MATH-520 Nonlinear Differential Equations
Spring for 2008-2009
Nonlinear differential equations arising from various branches of sciences, economics and finance have been playing an essential role in applied mathematics. Solutions to nonlinear equations always exhibit very interesting and rich phenomena and behaviors such as strange attractors, chaos, shock waves and soliton. This course emphasizes the study of qualitative dynamical behavior of solutions to some nonlinear equations. The topics include stability, bifurcations (changes in the nature of solutions as parameters are varied, for example, the creation of periodic orbits from an equilibrium point)), chaos for ordinary differential equations and some nonlinear wave phenomena such as shock waves and soliton for partial differential equations. Most of the material in this course will be presented by means of examples.
Prerequisites: Math-201 or Math-501 or equivalent
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