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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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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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State space formulations of dynamical problems
Kozánek, Jan
The 3n and 4n state space formulations of system of n linear second-order ordinary differential equations with special right side are proposed. The paper is concerned to an other than common understanding of resonant phenomena of dynamical systems
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Počáteční chování bubliny páry v přehřáté kapalině
Vejražka, Jiří
The model is based on a simplified law for heat transfer of a growing and moving bubble and on solving the forces acting on this bubble. The model is represented by a system of ordinary differential equations and can be used until the time when bubbles start to wobble. An partially successful (but not convincing) attempt to validate this model by comparison with available experimental data was done. In most cases, the bubble behavior is controlled by a balance of the buoyancy with the added-mass force. In this aspect, the bubble behavior differs considerably from the case of constant-volume bubbles, for which the added-mass force is usually negligible. For the case of spherical bubbles, a simple analytical solutions are provided.
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