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Electronic Circuits Simulations and Parasitic Inductances
Ševčík, Roman ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with the solution of differential equations and systems of differential equations through the use of parasitic inductances. Thus obtained equations serve as input data for the simulation tool TKSL, which allows their solutions using the Taylor series. Furthermore, according to the proposal in C# is implemented a system for graphic display output data from TKSL. The system makes it possible to view trending as a continuous two-dimensional graphs.
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Platform .NET for Numerical Integration
Kopecký, Jiří ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This bachelor thesis deals with numeric solution of ordinary first-order differential equations and their systems. The first part of this thesis contains description of selected one-step integration methods. The second part is devoted to a language intended for differential equation notation. This part at first describes the study of languages of MATLAB, Maple and TKSL/386 simulation systems. Later, based on this study it presents a design of a new language. The penultimate part of the thesis deals with design and implementation of a system intended for the calculation of systems of differential equations. In the final part is then shown usage of this system to solve exercises from the Circuits Theory domain.
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Taylor Series Assembler
Valenta, Václav ; Kraus, Michal (referee) ; Kunovský, Jiří (advisor)
The objective of this work is to get familiar with numerical solution of differential equations. The solution is made by specialized microprocessor HC08. Basic arithmetic operations and algorithms which helps to make precise results are analyzed here.
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Control Systems
Vala, Jiří ; Konvalina, Jiří (referee) ; Kunovský, Jiří (advisor)
The MSc Thesis deals with real-time modelling, especially with the control circuits, where we focus on the regulation circuit with auxiliary model of the regulated system. The introduction contains the Theory of Controls and regulation. The work is divided into two basic parts. The first part deals with the problems from the theoretical point of view. The theoretical part is concerned with the general systems. Various definitions of systems, their partition and mathematical methods for their description are mentioned after introducing. A description the regulation circuits, their partition, structures and types follows. There are shown the particular regulators and different types of regulated systems in details. Mathematical methods applied to solve the differential equations that describe the models of the systems are summarized in the second part of the work. The end of this chapter is concerned with the TKSL system. In the practical part I have produced Microsoft Power Point program which summarizes the results of experiments, made in the TKSL and TKSL/C system. The output of simulation was transformed into the graphs in the format of Microsoft Excel. The last part deals with suggestion and implementation simulators of control circuits.
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Finite Integrals Semi-Analytical Computations
Veigend, Petr ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This bachelor thesis explains the topic of semi-analytical computation of finite integrals. It contains the mathematical definition of finite integral, along with definitions and examples for several methods that can be used to solve finite integrals analytically. For the most part however, the thesis is trying to explain how to effectively and precisely approximate finite integrals on a computer. It deals with approximations by polynomials, but mostly with the correspondence between finite integrals and differential equations. This correspondence is used in two software projects that are the part of this thesis.
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Numerical Integrators in Control Theory
Novák, Adam ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
This bachelor thesis deal with the topic of partial differential equations of parallel solutions from focus on control of dynamic systems working with real-time built-in control model. First, it is focused on real-time systems. The next section deals with the analysis of differential equations and types of differential equations. Consequently, numerical integration and derivation are discussed. The thesis deals with individual numerical methods, which are used to calculate a differential equations. This thesis also deals with individual fluids that can influence the calculation of differencial equations in the Modern Taylor method. The result is a competitive application that allows a quick and accurate solution of real-time management model and the subsequent calculation of the differential equations generated using the Modern Taylor Series Method.
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Epidemic models
Machalová, Monika ; Šremr, Jiří (referee) ; Opluštil, Zdeněk (advisor)
Epidemiological models and their analysis are an essential tool for studying, understanding, and controlling the spread of epidemics. It is a discipline in which we are trying to answer questions such as how long an epidemic will last, what its flow will be, or how much it will affect the population. There are a large number of models and approaches for describing these epidemics and their behavior. In this thesis, we focus on models described by a system of differential equations, and we analyze these models in terms of stability.
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Control of linear systems
Cesneková, Ivana ; Milota, Jaroslav (advisor) ; Honzík, Petr (referee)
The aim of this work is to look into the theory of linear systems via population model represented by partial differential equations with boundary and initial condition. Special attention is devoted to the strongly continuous semig- roups on a complex Banach space. For this purpose, the notion of a homogeneous and inhomogeneous Cauchy problem is introduced and we solve our model in this abstract formulation. The system behaviour is based on properties of the resolvent set and spectrum. Controllability question limits to solve the uniformly exponen- tially stability and the exponentially stabilizability. The point of this problem is in the case of the unstability to show exponencially stability of the system by using feedback. Keywords: control, differential equations, stability, controllability 1
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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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