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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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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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Semianalytical Computation of Fourier Series Coeficients
Hégr, Tomáš ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This bachelor thesis deals with semianalytical computation of the coefficients of the Fourier series. The aim of this work is to create a graphical user interface for program TKSL/C. The work contains the theory of Fourier series and Fourier transforms. The state of the art software is described in the following chapter. In the next parts the thesis describes the concept of the implementation of the user interface, some tutorial examples which were used and the summary of user testing.
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Multiple Integrals
Valešová, Nikola ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
The problem of definite integral and differential equation computation is still a significant part of many scientific branches and the solution of integral calculus tasks can be found in many industrial fields too. During the computation of such tasks, the accuracy and high-speed requirements are often confronted. These requirements are crucial during the process of the suitable method choice. The aim of this thesis is to propose, describe, implement and test a new numerical method, which combines the solution of definite integrals by transforming them into differential equations solved by the Taylor series with the traditional methods, which use the Newton-Cotes formulas. As a result, a new application has been developed, that provides fast results of definite two-dimensional integrals and reaches at least the precision of MATLAB. The major accomplishment of this thesis is the development of a new numerical method and its comparison to other established ways of computation.
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Frequency and Transient Responses Based on Differential Equations
Turoňová, Lenka ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This bachelor thesis deals with the investigation of amplitude and phase frequency responses of linear electrical circuits. It compares classical methods of investigation using a symbolic-complex method with investigation using differential equations. For graphical representation of the responses in the case of the symbolic-complex method there was used for demonstration of examples programs MATLAB and Maple. The aim of this work was also to create graphical user interface over TKSL/C, which allows input of differential equations and plotting amplitude and phase frequency responses.
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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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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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Multiple Integrals
Valešová, Nikola ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
The problem of definite integral and differential equation computation is still a significant part of many scientific branches and the solution of integral calculus tasks can be found in many industrial fields too. During the computation of such tasks, the accuracy and high-speed requirements are often confronted. These requirements are crucial during the process of the suitable method choice. The aim of this thesis is to propose, describe, implement and test a new numerical method, which combines the solution of definite integrals by transforming them into differential equations solved by the Taylor series with the traditional methods, which use the Newton-Cotes formulas. As a result, a new application has been developed, that provides fast results of definite two-dimensional integrals and reaches at least the precision of MATLAB. The major accomplishment of this thesis is the development of a new numerical method and its comparison to other established ways of computation.
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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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