Asymptotic series, local and uniform expansions. Strongly damped systems, boundary layer theory, WKB method. Periodic and transient motion, Lindstedt's method and multiple scales. Non-linear phenomena and theory of stability. Averaging approximations. Wave equation and Green functions. Approximations for short and long wave lengths. Non-linear waves, kinematic waves. Hyperbolic waves and 1D gas dynamics. Dispersive waves and the method of steepest descent.
Intended learning outcomes *
The course aims at an understanding of important phenomena and methods of modern mechanics, introduced in the contexts of oscillations-ODE and waves-PDE.
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Literature and preparations
Specific prerequisites *
Compulsory courses within the competence program Mechanics.