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Solving of partial differential equations by Fourier method
Barvenčík, Oldřich ; Opluštil, Zdeněk (referee) ; Nechvátal, Luděk (advisor)
Bachelor thesis is a survey text which deals with solving partial deferential equations by Fourier method, i.e. method when we look for a solution of (initial) boundary value problem in form of the infinite Fourier series. The key step is a hypothesis that the solution can be expressed in form with separated variables, therefore the method is sometimes called separation of variables method. The essence can be demonstrated on parabolic and hyperbolic homogeneous problems. In the thesis both types in one (space) dimension are systematically analyzed, at first homogeneous problem, then homogeneous one with non-homogeneous boundary conditions and finally completely non-homogeneous problem.
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Statistical Classification Methods
Barvenčík, Oldřich ; Žák, Libor (referee) ; Michálek, Jaroslav (advisor)
The thesis deals with selected classification methods. The thesis describes the basis of cluster analysis, discriminant analysis and theory of classification trees. The usage is demonstrated by classification of simulated data, the calculation is made in the program STATISTICA. In practical part of the thesis there is the comparison of the methods for classification of real data files of various extent. Classification methods are used for solving of the real task – prediction of air pollution based of the weather forecast.
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Statistical Classification Methods
Barvenčík, Oldřich ; Žák, Libor (referee) ; Michálek, Jaroslav (advisor)
The thesis deals with selected classification methods. The thesis describes the basis of cluster analysis, discriminant analysis and theory of classification trees. The usage is demonstrated by classification of simulated data, the calculation is made in the program STATISTICA. In practical part of the thesis there is the comparison of the methods for classification of real data files of various extent. Classification methods are used for solving of the real task – prediction of air pollution based of the weather forecast.
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Solving of partial differential equations by Fourier method
Barvenčík, Oldřich ; Opluštil, Zdeněk (referee) ; Nechvátal, Luděk (advisor)
Bachelor thesis is a survey text which deals with solving partial deferential equations by Fourier method, i.e. method when we look for a solution of (initial) boundary value problem in form of the infinite Fourier series. The key step is a hypothesis that the solution can be expressed in form with separated variables, therefore the method is sometimes called separation of variables method. The essence can be demonstrated on parabolic and hyperbolic homogeneous problems. In the thesis both types in one (space) dimension are systematically analyzed, at first homogeneous problem, then homogeneous one with non-homogeneous boundary conditions and finally completely non-homogeneous problem.
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