Courses:

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Electricity and Magnetism (8.02), Differential Equations (18.03). Knowledge of ordinary differential equations is essential. Some linear algebra (knowledge of eigenvectors and eigenvalues) is also necessary. Having some experience with numerical computation is helpful but not necessary. This is an undergraduate course. Graduate students are reminded that this course carries no graduate credit and are encouraged to take Nonlinear Dynamics and Chaos (18.385J) instead.

This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering.

The course concentrates on simple models of dynamical systems, their relevance to natural phenomena, and methods of data analysis and interpretation. The emphasis is on nonlinear phenomena that may be described by a few variables that evolve with time. The theory of nonlinear continuum systems is covered in the sequel to this course, Nonlinear Dynamics II: Continuum Systems (12.207J/18.354J).

To promote the notion of numerical experiments, we will create several laboratory-like problem sets that require the use of a computer. The computer exercises will usually use MATLAB®, but students are free to use whatever software tools and computers they desire. No previous experience with numerical computation is necessary.

There will be weekly (or nearly weekly) problem sets. Some problems will be analytical while others will require use of a computer.

There will be a midterm examination in class.

At the end of the semester a major problem set (in lieu of a final exam) will be assigned, to be due on the last day of classes. This assignment will require the assimilation of the semester's work.

Problem sets should represent the student's own work but cooperation in the form of, say, comparison of one's numerical results with another's, or helpful hints, is welcome. The final problem set, however, should be an entirely individual effort. Students are not permitted to consult previously corrected problem sets, or solution sets or exams from previous years. The final grade will be based approximately as follows:

The most important book, which we recommend that you purchase, is:

Strogatz, S. Nonlinear Dynamics and Chaos. Boulder, CO: Westview Press, 1994. ISBN: 9780201543445.
Strogatz will be especially valuable for our discussion of stability of ordinary differential equations.

In our discussions of data analysis techniques, the following book may be useful:

Baker, G. L., and J. P. Gollub. Chaotic Dynamics. 2nd ed. Cambridge, UK: Cambridge University Press, 1996. ISBN: 9780521471060 (hardback).

Also of interest, due to its elementary and physical presentation, is:

Berg´e, P., Y. Pomeau, and C. Vidal. Order within Chaos. New York, NY: John Wiley & Sons, 1987. ISBN: 9780471849674.

Additional book recommendations are found in the readings section.