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Characterization of basic functions
Petrášová, Anna ; Řehák, Pavel (referee) ; Čermák, Jan (advisor)
This bachelor thesis deals with characterization of basic functions, namely selected elementary and higher functions. Functional equations provide a useful tool for characterizing these functions. There is performed characterization of the linear function, power function and its special cases, logarithmic and exponential function, trigonometric functions and Euler Gamma function.
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Design and realization of mathematical operations in FPGA circuits
Soukup, Luděk ; Šteffan, Pavel (referee) ; Fujcik, Lukáš (advisor)
This bachelor’s thesis deals with the issue of realization of mathematical operations in digital circuits with a focus on FPGA and ASIC architectures. The attention is focused to algorithms for addition, subtraction, multiplication and division, further to algorithms for computing trigonometric functions. Chosen algorithms are described in VHDL language, synthesized, and they are compared in terms of acquired information about computing time and area which is required for its realization. In the final part of the thesis the possibility of implementation these algorithms is discussed.
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Goniometric functions in physical applications
Hanzlík, František ; Kvasz, Ladislav (advisor) ; Mošna, František (referee)
The aim of the bachelor thesis is to present practical applications of goniometric functions in various fields of mechanics. These are areas that are part of our daily lives in one way or another. The work describes or explaines the necessary context in order to make the text understandable to a high school graduate. The work can be used as a teaching tool for teachers of physics or mathematics in secondary schools. Emphasis is placed on the application of goniometric functions. Previous knowledge of goniometric functions, especially goniometric patterns, is assumed. Much of the work is processed on the basis of internationally recognized lectures in physics. The work is not an exhaustive list of areas of physics in which goniometric functions can be applied. However, it is proof that goniometric functions are necessary to describe a number of elementary physical phenomena.
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Applications of trigonometric functions
Hanzlík, František ; Pilous, Derek (advisor) ; Zamboj, Michal (referee)
This bachelor's work is determined to professional and lay public which is interested in widening its knowledge of goniometric functions and primarily in the examples of its applications. The target of this work is to demonstrate the potential of applications of goniometric functions in various fields of science in which their appearance is characteristic. The beginning to the work is dedicated to introduction of goniometric functions at secondary school level. Then, important basic theorems are formulated which are connected to the theme of this work (sine theorem, cosine theorem, sum formulas). Without knowledge of these formulas, it is impossible to perform non-elementary calculations, therefore the formulas are always given with proof. The examples of applications of goniometric functions have an overlap in areas beyond mathematics, therefore one part of each topic is short introduction. However, the core part of the tasks is focused on goniometric functions. Greater space is devoted to numerical procedures and to properties if goniometric functions. In theoretical part, only basic terms and definitions are mentioned which are necessary to practical part. The examples chosen are for most of topics typical. As a rule, single examples of applications of goniometric functions are not related to...
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Characterization of basic functions
Petrášová, Anna ; Řehák, Pavel (referee) ; Čermák, Jan (advisor)
This bachelor thesis deals with characterization of basic functions, namely selected elementary and higher functions. Functional equations provide a useful tool for characterizing these functions. There is performed characterization of the linear function, power function and its special cases, logarithmic and exponential function, trigonometric functions and Euler Gamma function.
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Exploring qualities of functions with GeoGebra software
KODADOVÁ, Veronika
My thesis is about functions, like linear functions, quadratic functions, goniometric functions etc. Goal of my work ist to design appropriate tasks with focus on function links. Students can with help of matematic program GeoGebra discover and adopt needed properties of functions. In this work you can find Cartesian coordinates and overview of basic properties of functions too.
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The use of new technologies in teaching mathematics
BUMBÁLEK, Roman
Modern information technologies accompany all of us in our daily life. They not only use to serve to our work and for the entertainment, they even have got a great potential to be used in the education. The submitted thesis deals with the appropriate utilization of the special IT application in the pedagogic process, especially in teaching of maths, the topic of trigonometric functions. The aim of this thesis is to create structures with a high potential of the modern technology handling. To tackle this task the graphical program GeoGebra was chosen due to its qualities for creating dynamic structures and the other advantages presented further in the thesis. To the created constructions the detailed instructions how they can be constructed are added. The thesis is also accompanied by worksheets with solved tasks, focusing on the application of trigonometric functions in real situations.
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Design and realization of mathematical operations in FPGA circuits
Soukup, Luděk ; Šteffan, Pavel (referee) ; Fujcik, Lukáš (advisor)
This bachelor’s thesis deals with the issue of realization of mathematical operations in digital circuits with a focus on FPGA and ASIC architectures. The attention is focused to algorithms for addition, subtraction, multiplication and division, further to algorithms for computing trigonometric functions. Chosen algorithms are described in VHDL language, synthesized, and they are compared in terms of acquired information about computing time and area which is required for its realization. In the final part of the thesis the possibility of implementation these algorithms is discussed.
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Use computers by teaching mathematics at elementary school
MÁCHA, Pavel
This work thesis is dealing with interactive geometry software GeoGebra. Several use cases for educational purposes in elementary schools are proposed and described in detail. This work is mainly focused on construction of triangles, trigonometric functions, systems of equations and tasks related to motion and presentation of cube. Each example is followed by an application created in GeoGebra. With these GeoGebra applications you can easily change parameters with sliders and therefore further work is possible. This thesis provides step-by-step guide how to create each example which is helpful for both teachers and their pupils. Attached CD contains all discussed examples which can be directly used by teachers in elementary schools to support a classwork during math lectures. In the final part of this thesis advantages and drawbacks of dynamic geometry are proposed and short comparison of GeoGebra and Cabri programs is suggested.
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