CSCI 4446/6446 Course materials for Spring 2006:

• 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.
• Final Project Guidelines
• 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:
  • Some news posts from sci.nonlinear about numerical chaos .
  • Section 2.6 of the ODE Notes listed below (particularly for the last problem on this set)
  • Some pictures showing how different integration algorithms and different computers affect numerical solution of the Lorenz equations.
  • Some pictures showing how changing arithmetic precision affects the numerics.
  • A paper showing how to crochet the stable manifold of one of the fixed points in the Lorenz system.
• 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: 28 April for CSCI 6446 students. We will start at 1:55pm that day and probably run 5-10 min late. 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.
• 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:

• on Taylor series and error in numerical methods (not required, but possibly useful)
• on ordinary differential equations (ODEs) and solving them numerically
• on time-series analysis (TSA)
• on the variational equation
• on Wolf's algorithm for computing the Lyapunov exponent
• on classical mechanics

Some interesting links: (caveat emptor!)

• 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:
  • PhysioNet: public databases of ECG, neurological and other types of data.
  • The MIT-BIH EKG database.
  • Economic Time Series Page (Dec 2004: hung while coming up; need to check again)
  • Rainfall and temperature data from the Indian subcontinent (Dec 2004: this server is experiencing problems; need to check again
  • Sea surface temperatures, pressures, etc.
  • The Linguistic Data Consortium (LDC)'s TDT2 Mandarin Language Audio Corpus (Voice of America news broadcasts collected daily over a period of six months (February-June of 1998).
  • An impressive search engine for all kinds of weather data, run by NCAR (courtesy of Phillip Dressen) is a search engine for various types of Data from all over the world in all sorts of formats. So you might be able to find something interesting and
  • I also have a bunch of heart-rate data that was collected from the members of the spring 1999 version of this class for use in a project that year, as well as a CD full of various other time series data. The heartrate files are archived on tape; please contact me if you need them.
  • Let me know if you find others so I can post them here.