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National Repository of Grey Literature 3 records found  Search took 0.00 seconds. 
Defining the exponential function and logarithm
 Franc, Tomáš ; Bárta, Tomáš (advisor) ; Veselý, Jiří (referee)
In this diploma thesis we will introduce six de nitions of the natural exponential function and ve de nitions of the natural logarithmic function. We will prove the de nitions' correctness, derive basic properties of both funcions and show the equivalence of all de nitions for each function. We will see how these funcions are de ned in some textbooks for universities and in textbooks for grammar schools. We will discuss the bene ts and drawbacks of all de nitions and will use the criteria such as required theory and difficulty or length of proofs. At the end of the thesis we will make some recommendations regarding de ning these functions at high schools and universities and we will give several suggestions for an additional research.
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Defining the exponential function and logarithm
 Franc, Tomáš ; Bárta, Tomáš (advisor) ; Veselý, Jiří (referee)
In this diploma thesis we will introduce six de nitions of the natural exponential function and ve de nitions of the natural logarithmic function. We will prove the de nitions' correctness, derive basic properties of both funcions and show the equivalence of all de nitions for each function. We will see how these funcions are de ned in some textbooks for universities and in textbooks for grammar schools. We will discuss the bene ts and drawbacks of all de nitions and will use the criteria such as required theory and difficulty or length of proofs. At the end of the thesis we will make some recommendations regarding de ning these functions at high schools and universities and we will give several suggestions for an additional research.
Detailed record
Shadow Mapping: Shadow Filtering in OpenGL
 Maresz, Šimon ; Polok, Lukáš (referee) ; Kobrtek, Jozef (advisor)
This thesis deals with filtration of shadow rendering in 3D scene with a focus on quality of rendered shadows. As part of this work was to create a sample application that implements the chosen algorithms that modifies the Shadow Mapping algorithm to render softer and more realistic shadows. The program was created in the integrated development environment Microsoft Visual Studio 2010 in C++. At the beginning the algorithms are explained for rendering of shadows. The conclusion is then engaged in testing and comparing of achieved results.
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