Math 421:  Dynamical Systems

Spring 2010 Course Page

Instructor:  Dr. Richard Brown

Lecture:    TTh 1:30pm - 2:45pm

Room:  Krieger 308

Text:

A First Course in Dynamics, 1st Edition Hasselblatt, Boris and Katok, Anatole Cambridge University Press, 2003 ISBN 0 521 58750 6

Errata to the book.

 

 

 

Course Syllabus and Homework Assignment Schedule

 

 

 

There are Java Applets that are quite useful in understanding the nature of Ordinary Differential Equations, one of the common places to study dynamics.  They can be found here: 

 

JAVA Applets for ODEs

 

For now, pay attention to the Slope Field Calculators, particularly this framed version, which will load in a separate window.  I suggest you play with these applets.

 

(Selected) Applications

• Contraction Map Example:  Proof of existence and Uniqueness of first order ODEs

• Bifurcation Example:  Fish populations from my 110.302 course in ODEs

• The website, www.cut-the-knot.org is filled with Java applets designed to explore mathematical topics.  Try the following:

  • Emergence of Chaos:  An exploration of the quadratic map for parameter values between 3 and 4.

  • Canter Sets:  An applet that uses the "tent" map (a unimodal map of the unit interval comprised of linear pieces meeting in a point.  The height of the peak determines whether which orbits escape the interval and which remain.

(Selected) Homework Solutions

• Homework Set 1

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For those of you who would like help outside of that of the professor or TAs, there is a free service offered by the Mathematics Help Room.  Click for more details.

last updated 01/19/2010