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Perturbation methods in the theory of ODEs
 Hubatová, Michaela ; Pražák, Dalibor (advisor) ; Bárta, Tomáš (referee)
This thesis extends the basic ordinary differential equations (ODE) course, specifically considering perturbations of ODEs. We introduce uniformly asympto- tic approximation and uniformly ordered approximation. We provide a perturba- tion-based method of computing derivatives of ODE solutions with respect to: an initial value, a parameter, and initial time. We present the method of averaging, error estimate, and a theorem about the existence and stability of a periodic so- lution to ODEs in periodic standard form. Furthermore, we apply the method of averaging to determine the period of a periodic solution of Duffing equation without forcing or damping. All the terms and methods of perturbation theory used in the thesis are accompanied with examples. 1
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