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Foundations of Fractional Calculus on Time Scales
Dolník, Matej ; Nechvátal, Luděk (referee) ; Kisela, Tomáš (advisor)
Bakalářská práce pojednává o zlomkovém kalkule na časových škálach, přesněji - zavádí zlomkový kalkulus na časových škálach a taktéž vyšetřuje jednoznačnost axiomatické definice zavádějící mocninné funkce. Po zavedení základních pojmů je předmětem diskuze hlavně zobecněná Laplaceova transformace a důkaz jednoznačnosti zobecněné Laplaceovy transformace, která je použita jako nástroj pro dokázání jednoznačnosti zlomkových mocniných funkcií na časových škálach.
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Stability and chaotic behaviour of the Lorenz system
Oborná, Eliška ; Nechvátal, Luděk (referee) ; Čermák, Jan (advisor)
This bachelor's thesis analyzes the behavior of the Lorenz's model of convective flow in the atmosphere depending on the Rayleigh number. It offers several methods when analyzing stability of nonlinear systems of the first order autonomous differential equations. Part of the work also consists of introduction to deterministic chaos which appears in dynamic systems with a parameter. The work is supported by graphic interpretation of a stable and chaotic behavior by using the software Maple.
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Modelling and simulation in aviation
Prešinský, Ján ; Nechvátal, Luděk (referee) ; Zatočilová, Jitka (advisor)
This bachelor thesis is focused on specifying the orientation of aircraft in normal Earth- xed frame. It is devoted to Euler angles representation and quaternions representation. Moreover, it introduces the equations of motion with 3 and 6 degrees of freedom and proposes the numerical method for solving these equations, which are expressed by the set of non-linear diferential equations.
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Mathematical models in hydromechanics (and aerodynamics)
Ježková, Jitka ; Zatočilová, Jitka (referee) ; Nechvátal, Luděk (advisor)
Bachelor thesis is a summarizing text which deals with the state and the motion of ideal liquid and gas. The main goal is to derive Euler equations describing the flow of fluids. From these equations we can obtain Bernoulli equation that is directly used to solve problems of fluid flow. The next step is to derive the continuity equation expressing the fact that the mass is preserved in the system. In the case of ideal gas the state equation of ideal gas is added and therefore solutions of various types of tasks of hydrodynamics and aerodynamics can be achieved.
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Solution of inverse problems in the area of material and heat exchangers
Kůdelová, Tereza ; Nechvátal, Luděk (referee) ; Čermák, Jan (advisor)
This bachelor's thesis deals with the dynamic behavior of heat exchangers which is described by the system of dierential equations. In this conection it includes a general information about necessary theoretical background especialy concerning heat transfer. Further, it mentions also the basic types of arrangement of heat exchangers that may occur in practice. The main goal is to answer the questions of controllability, observability and identifiability of the parameters obtained by solving corresponding inverse problem.
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Calculations and applications of fractional calculus
Zemčíková, Michaela ; Nechvátal, Luděk (referee) ; Čermák, Jan (advisor)
This bachelor’s thesis deals with the calculations and applications of fractional calculus. The aim of this thesis is to mention some basic fundamentals, definitions and properties of fractional calculus, that will be used for calculations of fractional integrals and derivations of selected elementary functions focus on power functions. In next part thesis will be concerned with fractional diffusion equation, which describes subdiffusive processes. Its result will be compared with the standard diffusion.
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Dynamics of flight and control
Šabartová, Zuzana ; Tomášek, Petr (referee) ; Nechvátal, Luděk (advisor)
This bachelor thesis deals with an analysis of the equations of motion for aircrafts. The equations could be linearized by assuming the steady state flight with small perturbations so that we can use the theory of control. The result of the thesis besides a theoretic aspect is a simulation of motion response due to change of control terms position in MATLAB & Simulink for two particular airplanes.
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Telegraph Equation
Továrek, Tomáš ; Nechvátal, Luděk (referee) ; Franců, Jan (advisor)
Telegraph equations simulate propagation of the electric signal in an electrical transmission line. This pair of partial diferential equations is derived from physical laws. Behaviour of their solution,. especially effect of impedance match of transmission line on signal distortion is studied. The results are illustrated by numerical experiments.
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Solving of partial differential equations by Fourier method
Barvenčík, Oldřich ; Opluštil, Zdeněk (referee) ; Nechvátal, Luděk (advisor)
Bachelor thesis is a survey text which deals with solving partial deferential equations by Fourier method, i.e. method when we look for a solution of (initial) boundary value problem in form of the infinite Fourier series. The key step is a hypothesis that the solution can be expressed in form with separated variables, therefore the method is sometimes called separation of variables method. The essence can be demonstrated on parabolic and hyperbolic homogeneous problems. In the thesis both types in one (space) dimension are systematically analyzed, at first homogeneous problem, then homogeneous one with non-homogeneous boundary conditions and finally completely non-homogeneous problem.
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