Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Prerequisites
(8.02 Physics II: Electricity And Magnetism or 8.021 Physics II: Electricity And Magnetism or 8.022 Physics II: Electricity And Magnetism) and (18.03 Differential Equations or 18.032 Differential Equations)
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.
Course Description
This course provides an introduction to 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, mathematical theory underlying their behavior, 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.
To promote the notion of numerical experiments, we assign several laboratory-like problem sets that involve numerical simulation of dynamical systems. Python and Matlab code will often be provided, but students are free to use whatever tools they desire.
Textbook
Strogatz, S. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press, 2020. ISBN: 9780738204536.
References
Among the many books on nonlinear dynamics and chaos, you may find it interesting to consult, either during or after the course, the following:
- Berge, P., Y. Pomeau, and C. Vidal. Order within Chaos: Towards a Deterministic Approach to Turbulence. Wiley-VCH, 1987. ISBN: 9780471849674. (An undergraduate-level physical introduction to the subject.)
- Cross, M. and H. Greenside. Pattern Formation and Dynamics in Nonequilibrium Systems. Cambridge University Press, 2009. ISBN: 9780521770507.
- Cvitanovic, P. Universality in Chaos. Adam Hilger, Ltd., 1989. ISBN: 9780852747650. (Contains reprints of a number of original research papers in the field.)
- Cvitanovic, P., R. Artuso, R. Mainieri, G. Tanner, and G. Vattay. Chaos: Classical and Quantum (PDF - 8.4 MB)
- Gleick, J. Chaos. Viking Books, 1987. ISBN: 9780749386061. (An excellent popular introduction.)
- Guckenheimer, J. and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, 1983. ISBN: 9780387908199. (A graduate-level applied mathematics textbook.)
- Schuster, H. and W. Just. Deterministic Chaos: An Introduction, 4th edition. Wiley-VCH, 2005. ISBN: 9783527404155. (An advanced book of interest to physicists.)
- Turcotte, D. Fractals and Chaos in Geology and Geophysics, 2nd edition. Cambridge University Press, New York, 1997. ISBN: 9780521567336.
Requirements
There are no exams.
There are ten problem sets, assigned usually once per week, but occasionally less frequently. Some problems will be analytical while others will require use of a computer. The problem sets must be completed and turned in on time for grading. Requests for extensions in exceptional circumstances must be made in advance.
Students are also required to complete a final project and briefly present their work during the final meeting of the class. A written report is also due at that time. The final project could be either an analysis of an interesting paper or topic in the scientific literature, an attempt of your own to apply what you have learned to your own interests, or a combination of the two.
Grading
Problem sets count for about 80% of the grade and the final project about 20%.
