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Optimization in engineering problems
Klepáč, Jaromír ; Popela, Pavel (referee) ; Mrázková, Eva (advisor)
This bachelor thesis deals with optimization in engineering problems. In particular, it focuses on a task of optimal dimensions design of continuously loaded beam with specic requirements on nal beam weight and rigidity. For the purpose of well understanding of all the terms used during solving of an illustrative task, the thesis contains a brief introduction into the optimization problems, ordinary dierential equations, and theory of elasticity as well. Results obtained through optimization in the GAMS software will be checked by analytic solution and compared with an alternative calculation in the ANSYS software.
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An analysis of differential equations for systems involving bottlenecks
Borkovec, Ondřej ; Opluštil, Zdeněk (referee) ; Kisela, Tomáš (advisor)
This thesis deals with modelling of the flow of products through systems involving bottlenecks using ordinary differential equations. The model is based on hydrodynamics analogy. Further, the conditions for the sustainability of a system, that is the requirements needed not to exceed the maximal capacity, so that the flow of products can flow continuously through the given spot. A model is used to solve examples for vayrying systems.
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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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Numerical analysis of stiff differential equations
Pavelka, Ondřej ; Zatočilová, Jitka (referee) ; Tomášek, Petr (advisor)
This bachelor's thesis deals with numerical solution of ordinary differential equations. The first part of the thesis introduces and describes the numerical methods for ordinary differential equations. The next part is about stability of numerical methods. The aim of the thesis is to analyze the stiffness of the systems of differential equations, select a suitable numerical method and solve the systems in the MATLAB.
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Integrals and differential equations in apllied problems - a digest of solved examples.
HOLUB, Miroslav
The main topic of the Thesis is the creation of a collection of selected solved interesting tasks intended for expanding the teaching of mathematics seminars at secondary schools, or as supplementary literature for students of various fields of university. The first part deals with the possibilities of applications of integral calculus in problems from common practice. Specific topics of some tasks can also be used in areas of professional circles. The second part of the Thesis focuses on mathematically solved problems, based on exceptional circumstances from everyday life. The goal of each example is to compile an ODE, determine the initial conditions, solve the equation and confront the task.
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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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Numerical analysis of stiff differential equations
Pavelka, Ondřej ; Zatočilová, Jitka (referee) ; Tomášek, Petr (advisor)
This bachelor's thesis deals with numerical solution of ordinary differential equations. The first part of the thesis introduces and describes the numerical methods for ordinary differential equations. The next part is about stability of numerical methods. The aim of the thesis is to analyze the stiffness of the systems of differential equations, select a suitable numerical method and solve the systems in the MATLAB.
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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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