CSCI 4446/6446 Course materials for Spring 2010:

• General information and administrivia
• Books on reserve for the course in the Gemmill Engineering Library.
• Detailed syllabus (am updating this -Liz Dec 2011)
• 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. Click here for a detailed list of the assigned reading for this topic, here for a schematic of Wolf's algorithm, and here for a Linear Algebra package that finds eigenvalues. There are lots of other references and resources for this problem set in the "interesting links" section below, including the TISEAN home page.
• 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: 24 and 26 April, in class. (If the CSCI 5446 enrollment exceeds 15, we will move these to an evening or weekend.) 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.

Slides:

• Lecture 1 (17 Jan)
• Lecture 2 (19 Jan)
• Lecture 3 (24 Jan) (with annotations)
• Lecture 4 (26 Jan) (with annotations)
• Lecture 5 (31 Jan) (with annotations)
• Lecture 6 (2 Feb) (with annotations)
• Lecture 7 (6 Feb) (with annotations)
• Lecture 8 (8 Feb) (with annotations)

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 and/or links: (caveat emptor!)

• The movement of an array of pendula with different lengths
• A much nicer double pendulum than mine!
• "Guide to Takens' Theorem" paper (heavy going, mathematically, but very comprehensive).
• Chaotic variations on birdsong
• Rigid body dynamics in zero gravity on the international space station.
• Google labs' Julia Map website, which uses the Google Maps API (!) to render fractals. The process is explained here.
• A youtube video about controlling inverted pendula, both single & double.
• An applet that simulates the Lorenz equations, allowing you to enter initial conditions with a mouse click.
• A gorgeous youtube video that zooms in on the Mandelbrot set.
• Another gorgeous video of an evolving 3D fractal surface.
• A 'chalkmation' youtube video - complete with music - about the Mandelbrot set (warning: a bit of foul language at the end).
• The TISEAN time-series analysis toolkit. The TISEAN site has binaries for UNIX & windows, but you can get Mac binaries here. You may need this fortran library to get it to work. Here are some examples of how to run all of this from MATLAB. Thanks to Rob Scheeler for finding the Mac stuff.
• 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.
• Wolfram's Mathworld site.
• The FAQ for sci.nonlinear (to which you should all subscribe, along with comp.theory.dynamic-sys)
• The Santa Fe Institute, which has a couple of great educational programs for graduate students (the Complex Systems Summer School) and undergraduates (called "Research Experiences for Undergraduates").
• 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. (look under the "data library" link from this page - the brown computer in the array of "Resources" icons)
  • 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.