Wann und wo: Mo 14 - 16, SR 127
Vorbesprechung: war am Mi 10.02.2016, 11:00, SR 414.
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The focus of this seminar is an introduction to nonlinear dynamics
with an emphasis on applications to physics, engineering, biology, and
The main object of study are systems of ordinary differential equations. When the system is linear, like the case of the simple harmonic oscillator, m ÿ + k y =0, describing the vibrations of a mass hanging from a linear spring, an explicit solution is easy to write down. When not, then we are in the nonlinear case and then it is often hard to write down a solution. Even when we succeed in this endeavour, like in the case of the pendulum, ÿ + k sin( y) =0, the result is often impenetrable. During this seminar we will learn how to use a combination of analytical methods and geometrical thinking to infer predictions about the behaviour of the solutions, i.e. about the dynamics of the system. We will see that such a system can either settle down to an equilibrium, or it can repeat itself in cycles (and it is thus periodic), or it can exhibit an aperiodic, seemingly unpredictable behaviour (and it is thus chaotic). All these types of behaviours will be illustrated with concrete examples from applied sciences. However, no familiarity with physics, biology, or chemistry is going to be assumed, and everything will be built up from scratch. The prerequisites are knowledge of calculus (graphs of functions, multivariable functions and their partial derivatives, the Jacobian of a function, Taylor series) and linear algebra (matrices, eigenvectors, and eigenvalues).
The seminar will cover Chapter 1 to Chapter 9 of Strogatz' book, "Nonlinear Dynamics and Chaos: with applications to physics, biology, chemistry, and engineering". The talks will be in the language of choice of the speaker: either English or German.
Tutorium: Dr. Anda Degeratu, Di, 14:00-16:00, Raum 328