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Integral transforms and their applications
Béreš, Lukáš ; Štarha, Pavel (oponent) ; Franců, Jan (vedoucí práce)
This bachelor's thesis deals with integral transforms and their applications. Its aim is to get together basic properties of Laplace and Fourier transforms and then illustrate their application in solving partial dierential equations, by calculating specic tasks with numerical experiments in MATLAB software.
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Mathematical modelling with differential equations
Béreš, Lukáš ; Šremr, Jiří (oponent) ; Opluštil, Zdeněk (vedoucí práce)
The master's thesis is focused on the nonlinear differential equations. It contains theorems important to determine the behaviour of the nonlinear system only by study of the linearized system, which is subsequently shown on the equation of the mathematical pendulum. Furthermore, the thesis deals with differential equations with delay. The delay complicates finding the solution, which is shown on the simplified equation of a gantry crane. Subsequently is investigated the oscillation of the linear equation with non-constant delay. Determining the conditions for the coefficients in the equation, such that every solution is oscillatory.
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Mathematical modelling with differential equations
Béreš, Lukáš ; Šremr, Jiří (oponent) ; Opluštil, Zdeněk (vedoucí práce)
The master's thesis is focused on the nonlinear differential equations. It contains theorems important to determine the behaviour of the nonlinear system only by study of the linearized system, which is subsequently shown on the equation of the mathematical pendulum. Furthermore, the thesis deals with differential equations with delay. The delay complicates finding the solution, which is shown on the simplified equation of a gantry crane. Subsequently is investigated the oscillation of the linear equation with non-constant delay. Determining the conditions for the coefficients in the equation, such that every solution is oscillatory.
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Integral transforms and their applications
Béreš, Lukáš ; Štarha, Pavel (oponent) ; Franců, Jan (vedoucí práce)
This bachelor's thesis deals with integral transforms and their applications. Its aim is to get together basic properties of Laplace and Fourier transforms and then illustrate their application in solving partial dierential equations, by calculating specic tasks with numerical experiments in MATLAB software.
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