Instructor: Professor Martin Lesser : Telephone (08) 790 7580
Email: mlesser@mech.kth.se Office: Level 6 of Osqb. 18
Text: Nonlinear Dynamics and Chaos by Steven H. Strogatz
Available at the Student Book Store

Prerequisites:
Basic Mechanics, Basic Differential Equations, Linear Algebra

General Course Description:
The course takes a non-abstract and applications oriented approach to the tools used for the study of dynamic systems, mainly but not exclusively in the subject of mechanics. These tools include bifurcation theory, phase space analysis of systems of differential and difference equations, asymptotic analysis of attracting states including fixed points, limit cycles, almost periodic motion and strange or chaotic attractors. We will also examine the concepts of fractals, fractal dimension and attractor reconstruction. Mechanical systems studied include the whirling bead on a wire, the forced pendulum, various nonlinear oscillators and the convective system governed by the Lorenz equations.
Assignments and Grading:
There will be three assignments and a short oral exam based on the assignments and course text. The first two assignments must be handed in before the last day of the course on the 28th of February! The last assignment is due on Friday the 7th of March. Lateness will result in a more difficult final oral! Graduate students will receive a pass or fail grade and can expect a longer oral examination. Exams can be scheduled via email or at the last course meeting. Note that the problem sets will not be graded but selected problems will be discussed as part of the oral exam. I also reserve the right to assign additional problems that may arise in class discussions.

Assignment 1
2.1.5,2.2.7,2.2.10,2.2.13,2.4.7,2.6.2,2.7.5,3.1.4,3.2.3,3.4.2,3.5.4,3.5.5,3.6.5,4.4.2
Assignment 2
5.1.9,5.1.10,5.2.13,6.1.6,6.3.6,6.5.15,6.7.2,6.8.8,7.1.8,7.2.10,7.3.3,8.1.8,8.2.3,8.4.3,8.7.1
Assignment 3
9.2.1,9.3.8,9.4.2,10.1.9,10.3.7,10.5.1,11.1.7,11.3.7,12.1.2,12.2.5,12.5.4

Reading and Lectures:
The book consists of 12 chapters. You should attempt to read all the text with the exception of the following sections: 3.7,4.5,4.6,5.3 and 9.6. Though the book is quite readable, this is a large task for the short period of 6 weeks and I do not expect complete comprehension. The problem assignments are a guide to what is most important in the way of understanding. The lectures will follow the text closely but again due to the time available will not cover all the reading. Roughly we will spend 2 weeks on each of the three main sections of the text. In summary reading the book and doing the problems are primary. The lectures are intended to aid you in this task.

Office Hours:
I will be available on Thursday from 13:00 to 15:00 during the period of the course. Other times can be scheduled on an individual basis via email or telephone.

Class List:
Tuesdays weeks 4,6,7,8,9 in room L43 at 13:00
Tuesday week 5 in room L44 at 13:00
Fridays weeks 4-9 in room E53 at 10:00

Interesting Web sites that are a gateway into the net dynamic systems world.
http://math.bu.edu/DYSYS/chaos-game/chaos-game.html Great stuff about the "chaos game" as a way to define fractal sets.
http://amath.colorado.edu/faculty/jdm/faq.html A useful dynamical systems FAQ
http://www.enm.bris.ac.uk/staff/hinke/dss/ Very complete guide to software on many platforms.
http://www.exploratorium.edu/complexity/menu.html Very nice tutorial at basic level with history.
http://tp.lc.ehu.es/jma.html Excellent free pc software with complete manual that is a text in itself
http://hypertextbook.com/chaos/ Online text on dynamics systems with guide to Mac software.
http://gonzo.springer-ny.com/nst/ One of many journals on nonlinear science. Free access to lots of the content.
http://ocw.mit.edu/18/18.06/f02/video-lectures/index.html If you need a review of linear algebra this is the place. A complete net based video course based on Gilbert Strange's MIT course and book.