Welcome to the web page for Math 132S (Spring 2010)

Tuesday and Thursday, 11:40 AM - 12:55 PM,

Office hours: Monday and Wednesday900 AM to 1000 AM.

Here are posted useful information concerning the organization of the lecture, as well as the syllabus and the homework assignments.

Textbook

The textbook adopted in this class is "Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations by P. Glendinning.

You can also look at Nils Berglund webpage for online notes: http://www.univ-orleans.fr/mapmo/membres/berglund/geom.html and http://www.univ-orleans.fr/mapmo/membres/berglund/pert.html

Some Suggestions for the Project

You have the possibility to choose any project you like that relates to the study of the qualitative behavior of nonlinear ODEs. The main criterion is that you learn a technique that you can orally present during 20 minutes to the class during the last two weeks of the class.

You can also think about the following propositions:

•  The dynamics of repeated impacts with a sinusoidally vibrating table
•  Remarks on Sharkovsky's Theorem
•  Prove the Center Manifold Theorem
• Prove the Poincare-Bendixon Theorem, cf. www.math.hmc.edu/~levy/181_web/Zimmerman_web.pdf
• Prove the Poincare-Siegel Theorem, cf. the following introductory papers on the method of Poincare normal forms:NF1, NF2, NF3, NF4.
• Animal Gaits http://people.mbi.ohio-state.edu/mgolubitsky/reprintweb-0.5/output/key.Gaits.html
•  Huyghen's clocks, cfhttp://www.americanscientist.org/issues/pub/huygenss-clocks-revisited and http://rspa.royalsocietypublishing.org/content/458/2019/563.full.pdf
• Global Stabilization of an Inverted Pendulum
• On Linear Normal Forms, cf. On matrices depending on parameters
•  Moon-Earth-Sun: The oldest three-body problem
• Review of different techniques for the construction of Lyapunov functions.Michael Brin (Author) it Amazon's Michael Brin Pagell the books, read about the author, and more.See search resultsor this authAre you an author? Learn about Author P

search resultsis autMiscellaneous Reading

•  http://www.scholarpedia.org/article/History_of_dynamical_systems and http://www.princeton.edu/mae/people/faculty/holmes/lectures/

Are you an author? Learn about Author CentraGrade

There will be two midterm exams on February 18th and April 13th. The last two weeks of class will be for the oral presentations of the projects.

Letter grades will be assigned only at the end of the semester.

Homework Assignments

Homework is indispensable for a good understanding of the material. Mathematics is actually more about understanding than about memorizing. You are strongly encouraged to work all of them out. Check your email for the assignments.

Remarks

• No makeup exams. A missed exam counts as zero points.
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• The three lowest scores will be dropped when calculating your homework grade.
• Unless I state otherwise, you are allowed to discuss the homework with others in the class. However, each student must turn in his or her own work.
• Late homework will not be accepted under any circumstances, as it is a major inconvenience to the grader.
• Only selected problems from selected sets will be graded.
• Please print your name, staple your homework, and write down the homework number.
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• Grades will be posted in Blackboard
• The Duke Community Standard is taken very seriously. Make certain you are familiar with it.