CSCI 4446/6446 Course materials for Spring 2010:

• General information and administrivia
• The e-reserves site.
• Detailed syllabus
• Problem Set 1 : logistic map. 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: 20 and 22 April for CSCI 5446 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:

• 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!)

• A chaotic musical instrument that was apparently inspired by one of my lectures (?!?!?)
• 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. Grad students: I encourage you to submit an abstract about your project to this conference.
• The Center for Computational Biology, a CU-Denver/UCHSC joint venture.
• Mathworld is back!!
• 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
• 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.
• 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.
  • 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).
  • Let me know if you find others so I can post them here.