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Optimal control in engineering processes
Jakal, Martin ; Štoudková Růžičková, Viera (referee) ; Tomášek, Petr (advisor)
This thesis deals with electric train optimal control problem with a focus on time and energy optimization. The problem is extended by considering specific speed contraints. We are able to design the sequence of control settings by the use of the optimal control theory. Optimization tools in Matlab environment are used to determine the numerical solution of the considered task.
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The solving of ordinary differential equations by means of the infinite series method.
Dražková, Jana ; Štoudková Růžičková, Viera (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is concerned with the solving of ordinary differential equations by means of the infinite series methods, in particular, the power series and the Fourier series. The aim of this thesis is to find the solution of the initial value problem for ordinary differential equations by use of the power series and compare this approach to traditional analytic methods. Further, the thesis deals with the solving of the second order linear ordinary differential equations with a periodic forcing term via the Fourier series method.
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Autonomous Differential Equations and their Use in Economics
Škrabáková, Katarína ; Štoudková Růžičková, Viera (referee) ; Tomášek, Petr (advisor)
This thesis focuses on autonomous differential equations and their application to economics. There are four economic models formulated in this thesis - the Walrasian auctioneer model, Goodwin’s Growth Cycle Model, and two models of economic growth, the Harrod–Domar model and the Solow–Swan model. All the models are subjected to rigorous mathematical analysis and complemented with appropriate economic interpretations. Specifically for the Walrasian general equilibrium model, several qualitatively different types of demand are discussed.
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Duffing equation in mathematical modelling of non-linear oscillators
Vozárová, Juliana ; Štoudková Růžičková, Viera (referee) ; Šremr, Jiří (advisor)
The thesis deals with the behaviour of non-linear oscilators. Within their models there often appears the Duffing equation. The aims of this investigation include fundamentals of the theory of differential equations, interpretation of the Duffing equation and its analysis. To fulfill these aims, this investigation utilizes qualitative theory of the differential equations. It means that closed form solutions to the equations are not looked for but qualitative behaviour and properties of the solutions are studied. Some of the properties of solutions can be obtained from phase portraits.
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Mathematical models in epidemiology
Skopalová, Kristýna ; Štoudková Růžičková, Viera (referee) ; Čermák, Jan (advisor)
This bachelor's thesis deals with the mathematical models which are used in epidemiology. The aim of this thesis is a description and a creation of basic Kermack-McKendrick model and its analysis. The thesis is also dedicated to modification of this model and illustration on the concrete data. Last but not least, the stability of the selected models is checked in the stationary points.
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