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Analysis of the Problem of a Cyclic Pursuit
Kučerová, Vendula ; Tomášek, Petr (referee) ; Čermák, Jan (advisor)
This bachelor's thesis analyzes the problem of cyclic pursuit. It deals with the characterization of cyclic pursuit problems and describes how the theory of differential equations is employed in this area. The formulation of a mathematical model is emphasized, followed by its exact solution and further analysis supported by graphical visualization of the obtained solutions.
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The applications of differential equations in the temperature regulation
Horáček, Jan ; Švarc, Ivan (referee) ; Dosoudilová, Monika (advisor)
This bachelor's thesis deals with the importance of differential equations in control theory. The review section is devoted to a reminder of the mathematical apparatus of linear differential equations and the methods of solving them, including the characteristic equation and the Laplace transform. Furthermore, the research part deals with control, transfer function and stability. The final section is devoted to the solution of a real room temperature change problem including software verification.
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AC Electronic Circuits Simulator
Janko, Roman ; Kopřiva, Jan (referee) ; Kunovský, Jiří (advisor)
The thesis summarizes the selected numerical solutions of linear differential equations and some standard methods for investigating the frequency and phase characteristics of electronic circuits. The part of thesis is also a small collection of sample examples to investigate the frequency and phase characteristics of R, L, C electronic circuits. There are designed and implemented user interface for electronic circuit schematic entry and graphical display of frequency and phase characteristics of the analysis of electronic circuits. In conclusion, this thesis is briefly reviewed time-consuming calculation of selected frequency and phase characteristics of electronic circuits.
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Algebraic Equations Comparisons
Nečasová, Gabriela ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
The thesis deals with the topic of comparative calculation of algebraic equations. First it describes the comparison of the overall number of operations at direct and iteration met\-hods, as well as gives concrete examples of the methods and explains solutions of direct and iteration methods. Another part focuses on possible methods of converting systems of linear algebraic equations to the system of differential equations. The end of the thesis describes method of working with TKSL/C, Matlab and Maple. In this thesis, there was designed graphical user interface serving for comfortable communication with TKSL/C programme. Graphical user interface was tested on concrete tasks demonstrating the conversion of system of linear algebraic equations to the system of differential equations.
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Autonomous Electronic Circuits Simulation Method
Minárik, Michal ; Konvalina, Jiří (referee) ; Kunovský, Jiří (advisor)
This work deals with a methodology of description of linear electrical circuits through the use of differential equations and autonomical method. It compares commom numerical methods with Taylor series method implemented in TKSL. It's focused on analysis of applicability of autonomical method to various circuits, complexity of circuit diagram transformation to system of equations and transcription to TKSL.
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Pursuit problems: basic models and their analysis
Neugebauer, Tomáš ; Řehák, Pavel (referee) ; Čermák, Jan (advisor)
This thesis is focused on creation of mathematical models and analysis of basic pursuit problems. In particular, the Perrault's problem, the Bouguer's problem, the Hathaway’s problem, the snail–racehorse problem and the Bailey's problem are involved. Each of the problems is solved analytically or numerically, including qualitative analysis.
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