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Solving methods of systems of linear equations
Šotolová, Petra ; Jančařík, Antonín (advisor) ; Novotná, Jarmila (referee)
My bachelor's thesis is focused on methods for solving systems of linear equations. Its aim is to explain the application of these methods for solving systems of linear equations and to assign advantages and the type of system for which each method is advantageous. The thesis should be suitable for elementary and secondary school students, university students, as well as individuals not studying mathematics. It describes substitution method, addition method, comparison method, graphical method, Gaussian elimination, Gauss-Jordan elimination, inverse matrix and Cramer's rule and their application in solving systems of two or more linear equations with two or more unknowns. It includes a general explanation and a specific procedure with examples, advantages and disadvantages of each method, and types of systems for which the method would be used. The thesis examines the number of solutions of systems of equations depending on the form of the system. It also explains basic concepts and provides simplified definitions of the terms used.
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Stress-strain analysis of a crane arm
Mora, Lukáš ; Halabuk, Dávid (referee) ; Fuis, Vladimír (advisor)
The content of this bachelor’s work is a summarization of types of tower cranes and subsequent stress-strain analysis of the crane arm of the crane type 150EC-B8 Litronic located on the Šumavská street in Brno. Analytical stress-strain analysis is calculated with equations of equilibrium using joint method in various types of loading of the construction with MAPLE software. Numerical calculation is executed on 3D model of the construction in software ANSYS. The aim of this bachelor work is the verification of the correctness and comparison results of analytic calculation with numeric calculation and evaluation of the results from a limit states and deformation standpoint.
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Algebraic Equations Solution Convergence
Sehnalová, Pavla ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
The work describes techniques for solving systems of linear and differential equations. It explains the definition of conversion from system of linear to system of differential equations. The method of the elementary transmission and the transform algorithm are presented. Both of methods are demonstrated on simply examples and properties of conversion are shown. The work compares fast and accurate solutions of methods and algorithm. For computing examples and solving experiments following programs were used: TKSL and TKSL/C. The program TKSL/C was enriched with the graphic user interface which makes the conversion of systems and computing results easier.
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Algebraic Equations Calculations
Kuchařová, Eva ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work investigates the solution of linear algebraic equations by a conversion to the system of differential equations. Moreover, several more frequently used methods are described in addition. The theoretical part of work describes the mathematical. Next, the examples of using the Matlab a TKSL programs are presented to show and compare the results of calculations. The source codes used are included. The work proves that the solution of algebraic equations by the conversion to the system of differential equations is applicable and further solved by the Euler's method. The parallel solution is also described. As the output of this work, the lin2dif program was developed. It realizes the conversion among the systems of equations. Finally, the description of the work progress, design, implementation and usage of the program are summarized.
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Students' procedures for mathematical word problems solvable by systems of equations during the school leaving examination
Doubrava, Jiří ; Chvál, Martin (advisor) ; Vondrová, Naďa (referee)
This diploma thesis investigates different approaches to solving word problems with systems of equations. The thesis aims to discover which strategies are used by senior students when solving these word problems and documents the processes involved. The research presented in the thesis is based on an in-depth analysis of the database of student cut-outs from five word problems of the common part of the Maturita exam, specifically from the spring terms between the years 2016 and 2020. The theoretical part involves an analysis of three textbooks for high school students in the Czech Republic which incorporate the named phenomena. Furthermore, this part includes a list of student strategies for solving word problems, moreover, the reader is provided with a description of the state Maturita exam in Mathematics. The empirical part contains an overview of several possible procedures prepared during an a priori analysis. It also presents psychometric features of the chosen word problems by incorporating statistical outcomes. In addition, cut-outs of students' answers are divided into various groups based on the chosen solving strategies, thus demonstrating the possible techniques used by the students when solving this type of tasks. The principal conclusions demonstrate immense omissions, supporting the...
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Exercises and problems in linear algebra
ČAPKOVÁ, Klára
The aim of this thesis is to create a collection of solved examples and problems of linear algebra, which could serve as a learning tool for the first-year students of the Faculty of Education of University of South Bohemia in České Budějovice. The most important part of this thesis is the electronic processing of the collection in a program GeoGebra and its visual interpretation of examples and problems by 3D pictures, QR codes and hyperlinks that specify the solutions.
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Solving strategies for word problems that can be solved with equations
Chromá, Stanislava ; Novotná, Jarmila (advisor) ; Pilous, Derek (referee)
The aim of this work is to get acquainted with the issue of solving word problems by means of equations, to state and to analyse various ways of solving them. The thesis also includes the comparison of strategies for solving word problems that are selected by students who have been already taught the given type of the equation, and students who have not yet mastered these procedures. The introductory part of the work deals with word problems in general. There the terms such as the word problems, procedures, methods and strategies used for solving word problems are specified. In the next part of the text, the basic types of equations are characterized. For each type of the equation, one typical word problem was selected and it was experimentally found out which solving strategies were used by students most often. Keywords: word problem, algebraic equation, non-algebraic equation, system of equations
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Stress-strain analysis of a crane arm
Mora, Lukáš ; Halabuk, Dávid (referee) ; Fuis, Vladimír (advisor)
The content of this bachelor’s work is a summarization of types of tower cranes and subsequent stress-strain analysis of the crane arm of the crane type 150EC-B8 Litronic located on the Šumavská street in Brno. Analytical stress-strain analysis is calculated with equations of equilibrium using joint method in various types of loading of the construction with MAPLE software. Numerical calculation is executed on 3D model of the construction in software ANSYS. The aim of this bachelor work is the verification of the correctness and comparison results of analytic calculation with numeric calculation and evaluation of the results from a limit states and deformation standpoint.
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Solving strategies for word problems that can be solved with equations
Chromá, Stanislava ; Novotná, Jarmila (advisor) ; Pilous, Derek (referee)
The aim of this work is to get acquainted with the issue of solving word problems by means of equations, to state and to analyse various ways of solving them. The thesis also includes the comparison of strategies for solving word problems that are selected by students who have been already taught the given type of the equation, and students who have not yet mastered these procedures. The introductory part of the work deals with word problems in general. There the terms such as the word problems, procedures, methods and strategies used for solving word problems are specified. In the next part of the text, the basic types of equations are characterized. For each type of the equation, one typical word problem was selected and it was experimentally found out which solving strategies were used by students most often. Keywords: word problem, algebraic equation, non-algebraic equation, system of equations
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The equations and systems of equations in problems from Mathematical Olympiad categories A, B and C
ŠIMÁNKOVÁ, Zuzana
The diploma thesis included of informations of a Mathematical Olympiad, equations and systems of equations. The theoretical part contains a historical development and its organization, next it contains informations about equations and their teaching as it is given in the National Curriculum. The practical part consists of a collection of exercises on the topic of equations and systems of equations, which were included in the competition Mathematical Olympiad. Examples in the collection are divided into categories vhich appeard, and ranked by difficulty. Further practical part includes evaluation works heets completed by students of Pedagogicial faculty, University of South Bohemia. This thesis may serve as preparation pupils on Mathematical Olympiad or as a collection of examples for talented pupils
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