Math 421:  Dynamical Systems

Spring 2013 Course Page

Instructor:  Dr. Richard Brown

Lecture:   TTh 3:00pm - 4:15pm  Room:  Krieger 309

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.

 

Some documents of interest: 

• Lecture Notes:

  • Week 1:  Lecture 1, Lecture 2

  • Week 2:  Lecture 1, Lecture 2

  • Week 3:  Lecture 1, Lecture 2

  • Week 4:  Lecture 1, Lecture 2

  • Week 5:  Lecture 1, Lecture 2

  • Week 6:  Lecture 1, Lecture 2

  • Week 7:  Lecture 1, Lecture 2

  • Week 8:  Both Lectures

  • Week 9:  Lecture 1, Lecture 2

  • Week 10:  Both Lectures

  • Week 11: Lecture 1, Lecture 2

  • Week 12:  Both Lectures

• Extras:

  • Contraction Map Worksheet:  Picard Iterations.

  • Logistics Cobwebbing:  A Geogebra Application to demonstrate cobwebbing an orbit of the Logistic Map on the unit interval.

  • Mandelbrot and Julia Set Calculator:  A nice piece of software to explore magnifications of the Mandelbrot Set and its various Julia Sets for the quadratic map with choice of complex constant value c.

  • Solutions to selected homework problems are on the syllabus calendar.  However, Chris Kauffman has produced a version of the proof of 2.2.6 here.  A very nice treatment.

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 02/5/2013