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Introduction of complex numbers in history of algebra
Rybáková, Tereza ; Kvasz, Ladislav (advisor) ; Jančařík, Antonín (referee)
Title: Introduction of complex numbers in history of algebra Author: Ing. Tereza Rybáková Supervisor: prof. RNDr. Ladislav Kvasz, DSc., Dr. The aim of this thesis is to compare the introduction of complex numbers in history of algebra and its different introduction in textbooks at high schools. This thesis consists of three main chapters. The first chapter is dedicated to historical overview of important personalities who work with complex numbers. It is a short overview of personalities from 16th till 18th century and their connection to complex numbers. The second and the third chapters are focused more practically and their goal is to compare selected books from 16th till 18th century or the textbooks. In second chapter the selected books from 16th till 18th century are described and compared with each other. The square roots of negative number, lately called imaginary numbers, were first mentioned in this time period. Their final comparison is very important and it could be used as a recommendation or inspiration for students - future teachers in mathematics. The third chapter compares four selected textbooks at high school from different period of time and emphasize on explanation of history. It describes the differences in introduction of complex numbers, its definition and main...
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Alternating current circuits in physics education
Cinkraut, Kamil ; Žilavý, Peter (advisor) ; Kácovský, Petr (referee)
The aim of the paper is to define and explain terms of phasor and phasor diagram for students of secondary education level in the Czech republic. It is providing a link between the theoretical foundation of the terms in the mathematics based textbooks available on the market and its establishement and practical use in the teaching process. The purpose of the thesis is to explain the problematic of phasor and phasor diagram in the elecrtic load with the alternating current power supply, which consists of rezistor (R), inductor (L) and capacitor (C). In the second part of the paper, the problematic of the complex numbers and its use is described. In this part, the solution of series or parallel RLC circuit is found by the use of phasor diagram or complex numbers. The paper is furthermore providing reader with problems with solution, which serve as an example for the teaching purposes. The paper is providing the reader with a combination of the theoretical foundation of phasor and phasor diagram with their practical use and application, in order to enable a coherent and understandable explanation of the terms.
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Complex numbers: definition and geometrical applications
Helus, Jiří ; Halas, Zdeněk (advisor) ; Staněk, Jakub (referee)
The thesis describes the introduction of complex numbers in teaching at secondary school, highlights problems that are associated with their introduction and mentions the possible use of complex numbers, espe- cially in geometry. The initial motivational considerations are followed by a brief introduction of complex numbers into the historical context. When introducing complex numbers, we take into account didactic aspects and draw attention to possible problems of interpretation. The chapter is sup- plemented with a reference to hyper complex numbers (quaternions, octets). Furthermore I show how it is possible to geometrically illustrate operations with complex numbers, namely addition, subtraction, multiplication and di- vision. The thesis also describes how Moivre's theorem can be interpreted by rotation. The following part is an analytical geometry built with complex numbers, focusing on point, line, circle, ellipse, and triangle. Next, we search for the square root of the complex number and the solution of the quadratic equation graphically. Finally, we prove Napoleon's theorem and existence of Feuerbach's circle using complex numbers. 1
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Geometrie komplexních čísel
LÁLOVÁ, Eva
This thesis deals with a theory of complex numbers and contains three main parts. The first part is dedicated to the disquisition of complex numbers as we know it from secondary schools. In this part we summarize the basic knowledge of the secondary schools and the use of complex numbers is illustrated by a few arithmetical problems. In the second part we deal with complex numbers in terms of vector spaces and algebraic structures and compare secondary school and university disquisition of complex numbers. In the third part we apply the knowledge from the previous chapters on several problems including problems from mathematical olympiads.
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Introduction of complex numbers in history of algebra
Rybáková, Tereza ; Kvasz, Ladislav (advisor) ; Jančařík, Antonín (referee)
Title: Introduction of complex numbers in history of algebra Author: Ing. Tereza Rybáková Supervisor: prof. RNDr. Ladislav Kvasz, DSc., Dr. The aim of this thesis is to compare the introduction of complex numbers in history of algebra and its different introduction in textbooks at high schools. This thesis consists of three main chapters. The first chapter is dedicated to historical overview of important personalities who work with complex numbers. It is a short overview of personalities from 16th till 18th century and their connection to complex numbers. The second and the third chapters are focused more practically and their goal is to compare selected books from 16th till 18th century or the textbooks. In second chapter the selected books from 16th till 18th century are described and compared with each other. The square roots of negative number, lately called imaginary numbers, were first mentioned in this time period. Their final comparison is very important and it could be used as a recommendation or inspiration for students - future teachers in mathematics. The third chapter compares four selected textbooks at high school from different period of time and emphasize on explanation of history. It describes the differences in introduction of complex numbers, its definition and main...
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Mathematics in Physics
BLAŽEK, Jiří
The presented work deals with mathematical tools, which are used to describe harmonic oscillations and waves in secondary schools. Harmonic quantities are most frequently represented as projections of rotating symbolic vectors ? phasors, nevertheless most attention is paid to representation of harmonic quantities by complex numbers. It is shown that both these methods are in fact formalized methods of solution of differential-algebraic equations, describing relevant physical phenomena. All these approaches are applied simultaneously and compared to each other during solution of model examples. The work is primarily intended for teachers of physics in secondary schools and for students of physics of pedagogical faculties.
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Complex numbers, quaternions and their applications
BRDLÍK, Pavel
The bachelor thesis is dedicated to the topic of complex numbers and quaternions and their application. The main goal of this thesis is to familiarize with the subject of complex numbers and quaternions and their important properties and to present these terms with suitably selected examples. Complex numbers can be used among others to represent a planar rotational movement, quaternions can be used to represent rotations in three-dimensional space. The aim of this thesis is to provide a well arranged summary of the theory and a sample solution of practical examples that would illustratively demonstrate the application of complex numbers and quaternions by description of planar or spatial movements or their further applications.
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High mathematics teaching text creation with using of the e-learning
NOVÁKOVÁ, Alena
Teaching text containing the following chapters of higher mathematics: complex numbers, matrices, determinants, numerical solution of equations, differential calculus of functions of several variables, vector analysis, differential equations. The text is supported by illustrated examples with the main aim of using the given mathematical concepts and theorems in physics. Part of this teaching text is its electronic form {\clqq}Electronic textbook of mathematics for physics``.
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