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Classical and fractional modelling of oscillatory motion
Hošek, Jaromír ; Tomášek, Petr (referee) ; Kisela, Tomáš (advisor)
In this thesis we deal with the issue of damped oscillations. Besides the classic description using member directly proportional to the first derivative position we focus on the model containing derivatives of non-integer order, so-called the fractional model of damped oscillations. The behavior of both models is studied through the test applications describing the movement of one, two, respectively three bodies connected by springs. The main tool for solving is the Laplace transform method. Besides the computational aspects we discuss some qualitative properties of solutions, especially dependence on order derivative in the fractional model and the behavior of the center of gravity system position.
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Mathematical modelling of the population dynamics of hemiparasitic plants
SVĚTLÍKOVÁ, Petra
The hemiparasite-host interaction is rather complex, acting as parasitism belowground and as competition for light aboveground. Studies modelling this interaction are rare. The most recent model of the hemiparasite-host interaction was developed from the well-known Rosenzweig-MacArthur predator-prey model by Fibich et al. (2010). Here, I modied the light availability function of the model into a more general form and examined the hemiparasite-host coexistence along a productivity gradient of the environment. The behaviour of presented and analyzed model was shown to depend particularly on parameter g scaling light availability for hemiparasites at high host biomasses. While it suggested the host-hemiparasite coexistence only at intermediate productivities under low g, species could coexist even at high productivities under higher g.
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Differential equations with GeoGebra
OPAVOVÁ, Michaela
The main aim of this bachelor thesis called Differential equations with GeoGebra is to create a transparent collection of solved examples. Examples are numerically solved first, followed by their graphic interpretation by using mathematical program GeoGebra. Illustrations show us interesting solutions of examples. Another objective is to introduce students the program GeoGebra as a tool through which you can elegantly solve the example. The work is divided into three chapters, which deal with the basic type of differential equations, the method of separation of variables and linear differential equations with constant coefficients and zero right side. They are shown of the basic theory and then resolved examples. In These chapters are selected types of examples which meets student in Mathematical Analysis III. Therefore, this collection is useful as a study material for students of mathematical disciplines.
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Periodic solutions of damped oscillations
HOLUB, Miroslav
The main topic of the Thesis is qualitative analysis of linear differential equations of second order. The Thesis is divided into five parts. At the first part there are explained basic type of oscillators (mathematical pendulum and spring). The second part is devoted to definitions and theorems, which are necessary in the study of differential equations. The third part shows the model of linear differential equation of second order. The solution of this equation depending on various parameters is indicated in the fourth part. Some open questions are formulated in the last part.
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1st Order Differential Equations --- A Digest of Solved Examples
ŽELEZNÝ, Zdeněk
This thesis deals with the solution of differential equations of the first degree. The work is intended to serve as a textbook (a collection of exercises) for students of teaching mathematics at lower secondary schools. Each chapter contains a summary of basic concepts, solved task models of the related topic, sorted by difficulty, and finally tasks assigned for independent practicing. This thesis aims to present basic knowledge about ways of solving differential equations of the first degree, including practical skills for their solution.
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Fluid modelling in plasma physics
BŘEZINOVÁ, Jitka
This work is dealing with issues concerning mathematical and computer modeling of events describable with help of rst and second order differential equations. First part contains summary of basic procedures for searching differential equations using analythical methods, next chapter is focused on software used to solve chosen tasks and demonstration of speci c physics problems.
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High mathematics teaching text creation with using of the e-learning
NOVÁKOVÁ, Alena
Teaching text containing the following chapters of higher mathematics: complex numbers, matrices, determinants, numerical solution of equations, differential calculus of functions of several variables, vector analysis, differential equations. The text is supported by illustrated examples with the main aim of using the given mathematical concepts and theorems in physics. Part of this teaching text is its electronic form {\clqq}Electronic textbook of mathematics for physics``.
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Těžba v Predator-Prey modelu
Chrobok, Viktor ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
The paper is focused on the Predator-Prey model modified in the case of harvesting one or both populations. Firstly there is given a short description of the basic model and the sensitivity analysis. The first essential modification is percentage harvesting. This model could be easily converted to the basic one using a substitution. The next modification is constant harvesting. Solving this system requires linearization, which was properly done and brought valuable results applicable even for the basic or the percentage harvesting model. The next chapter describes regulation models, which could be used especially in applying environmental policies. All reasonable regulation models are shown after distinguishing between discrete and continuous harvesting. The last chapter contains an algorithm for maximizing the profit of a harvester using econometrical modelling tools.
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