Required text: 
Nonlinear Dynamics and Chaos, by S. Strogatz, Perseus Publishing.
(book is available as hard copy and as electronic copy at Rasmuson library)

Supplementary readings:
Chaotic dynamics,  by T. Tel and M. Gruiz, Cambridge (2007).
  many nice applications, and great explanations.
Chaos in dynamical systems,  by E. Ott, Cambridge (2002).
   also covers Hamiltonian chaos and quantum chaos.
Applied nonlinear dynamics, by A. Nayfeh, B. Balachandran, Wiley (2004).
   covers analytical, computational and experimental methods in one book!!
An exploration of Chaos,  by Argyris, Faust, and Haase, Elsevier (1994). 
   nice examples, some detailed calculations that are helpful for understanding
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, by Guckenheimer and Holmes, Springer (1983).
   THE standard book in nonlinear dynamics from an applied mathematical sciences point of view
Synchronization, a universal concept in nonlinear science, by Pikovsky, Rosenblum and Kurths, Cambridge (2001).
   a particular focus on synchronization, with many many examples across disciplines
Nonlinear time series analysis, by Kantz and Schreiber, Cambridge (1998)
   focuses on NLD and its applications to the analysis of time series, discusses pitfalls, shows many applications
Mathematical Biology I and II, by J.D. Murray, Springer (3rd edition, 2002) 
   on nonlinear dynamics with particular focus on biological systems
Mathematical Geoscience, by Andrew Fowler, Springer (2011)

There are many books on nonlinear dynamics in the library. Please explore them to see different approaches to our topics.

Course Content

Tentative course calendar

Course Goals, Student Learning Outcomes

Homework

homework assignments

Explore nonlinear dynamics with a project that includes a computational component! For example a bifurcation analysis of a dynamical system, the calculation of fractal dimensions of certain cracks; nonlinear time series analysis of an ECG, or other biological, financial, physical measurement series; correlations between two time series (synchronization); phase space analysis and quantification. Explore a topic related to this course on your own. The project needs to be based on a published paper or text book, online sources like Wikipedia are not allowed. A list of possible topics is given here: topics. You can also choose a topic of your interest in agreement with the instructor. All topics should be discussed with the instructor at least 5 days before the topic is due. 

Project on track: 1) project topics [20points]: submit tentative project title and a pdf file of the main literature source (paper, text book) that you use in your project. topics are due on Feb. 16. 2) project outline [30points]: submit a one page paper proposal that includes a) scientific background, b) hypothesis to test, and c) scientific approach and methods to be used. outline is due on March 2. 3) project simulation [50points]: submit one page that describes a) computational methods used, b) a first simulation result that demonstrates that you have a basic working computer program towards your project [this can be done through a figure and its description; figures don't count towards page requirements], and c) a brief outline of the remaining computational study to be done. project simulation is due march 16.

A one-hour in-term examination and a two hour final examination will be held during the semester. In-term exams will be held in the classroom. The exams will be closed books and closed notes.