Introduction to Dynamical Systems and Chaos (2017)
Lead instructor: David Feldman
Course Videos and Other Materials (zip files):
These zipped files contain all course materials for the given unit except for the homework solutions.
- Unit 1 Files (108MB)
- Unit 2 Files (451MB)
- Unit 3 Files (846MB)
- Unit 4 Files (362MB)
- Unit 5 Files (243MB)
- Unit 6 Files (433MB)
- Unit 7 Files (496MB)
- Unit 8 Files (359MB)
- Unit 9 Files (295MB)
- Unit 10 Files (510MB)
non-technical: these are books in the "popular science" style.
- Gleick, James. Chaos: Making a new science. Random House, 1997. Very readable, focuses on the scientists and mathematicians behind many of the key results in chaos. amazon.com
- Stewart, Ian. Does God play dice?: The new mathematics of chaos. Penguin UK, 1997. More mathematical detail and richness than Gleick's book. Also quite readable. amazon.com
Mitchell, Melanie. Complexity: a guided tour. Oxford University Press, 2009. A general book about complex systems. amazon.com
history and philosophy of science: these books and articles are mostly non-technical, but are scholarly pieces on the history and philosophy of science.
- In the Wake of Chaos: Unpredictable Order in Dynamical Systems. Stephen H. Kellert. University of Chicago Press. 1994. amazon.com
Smith, Peter. Explaining chaos. Cambridge University Press, 1998. More technical than Kellert. amazon.com
Aubin, David, and Amy Dahan Dalmedico. "Writing the History of Dynamical Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures." Historia Mathematica 29.3 (2002): 273-339. A long paper thoroughly examining some of the strands of thoughts that converged to form the field of chaos and dynamical systems. html
Bishop, Robert, "Chaos", The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.) html
Hoefer, Carl, "Causal Determinism", The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), Edward N. Zalta (ed.) html
textbooks with more mathematical details: i've listed these textbooks in approximate order from introductory to advanced.
Feldman, David P. Chaos and Fractals: An Elementary Introduction. Oxford University Press, 2012. At roughly the same level as this class. amazon.com
Flake, Gary William. The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptations. The MIT Press, 1998. In a few places uses calculus. A very clear and engaging introduction to chaos, fractals, and complex systems more generally. amazon.com
Sayama, Hiroki, Introduction to the Modeling and Analysis of Complex Systems. OpenSUNY Textbooks. Looks like a great survey of a range of topics in complex systems, including dynamical systems. A pdf is available here.
Kaplan, Daniel, and Leon Glass. Understanding Nonlinear Dynamics. Springer-Verlag, 1995. A basic introduction to dynamical systems. Uses calculus but does not assume prior coursework in differential equations. amazon.com
Strogatz, Steven. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering. Westview Press, 2001. Highly recommended. amazon.com
Peitgen, Heinz-Otto, Hartmut Jürgens, and Dietmar Saupe. Chaos and fractals: new frontiers of science. Springer, 2004. amazon.com
Smale, Stephen, Morris W. Hirsch, and Robert L. Devaney. Differential equations, dynamical systems, and an introduction to chaos. (3rd edition.) Academic Press. 2012. amazon.com
Devaney, Robert L. An Introduction to Chaotic Dynamical Systems. (2nd edition.) Westview Press, 2003. amazon.com
Ott, Edward. Chaos in Dynamical Systems. (2nd edition.) Cambridge University Press, 2002. amazon.com
lectures and documentaries
- Raymond Flood. Butterflies, Chaos and Fractals. Museum of London. 17 September 2013. link
- Nic Stacey and Jim Al-Khalili. The Secret Life of Chaos. BBC 4. January 2010. dailymotion.com vimeo.com (with arabic(?) subtitles)
- Jos Leys, Etienne Ghys, and Aurelien Alvarez, Chaos: A Mathematical Adventure. A set of videos availalbe in 11 different languagues. http://www.chaos-math.org/en.
- Steven Strogatz, Nonlinear Dynamics and Chaos. A series of 25 lectures from the course MAE5790 at Cornell University in Spring 2014. The lectures closely follow Strogatz's textbook, listed above. youtube.com