Topics: Theory for existence, uniqueness, continuation, and
dependence on parameters for solutions of ODE's. Linear systems with constant or periodic coefficients. Stability of equilibria and periodic orbits. Qualitative behavior, bifurcations of steady and periodic solutions, examples of chaos.
Ordinary differential equations (those with unknown functions of one variable, usually time), or more generally dynamical systems, model many processes in science and economics. The understanding of their behavior is one of the strongest links between mathematics and science. Subtleties include complex large-time behavior and the effect of combining fast and slow time scales.
This course is aimed at beginning mathematics graduate students. Others are welcome if they have the background
of a math major, especially linear algebra and real analysis For math grad students, the subject uses and applies concepts of these subjects. Qualitative properties and key examples exhibit phenomena which are more involved for partial differential equations and serve as a step toward deeper understanding of mathematical physics.
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