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Electronic circuits with fractal dynamics
Vojtová, Klára ; Guzan,, Milan (referee) ; Petržela, Jiří (advisor)
In the first section of this work is further analyzed the theories of differential equations and their computation and applications. The second part I addict to more detailed description of the Laplace transform, a sentence that is relevant to this area and also using the Laplace transform to solve electronic circuits. The third part of this project involves the theory of electronic circuits, especially the analysis and synthesis. The final and most important part is attended to circuits with fractal dynamics, design fractal approximation of the dynamics of capacitors in the frequency domain, has finally created its own electronic circuit measurement and evaluation results.
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Numerical Integration .NET Graphical Editor
Kučera, Martin ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This thesis deals with the numerical solution of systems of first-order differential equations with initial conditions, using chosen one-step methods. It describes the design, implementation and testing of the application that is able to use these methods to solve the tasks entered in form of block schemes. The first part is devoted to an introduction of the topic, it provides an example of calculation of several steps using chosen methods and compares the results. A substantial part of the report deals with form and function of each block used in the block schemes editor and the transformation process of input data to data usable for creating simulation. The penultimate chapter demonstrates the accuracy of the final application. It shows solutions of a few simple examples of practical usage. This chapter also includes comparison with other simulation systems.
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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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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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Electric Circuits Simulations
Šulc, Jiří ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
The aim of this bachelor's thesis was the design of elementary graphic computational editor in which quality schema designs of electrical circuits can be created easily and fast. The application is further able to automatically generate the system of equations describing the designed circuit which can be used in the TKSL simulation system for displaying of the solutions. The application is designed for student's use in order to support the teaching of the Circuit Theory. The bachelor's thesis further deals with the problem solving of differential equations by the way of numerical integration methods with direct use of the Taylor series. The complexity of the analytical and numerical algorithm of the differential equations in solving electrical circuits is analyzed on the examples.
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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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Algebraic Equations Calculations
Kuchařová, Eva ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work investigates the solution of linear algebraic equations by a conversion to the system of differential equations. Moreover, several more frequently used methods are described in addition. The theoretical part of work describes the mathematical. Next, the examples of using the Matlab a TKSL programs are presented to show and compare the results of calculations. The source codes used are included. The work proves that the solution of algebraic equations by the conversion to the system of differential equations is applicable and further solved by the Euler's method. The parallel solution is also described. As the output of this work, the lin2dif program was developed. It realizes the conversion among the systems of equations. Finally, the description of the work progress, design, implementation and usage of the program are summarized.
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Adjoint Differential Equations
Kmenta, Karel ; Pindryč, Milan (referee) ; Kunovský, Jiří (advisor)
This project deals with solving differential equations. The aim is find the correct algorithm transforming differential equations of higher order with time variable coefficients to equivalent systems of differential equations of first order. Subsequently verify its functionality for equations containing the involutioin goniometrical functions and finally implement this algorithm. The reason for this transformation is requirement to solve these differential equations by programme TKSL (Taylor Kunovský simulation language).
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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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