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Math
717— Spring 2002
Applied Dynamical Systems
| Instructor: |
John Guckenheimer |
| Time: |
TR 10:10-11:25 |
| Room: |
Malott 206 |
Prerequisites: Undergraduate analysis, multivariable calculus,
linear algebra and differential equations.
Nonlinear dynamical systems are used as models in every field of science
and engineering. Universal patterns of behavior, including "chaos,''
have been observed in large sets of examples. Mathematical theories describing
geometrically the qualitative behavior of "generic'' systems explain
many of these patterns. This course will discuss dynamical systems theory
and its application to examples. Several representative examples from
the life sciences and other disciplines will be described at the beginning
of the course and used throughout the semester to illustrate theoretical
ideas. Emphasis will be placed upon bifurcation, the qualitative changes
in solutions that occur as system parameters are varied. Computational
methods for the analysis of dynamical systems will also be discussed.
Both the performance of algorithms and their mathematical foundations
will be considered. Further development of these computational methods
is an active research area, and the course lectures will repeatedly deal
with this frontier. Computer laboratory sessions will be held.
Last modified:
April 7, 2003
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