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Curves hidden in differential equations
Žalobínová, Petra ; Pyrih, Pavel (advisor) ; Bárta, Tomáš (referee)
Bachelor thesis Curves hidden in differential equations is engaged in solving and deriving differential equations, leading to the selected curve, which are cycloid curve and curves described by the hyperbolic functions . The core of the work is outlined into four transparent chapters, where the first of them gives a brief insight into the theory of curves and differential equations. In the following chapters, the work is specifically devoted to two historically significant problems, which are brachistochrone and catenary problems, but also deals with eigen, more modern problem of dynamics of symbiotic populations. The text explains the procedure of deriving differential equations from the considered problems and shows their solutions, by multiple methods. The contribution of this work, apart from the formulation and solution of the problem of symbiotic populations, is processing and making additions to solutions of these problems using a variety of methods from cited literature. The most important addition is relatively new and less known proof of the uniqueness of solutions of brachistochrone problem, which is enhanced by eigen intermediate steps and explanations.
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