12.006J/18.353J Nonlinear Dynamics I: Chaos

Since 1989 I have taught a one-semester course on nonlinear dynamics and chaos to MIT
undergraduates. Students come from thoughout the institute, but predominantly from math
ematics, physics, and my own department (Earth, Atmospheric, and Planetary Sciences).
Since 1998 the course has been jointly sponsored by the Department of Mathematics.
The lecture notes that follow have undergone frequent revisions, but perhaps never more
so than in 2004, when they were (finally) converted to LaTeX. The conversion followed from
LaTeX notes prepared by Kurt Steinkraus, a student in 2003.
Advice and assistance from my TA’s has not only been much appreciated, but frequently
resulted in new ideas for the course. The TA’s included, in rough order of appearance, An
drew Gunstensen, John Olson, Olav van Genabeek, Kelvin Chan, Davide Stelitano, Joshua
Weitz, Alison Cohen, Greg Lawson, and David Forney. Thanks are of course also due to the
students themselves.
The construction of the course has been influenced heavily by the book by Berg´ e, Pomeau,
and Vidal [1]. Although some sections of the notes, particularly in the first half of the course,
derive directly from their book, a greater debt manifests itself in a shared “philosophy” and
organization: the introduction by way of oscillators, the emphasis on data analysis, the
extensive comparison between theory and experiment, and, perhaps most importantly, the
progression, in the second half of the course, from partial differential equations to ordinary
differential equations to maps.