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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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Differential and integral calculus in economic problems
RADOVÁ, Lenka
The thesis deals with the theory of differential and integral calculus and its application to economic problems. The main aim of the thesis is to create a comprehensive set of examples and to show the wide range of applications of differential and integral equations in economics. The theoretical part focuses on and presents practical applications of differential and integral calculus in economic problems and models. This part includes relevant economic theories and provides the theoretical basis for the practical part. The theoretical knowledge is further applied to economic problems that can be solved using derivatives and integrals, including an analysis of how and why these mathematical procedures are applied to a given type of problem. This subsection contains a brief description of the relevant theories, the corresponding methods, the characteristics of the models applied, etc. The practical part aims to use Maple software to visualise economic models into graphs based on real data. Maple can be used to simulate different economic situations to see how changes in input conditions affect output. The thesis includes solved examples, a study of mathematical and economic problems resulting in their solution, a comparison of results in an economic context, a discussion, and the formulation of conclusions.
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Dynamic Analysis of Track
Kulich, Pavel ; Salajka, Vlastislav (referee) ; Plášek, Otto (advisor)
The diploma thesis deals with analytical description of vehicle - track dynamic interface. There are described basic analytical models which are subsequently extended in order to get a more precise description of dynamic phenomena. The aim is to compile a model that faithfully describes the dynamic phenomena in the track. These new compiled models are qualitatively compared with data obtained by measuring in the track.
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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 Solution Convergence
Sehnalová, Pavla ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
The work describes techniques for solving systems of linear and differential equations. It explains the definition of conversion from system of linear to system of differential equations. The method of the elementary transmission and the transform algorithm are presented. Both of methods are demonstrated on simply examples and properties of conversion are shown. The work compares fast and accurate solutions of methods and algorithm. For computing examples and solving experiments following programs were used: TKSL and TKSL/C. The program TKSL/C was enriched with the graphic user interface which makes the conversion of systems and computing results easier.
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Finite element solution of axially loaded bars using linear element
Plucnar, Tomáš ; Návrat, Tomáš (referee) ; Vaverka, Jiří (advisor)
This bachelor thesis deals with the finite element method for axially loaded bars using linear basis functions. The theoretical part briefly describes the theory of axially loaded bars and states the individual steps that lead from the initial differential equation to a system of linear algebraic equations. A Weak formulation of the differential equation is used to derive the system. Using the theory described in the first part, an algorithm is created in Matlab, which is used to solve four problems. The results are then compared with the analytical solution and with the model in Ansys.
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Specialized Computer System Automatic Control
Opálka, Jan ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with the automatic control of calculations of specialized system. The reader is acquainted with the numerical solution of differential equations by Taylor series method and numerical integrators. The practical aim of this work is to analyze parallel characteristics of Taylor series method, specification of parallel math operations and design of control of this operations.
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Classical and fractional modelling of oscillatory motion
Hošek, Jaromír ; Tomášek, Petr (referee) ; Kisela, Tomáš (advisor)
In this thesis we deal with the issue of damped oscillations. Besides the classic description using member directly proportional to the first derivative position we focus on the model containing derivatives of non-integer order, so-called the fractional model of damped oscillations. The behavior of both models is studied through the test applications describing the movement of one, two, respectively three bodies connected by springs. The main tool for solving is the Laplace transform method. Besides the computational aspects we discuss some qualitative properties of solutions, especially dependence on order derivative in the fractional model and the behavior of the center of gravity system position.
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