Instructor: Associate Professor Lars Söderholm
Telephone 790 7152
Email: lars.soderholm@mech.kth.se Office: Level 6 of Osquars
backe 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 five home assignments and a final exam based
on the assignments and course text. The home assignments will
be handed out each of the first five weeks of the course and are to be handed
in the next week.
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. 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.
The course lasts weeks 4-9 and the lessons are
in M38
Mondays at 10
Tuesdays at 13
Home assignments |
To be handed in |
|
| Strogatz, 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 |
Tuesday January 27 |
|
| Strogatz, 3.4.2, 3.5.4, 3.5.5, 3.6.5, 4.4.2 |
Tuesday February 3 |
|
| Strogatz
5.1.9, 5.1.10, 5.2.13, 6.1.6, 6.3.6, 6.5.15, 6.7.2, 6.8.8 |
Tuesday February 10 |
|
| Strogatz 7.1.8,7.2.10,7.3.3,8.1.8,8.2.3,8.4.3 |
Tuesday February 17 |
|
| Strogatz 8.7.1,
9.2.1,9.3.8,9.4.2,10.1.9,10.3.7,10.5.1 |
Tuesday February 24 |