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Mathematical description of dynamic heat exchanger
Hvožďa, Jiří ; Hnízdil, Milan (referee) ; Kůdelová, Tereza (advisor)
This bachelor's thesis deals with an analysis of a dynamic heat exchanger, with neglect to position, described by the system of ordinary differential equations. It includes necessarily theoretical basis of ordinary differential eqations and thermomechanics, a study of ordinary differential eqations' solution existence, overview of types of heat exchangers according to various aspects.
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The solving of ordinary differential equations by means of the infinite series method.
Dražková, Jana ; Štoudková Růžičková, Viera (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is concerned with the solving of ordinary differential equations by means of the infinite series methods, in particular, the power series and the Fourier series. The aim of this thesis is to find the solution of the initial value problem for ordinary differential equations by use of the power series and compare this approach to traditional analytic methods. Further, the thesis deals with the solving of the second order linear ordinary differential equations with a periodic forcing term via the Fourier series method.
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Applications of ordinary differential equations with boundary conditions
Felixová, Lucie ; Opluštil, Zdeněk (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is concerned with the applications of ordinary differential equations with boundary conditions. The aim of this thesis is to find the solution of straight bar stability under different boundary conditions (hinging, clamping and their combinations), of bended bars under horizontal loading and of straight bars on an elastic foundation (Winkler's foundation). Further, the thesis deals with the derivation of the equation for temperature field in a thin rod and for mathematical pendulum.
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SSI Dividing Numerical Integrator
Suntcov, Roman ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
The thesis deals with numerical integration and hardware division operations. The reader is familiar with the numerical solution of differential equations through several different methods, for example Taylor's series. Furthermore, it is discussed the operation of division in the hardware and the method of its implementation in the FPGA. Subsequently, a parallel-parallel and serial-parallel integrator is designed. The practical aim of the thesis is to design and implement a serial-serial dividing integrator and create a simulator for it.
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Mathematical description of dynamic heat exchanger
Hvožďa, Jiří ; Hnízdil, Milan (referee) ; Kůdelová, Tereza (advisor)
This bachelor's thesis deals with an analysis of a dynamic heat exchanger, with neglect to position, described by the system of ordinary differential equations. It includes necessarily theoretical basis of ordinary differential eqations and thermomechanics, a study of ordinary differential eqations' solution existence, overview of types of heat exchangers according to various aspects.
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SSI Dividing Numerical Integrator
Suntcov, Roman ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
The thesis deals with numerical integration and hardware division operations. The reader is familiar with the numerical solution of differential equations through several different methods, for example Taylor's series. Furthermore, it is discussed the operation of division in the hardware and the method of its implementation in the FPGA. Subsequently, a parallel-parallel and serial-parallel integrator is designed. The practical aim of the thesis is to design and implement a serial-serial dividing integrator and create a simulator for it.
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Perturbation methods in the theory of ODEs
Hubatová, Michaela ; Pražák, Dalibor (advisor) ; Bárta, Tomáš (referee)
This thesis extends the basic ordinary differential equations (ODE) course, specifically considering perturbations of ODEs. We introduce uniformly asympto- tic approximation and uniformly ordered approximation. We provide a perturba- tion-based method of computing derivatives of ODE solutions with respect to: an initial value, a parameter, and initial time. We present the method of averaging, error estimate, and a theorem about the existence and stability of a periodic so- lution to ODEs in periodic standard form. Furthermore, we apply the method of averaging to determine the period of a periodic solution of Duffing equation without forcing or damping. All the terms and methods of perturbation theory used in the thesis are accompanied with examples. 1
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Stochastic modelling of epidemics
Drašnar, Jan ; Staněk, Jakub (advisor) ; Hlubinka, Daniel (referee)
This thesis uses a simple deterministic model represented by an ordinary di- fferential equation with two equilibrium points - depending on the initial state the illness either vanishes or persists forever. This model is expanded by adding some diffusion coefficients leading to different stochastic differential equations. They are analyzed to show how the choice of diffusion coefficients changes be- havior of the model in proximity of its equilibria and near the boundary of area with biological meaning. The theoretical results are than illustrated by computer simulations. 1
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Applications of ordinary differential equations with boundary conditions
Felixová, Lucie ; Opluštil, Zdeněk (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is concerned with the applications of ordinary differential equations with boundary conditions. The aim of this thesis is to find the solution of straight bar stability under different boundary conditions (hinging, clamping and their combinations), of bended bars under horizontal loading and of straight bars on an elastic foundation (Winkler's foundation). Further, the thesis deals with the derivation of the equation for temperature field in a thin rod and for mathematical pendulum.
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The solving of ordinary differential equations by means of the infinite series method.
Dražková, Jana ; Štoudková Růžičková, Viera (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is concerned with the solving of ordinary differential equations by means of the infinite series methods, in particular, the power series and the Fourier series. The aim of this thesis is to find the solution of the initial value problem for ordinary differential equations by use of the power series and compare this approach to traditional analytic methods. Further, the thesis deals with the solving of the second order linear ordinary differential equations with a periodic forcing term via the Fourier series method.
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