. Octave is designed to be completely compatible with Matlab, and most Matlab programs do run on Octave. There are se veral different versions of Octave available, but for Windows I like this one: d ownload and run the following two files:, and http:// The menus will be in Spanish. To change this, delete or rename the directory languages i n the bin directory where Octave has been installed (for example, C :\Octave\Octave-UPM-R7\bin).

After installing Octave UPM, You will also need to install a package for the command ode45 to work: odepkg-sms-0.8.4.tar.gz. First download the package. Then start up Octave UPM by double clicking on the icon. From the command window, issue the command pkg install "whereever-it-is/odepkg-sms-0.8.4.tar.gz". The whereever-it-is needs to be the directory where you downloaded the file odepkg-sms-0.8.4.tar.gz.

After odepkg-sms-0.8.4.tar.gz is installed, everytime you start up Octave UPM, you will need to first issue the command pkg load odepkg in order for ode45 to work.

Another version is available at:

Problems with the Instructor:  If you have any problem with this course, please report it to Professor Ian Aberbach (Director of Undergraduate Studies) either by phone (882-7682) or by e-mail (

American Disabilities Act:  If you need accommodations because of a disability, if you have emergency medical information to share with me, or if you need special arrangements in case the building must be evacuated, please inform me immediately. Please see me privately after class, or at my office. or contact me by email or by phone.

To request academic accommodations (for example, a notetaker), students must also register with the Office of Disability Services, (, S5 Memorial Union, 882-4696. It is the campus office responsible for reviewing documentation provided by students requesting academic accommodations, and for accommodations planning in cooperation with students and instructors, as needed and consistent with course requirements. For other MU resources for students with disabilities, click on "Disability Resources" on the MU homepage.

Academic Dishonesty:  Academic integrity is fundamental to the activities and principles of a university. All members of the academic community must be confident that each person's work has been responsibly and honorably acquired, developed, and presented. Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful. The academic community regards breaches of the academic integrity rules as extremely serious matters. Sanctions for such a breach may include academic sanctions from the instructor, including failing the course for any violation, to disciplinary sanctions ranging from probation to expulsion. When in doubt about plagiarism, paraphrasing, quoting, collaboration, or any other form of cheating, consult the course instructor.

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