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Definite Integrals in Maple, Matlab and TKSL
Barták, Jaroslav ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This thesis discourses different types of definite integrals calculations, applying Maple, Matlab and TKSL software. Additionally, the thesis compares above software in terms of usability of calculated results of each program. For verification of calculations and comparison of different interpretations, there are examples of source code attached. By virtue of this files it is possible to revise the calculations of definite integrals and compare complexity of its record. Finally, the paper also compares above programs considering their user-friendliness.
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Finite Integrals Numerical Computations
Mikulka, Jiří ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
The application of the finite integral of multiple variable functions is penetrating into more and more industries and science disciplines. The demands placed on solutions to these problems (such as high accuracy or high speed) are often quite contradictory. Therefore, it is not always possible to apply analytical approaches to these problems; numerical methods provide a suitable alternative. However, the ever-growing complexity of these problems places too high a demand on many of these numerical methods, and so neither of these methods are useful for solving such problems. The goal of this thesis is to design and implement a new numerical method that provides highly accurate and very fast computation of finite integrals of multiple variable functions. This new method combines pre-existing approaches in the field of numerical mathematics.
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Multiple Integrals
Valešová, Nikola ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
The problem of definite integral and differential equation computation is still a significant part of many scientific branches and the solution of integral calculus tasks can be found in many industrial fields too. During the computation of such tasks, the accuracy and high-speed requirements are often confronted. These requirements are crucial during the process of the suitable method choice. The aim of this thesis is to propose, describe, implement and test a new numerical method, which combines the solution of definite integrals by transforming them into differential equations solved by the Taylor series with the traditional methods, which use the Newton-Cotes formulas. As a result, a new application has been developed, that provides fast results of definite two-dimensional integrals and reaches at least the precision of MATLAB. The major accomplishment of this thesis is the development of a new numerical method and its comparison to other established ways of computation.
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Semi-Analytical Computations
Herzallah, Ahmad Sudqi Hussein ; Kopřiva, Jan (referee) ; Kunovský, Jiří (advisor)
This thesis discusses the analytical errors emerging from semi-analytical calculations. It also discusses about the modern method of Taylor's series for numerical calculations of ordinary differential equations and chosen methods of charachterized functions. The end solutions indicate favourable results for the semi-analytical calculations in the selected roles and responsible differential equations by direct execution of Taylor's series for solutions of polynomial functions, exponential functions & geometric functions using simulation program "TKSL". It also discusses about the definite & indefinite Intergals and methods for the solution of definite integrals. Followed by a brief introduction of Maple, Matlab & TKSL and further comparison of the result of the three programs & finding the best way of resolving the definite integrals.
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Finite Integrals Semi-Analytical Computations
Veigend, Petr ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This bachelor thesis explains the topic of semi-analytical computation of finite integrals. It contains the mathematical definition of finite integral, along with definitions and examples for several methods that can be used to solve finite integrals analytically. For the most part however, the thesis is trying to explain how to effectively and precisely approximate finite integrals on a computer. It deals with approximations by polynomials, but mostly with the correspondence between finite integrals and differential equations. This correspondence is used in two software projects that are the part of this thesis.
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|
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Multiple Integrals
Valešová, Nikola ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
The problem of definite integral and differential equation computation is still a significant part of many scientific branches and the solution of integral calculus tasks can be found in many industrial fields too. During the computation of such tasks, the accuracy and high-speed requirements are often confronted. These requirements are crucial during the process of the suitable method choice. The aim of this thesis is to propose, describe, implement and test a new numerical method, which combines the solution of definite integrals by transforming them into differential equations solved by the Taylor series with the traditional methods, which use the Newton-Cotes formulas. As a result, a new application has been developed, that provides fast results of definite two-dimensional integrals and reaches at least the precision of MATLAB. The major accomplishment of this thesis is the development of a new numerical method and its comparison to other established ways of computation.
|
|
|
Finite Integrals Semi-Analytical Computations
Veigend, Petr ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This bachelor thesis explains the topic of semi-analytical computation of finite integrals. It contains the mathematical definition of finite integral, along with definitions and examples for several methods that can be used to solve finite integrals analytically. For the most part however, the thesis is trying to explain how to effectively and precisely approximate finite integrals on a computer. It deals with approximations by polynomials, but mostly with the correspondence between finite integrals and differential equations. This correspondence is used in two software projects that are the part of this thesis.
|
|
|
Definite Integrals in Maple, Matlab and TKSL
Barták, Jaroslav ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This thesis discourses different types of definite integrals calculations, applying Maple, Matlab and TKSL software. Additionally, the thesis compares above software in terms of usability of calculated results of each program. For verification of calculations and comparison of different interpretations, there are examples of source code attached. By virtue of this files it is possible to revise the calculations of definite integrals and compare complexity of its record. Finally, the paper also compares above programs considering their user-friendliness.
|
|
|
Semi-Analytical Computations
Herzallah, Ahmad Sudqi Hussein ; Kopřiva, Jan (referee) ; Kunovský, Jiří (advisor)
This thesis discusses the analytical errors emerging from semi-analytical calculations. It also discusses about the modern method of Taylor's series for numerical calculations of ordinary differential equations and chosen methods of charachterized functions. The end solutions indicate favourable results for the semi-analytical calculations in the selected roles and responsible differential equations by direct execution of Taylor's series for solutions of polynomial functions, exponential functions & geometric functions using simulation program "TKSL". It also discusses about the definite & indefinite Intergals and methods for the solution of definite integrals. Followed by a brief introduction of Maple, Matlab & TKSL and further comparison of the result of the three programs & finding the best way of resolving the definite integrals.
|
|
|
Finite Integrals Numerical Computations
Mikulka, Jiří ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
The application of the finite integral of multiple variable functions is penetrating into more and more industries and science disciplines. The demands placed on solutions to these problems (such as high accuracy or high speed) are often quite contradictory. Therefore, it is not always possible to apply analytical approaches to these problems; numerical methods provide a suitable alternative. However, the ever-growing complexity of these problems places too high a demand on many of these numerical methods, and so neither of these methods are useful for solving such problems. The goal of this thesis is to design and implement a new numerical method that provides highly accurate and very fast computation of finite integrals of multiple variable functions. This new method combines pre-existing approaches in the field of numerical mathematics.
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