CSCI 4446/6446 Course materials for Spring 2009:
- Most of the files here are in postscript format. You can
download a postscript viewer here (or google "download
ghostscript" and take your pick)
-
General information and administrivia
-
The e-reserves
site.
- Detailed syllabus
- Problem Set 1 : logistic map.
Here's a pdf version if you're
having trouble seeing the second page.
Check out this
link to Wolfram Research for pictures of what some solutions to
2(b) look like. You may wish to review section 1 of the ODE notes
listed below if your knowledge of differential equations is at all
rusty.
- Problem Set 2 : bifurcation diagrams
and Feigenbaum's constant. Here is a very short tutorial on the unix
plotting tool gnuplot .
- Problem Set 3 : fractals. Here are
some examples of fractals
in the wild and in various
computational/mathematical systems.
- Problem Set 4 : Runge-Kutta and the
driven pendulum equations.
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Final Project Guidelines
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Problem Set 5 : adaptive Runge-Kutta and
the Lorenz and Rossler systems.
The following materials may be useful to you as
you do this problem set:
- Problem Set 6 : Poincare sections.
The netnews posts about numerical dynamics that are listed above (PS5)
may be useful here as well.
- Final Project Details
- Problem Set 7 : variational equation.
See the notes listed below.
-
Problem Set 8 : embedding. Click here for instructions on getting the data
for this problem set, and here for
an example of how to embed a data set. Sections 3 and 4 of the TSA
notes below should also help. Click
here for a detailed list of the assigned reading for this topic
and here to see Jay Kominek's mpeg
movie of what happens as you change tau (2.9MB file).
- Problem Set 9 : Lyapunov exponents.
See the "interesting links" listed below. Click here for a detailed list of the
assigned reading for this topic and
here for a schematic of the algorithm. NOTE: there's lots
of software on the web to do this, and almost all of it is baroquely
written, hard to figure out, and hard to get working. Do not
attempt to snarf-and-modify this kind of stuff for problem set 9, or
you will have a nasty battle on your hands. Click here for a Linear
Algebra package that finds eigenvalues.
- Problem Set 10 : fractal dimension.
Click here for a detailed list of
the assigned reading for this topic.
- Problem Set 11 : playing with bike
wheels, writing Lagrangians, and starting to explore the two-body
problem for a binary star. This material is covered in the first few
sections of the classical mechanics notes listed below. Click here for a picture defining true
anomaly.
- Problem Set 12 : integrating the
two-body equations. See section 4 of the classical mechanics notes
listed below. Here's an interesting
link that Kristine Washburn found about a variant of this problem.
You may also wish to check out the n-body section of Colonna's webpage
(listed below).
- PRESENTATIONS: 21 and 23 April for CSCI 6446 students.
Grads will give talks; undergrads will write a short paragraph about
each talk and email it to me. I will pass these along to the grads.
Here are some of my favorite presentation hints, and another take on the matter from the Chronicle
of Higher Education. Uri Alon's "materials for nurturing
scientists" page has some useful "how to give a good talk" material
as well.
- Problem Set 13 : integrating the
three-body equations for a binary-field star collision. See section
4.2 of the classical mechanics notes listed below.
Liz's written notes:
Some interesting links: (caveat emptor!)
- Chaos in the path of a Roomba
- The
Google Books link to the Strogatz text
- Stephen Wolfram's WolframTones
- NASA's movie of
Hyperion tumbling
- Remember that wonderful
"powers of ten" video from high-school physics?
- SIAM's dynamics
tutorials, many of which were contributed by grad students in courses
like this one.
- The Myphysicslab site,
which contains Java simulations of various interesting dynamical
systems.
- The Experimental Chaos
Conference, whose submission deadline this year is 25 May. I will
encourage people the best projects to submit an abstract to this
conference.
- The Center for
Computational Biology, a CU-Denver/UCHSC joint venture.
- Mathworld is back!!
- A
beginner's tutorial for matlab, courtesy of Kristian Sandberg.
- The
FAQ for sci.nonlinear (to which you should all
subscribe, along with comp.theory.dynamic-sys)
- The Santa Fe Institute and
a couple of its programs: the Complex Systems
Summer School and the Research Experiences for
Undergraduates.
- Mike Rosenstein's home
page, which contains some useful chaos-related software.
- NIST's Guide to
Available Mathematical Software
- Michael Banbrook's
Chaos Analysis
Software
- The Numerical Recipes webpage
- Some Java
demos developed by Michael Cross, who teaches the CSCI4446-equivalent
course at Caltech.
- The Chaos
Hypertextbook
- Helwig Loeffelmann's visualization
of dynamical systems page. The pages above that are interesting,
too.
- Jean-Francois Colonna's
"virtual space-time travel" page, which includes lots of stuff
about the Lorenz system, pendula, the n-body problem, etc. Very nice
graphics.
- Eric Weisstein's Encyclopedia of
Mathematics. A great place to look things up!
- Predrag Cvitanovic's UPO publications
page
- Some sources of economic and other time series data:
