| Methods of Nonlinear Analysis |
| ESAM 412-1 |
| Winter 2002 |
| Hermann Riecke |
The complexity of nonlinear systems often requires numerical methods for a quantitative investigation. However, to get insight into such systems analytical methods are invaluable. By considering well-defined limiting cases they allow the derivation of reduced equations that capture the essential features of the system. The reduced equations provide quantitative results in the corresponding parameter regimes, which encompass in particular transitions between qualitatively different behaviors of the system. In this class the central concepts and methods are introduced.
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Main topics:
Bifurcation theory, center manifold theorem,
separation of time scales, symmetries, pattern selection, amplitude
equations, Ginzburg-Landau equations, long-wave equations, phase
dynamics, secondary bifurcations.
Applications to fluid flow, chemical systems, biologically motivated systems.
This class will be a condensed version of the previous 2-quarter sequence 412-1,2, the syllabus for which is available at www.esam.nwu.edu/riecke under Overview of Classes.
For more detailed information call, stop by, or send e-mail:
| 491-8316 M458 h-riecke@nwu.edu |
Note: the class Interdisciplinary Nonlinear Dynamics
(ESAM-438), which I teach this Fall quarter, can be considered as
a preparatory class for 412-1.
For information about ESAM-438 see www.esam.nwu.edu/classes and
www.esam.nwu.edu/riecke