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Electronic Textbook in Introduction to Mathematical Methods of Physics
Kolář, Petr ; Žák, Vojtěch (advisor) ; Koupilová, Zdeňka (referee)
Title: Electronic Textbook in Introduction of Mathematical Methods of Physics Abstract: The objective of this work is to create a studing text not only for the first grade students of physics teaching at FMP CU but also for other students of phy- sical and technical domains at universities which should help them with an intro- duction into mathematic necessary in physics. The main matter of this work is based on preparations and texts of dr. A Hladík, prof. J. Podolský and dr. V. Žák for lectures and exercises of subject Introduction of Mathematical Methods of Physics. The author's experience is also reflected of course, especially his fresh experience with the age group for which is this text created. Equally, a small re- cherche of an existence and an availability of other sources pursuing given matters have been done. Some of these sources are recommended in this work. The cre- ated text should help readers with elementary matter of systems of coordinates, limits and derivations with a special consideration to their applications in physics. A contribution of this work for students is going to be a subject of other resear- ching. An extension of this text with other elementary parts of mathematical methods of physics is presumed too.
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Real Time Dynamic System Control
Adamík, Pavel ; Kaluža, Vlastimil (referee) ; Kunovský, Jiří (advisor)
This thesis focuses on the methodology of controlling dynamic systems in real time. It contents a review of the control theory basis and the elementary base of regulators construction. Then the list of matemathic formulaes follows as well as the math basis for the system simulations using a difeerential count and the problem of difeerential equations solving. Furthermore, there is a systematic approach to the design of general regulator enclosed, using modern simulation techniques. After the results confirmation in the Matlab system, the problematics of transport delay & quantization modelling follow.
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Application tasks of differential calculus of two variables
ŠVEJDOVÁ, Veronika
The aim of this work is to form the collection of answered riders of differencial calculus function with two variables. The work includes examples of determination of local function and solving of two-variable collocations. Examples will be arranged according difficulty and completed by graphical representation.
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Mathematical apparatus of thermodynamics
TESAŘOVÁ, Jaroslava
This Thesis deals with the use of the mathematical apparatus in thermodynamics, specifically the use of Calculus of functions of several variables. The main emphasis is placed on creating a mathematical derivation of the theoretical foundations of thermodynamics, for example Maxwell relations. The following thing explains the linear differential forms with the help of them the laws of thermodynamics are defined. In the Thesis there are examples with solution to illustrate mathematical procedures. To understand this Thesis the knowledge of Calculus is required.
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Optimization in systems of biological populations
Hašek, Pavel ; Chrobok, Viktor (advisor) ; Černý, Michal (referee)
This paper deals with optimization in systems of biological populations adjusted to harvesting. First, a description, behavior and evolution over time in basic models of Malthus, Verhulst and Gompertz, is solved in case of not harvesting and then harvesting. There are two options for harvesting, continuous and discrete harvesting. In case of continuous harvesting we have two ways how to harvest,with constant yield and constant effort. With simplifying assumptions it is possible to combine continuous and discrete model in the form of profit function for the harvesting and also gives us ability to implement harvesting costs. For profit-seeking function is best solved using numerical methods with model examples with help of the Maple solver. The last chapter is devoted to the introduction of interest to the harvesting models.
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