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Use of internet in teaching of goniometric equations and inequalities
Kepič, Matúš ; Robová, Jarmila (advisor) ; Odvárko, Oldřich (referee)
Title: Use of internet in teaching of goniometric equations and inequalities Author: Matúš Kepič Department: Department of Mathematics Education Supervisor: RNDr. Jarmila Robová, CSc. Supervisor's e-mail address: robova@karlin.mff.cuni.cz Abstract: This work serves as a teaching material for pupils and teachers of secondary school. It deals with subject of goniometrical equations and inequalities. The work contains a theoretical part where is clearly explained the basic theoretical knowledge of the goniometrical equations and inequalities. The emphasis is on practical section that contains the solved examples and the problems for practice which is accompanied by stepping solution. The work has a form of a web application, contains interactive elements (for example. step-by-step solution, multiple choice tests). It is freely accessible on the Internet. The work is accompanied by a CD, where is this thesis in .pdf format. Keywords: trigonometric functions, goniometrical equations, inequalities goniometrical
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Numerická kvadratura vyššího řádu ve 2D a 3D
Segeth, Karel ; Šolín, P. ; Doležel, I.
The construction of higher-order Gauss quadrature rules in 2D and 3D is it considered. Many open questions are related to the desing of (symmetric) formulae with minimum number of points. After outlining some of the state-of-the- art knowledge and open problems in contemporary numerical quadrature related to finite element methods, we present and discuss several techniques which can (and should) be used where the current knowledge of Gaussian quadrature rules is not sufficient.
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Mathematics on Internet
Dózsa, Martin ; Holub, Viliam (advisor) ; Eckhardt, Alan (referee)
The aim of this work is to create an easy-to-use mathematical tool, mainly for students specialized at mathematical education. UniMaxima focuses on calculations within the frame of mathematical analysis and (especially linear) algebra. It calculates derivatives, definite and indefinite integrals, decomposition to partial fractions, Taylor-series, sums, limits, matrices, eigenvalues, eigenvectors and determinants. It is also possible to plot functions of one or two variables. The advantage of UniMaxima is simple use, there is no need to install: it is enough to visit the project's website (with Firefox 3.0+) and input the formulae.
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Economic analysis and the Implicit Function Theorem
Solnický, Radek ; Johanis, Michal (referee) ; Pražák, Dalibor (advisor)
Nazev pracc: Vota o implicituich funkn'rh v ekonomicke analyse Autor: Radek Solnirky Pracovisto: Katrdra innteinatirke analyzy Vedouci bakalafske prace: RNDr. Prazak Dalibor, Ph.D. e-mail veclouciho: prazak@karlin.mff.cuni.cz Ahstrakt: V unioha ekonomickych modeled! popisuji'cich rovnovahy se vy- \i7.ivii popis .situaco pomoci grafu. Rovnovahu pak pferlstavuje prusecik kfi- vek- Loft'irky naslcdujc1 ota/ka. jak .se tatf) rovnovaha ziuenf, zmeniTun-li vucj.sf parametry mod(>lu. V ramci grafu jde o [)OMim nekterycli kfivek a vznik novyeh prusccikii. Z jejich pozice se UHUZUJC, v jakcni vztahu jc nova rovnovaha vzhledrm k puvothn. V tcto praci je pfcdstavena nietoda kom- parativni staticke analyzy, inatoinaticky exaktni metody, ktera zodpovkla tuto otazku be'/ nutnosti s]K)lehat se na intuitivni pojoti situacc grafein. Jo obc-nur odvo/on jejf po.stup a nasledne jc ilustrovan na nekolika pffkladecii. Kh'cova slova: ^-eta o iuiplicitni'ch funkci'ch, rcjvnovaha. produkeni funkcu, uzitkova funkcc Title: Economic Analysis and the Implicit. Function Theorem Author: Radok Solnicky Department: Department of Mathematical Analysis Supervisor: RNDr. Prazak Dalibor. Ph.D. Supervisor's e-mail address: prazak@karlin.raff.cuni.cz Abstract: In economic models describing various equilibria, graphs are used to illustrate the...
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Learning difficulties in mathematics and their re-education at the primary school
Tlapáková, Šárka ; Dvořák, Petr (referee) ; Kloboučková, Jaroslava (advisor)
Diplomová práce s názvem "Poruchy učení v matematice a jejich reedukace na základní škole" je zaměřena na studium obtíží v matematice, které se objevují u žáků prvních až devátých ročníků. Práce je rozdělena do tří hlavních kapitol, které jsou pak ještě dále děleny na dílčí podkapitoly. První část tvoří teoretický základ o specifických vývojových poruchách obecně. Ten je nutný pro další studium poruch učení v matematice a zasazuje tak poruchy učení v matematice do širšího kontextu specifických vývojových poruch. Druhá kapitola je zaměřena konkrétně na poruchy a narušení matematických funkcí. Celý tento úsek tvoří teorie nezbytná pro pochopení této problematiky v praxi. Poslední, tedy třetí kapitola je orientována právě na praxi. Její podkapitoly se zabývají statistikou na Základní škole v Heřmanově Městci, výukovými programy na PC a mojí spoluprací s integrovaným chlapcem. Cílem mé práce bylo obohatit si teoretické znalosti, poznat práci s integrovanými žáky na základní škole a zkusit s nimi pracovat.
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Study of factors influencing the function of MntH, membrane transport protein of E. coli
Jurková, Ingrid ; Urbánková, Eva (advisor) ; Krůšek, Jan (referee)
MntH belongs to the Nramp family of transport proteins, and plays an important role not only in homeostasis of iron and manganese, but also in bacterial defence against the immunity response of an infected host cell. MntH co-transports divalent metal ions into the cell together with protons with a stoichiometry dependent on the membrane potential and extracellular pH. Using the redistribution potential dye diS-C3(3), we measured the effects of MNTH expression and MntH-mediated metal transport on the cell membrane potential and intracellular pH. Cells expressing MNTH were found to be hyperpolarised and their membrane potential was depolarised upon the addition of metal ions. In the theoretical part of our work, we explored general four-, six-, and eight-state carrier models that were modified by introducing the voltage dependence of all rate constants. Using mathematical modelling, we simulated the effect of various model parameters (including membrane potential, substrate concentration, and carrier or substrate charge) on substrate influx. We observed some of the transport characteristics described for MntH proteins such as variable symport stoichiometry that is influenced by the membrane potential and pH. However, for a more detailed simulation of the eight-state carrier model, more information about...
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Detection of Global and Local Ischemic Changes in Electrical Field of the Heart
Šťovíček, Petr ; Kittnar, Otomar (advisor) ; Kneppo, Peter (referee) ; Horký, Karel (referee)
In this thesis, detailed investigation into the electrical field of the heart is presented in patients with various manifestations of myocardial ischemia. Methods of standard scalar electrocardiography and body surface potential mapping were used through statistical and mathematical analysis in order to compare their diagnostic performance. Body surface mapping proved to be more powerful research and diagnostic tool than standard electrocardiography and also constituted a framework for data entering the computer electrical model of the human heart and torso. Global and local ischemic changes were the primary objectives of the individual studies of this thesis. Different patient populations were studied including post myocardial infarction population, patients with variant angina and patients referred for percutaneous coronary angioplasty, and the population of patients suffering from ventricular arrhythmias related mostly to their postinfarction status. Traditional depolarization and repolarization changes were studied together with novel diagnostic parameters such as minimal potential loss within the QRS complex, single-beat cardiac micropotentials and distribution of the QT interval on the human thorax. Critical appraisal and error performance of so called QT interval dispersion was another important...
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Graphing Calculators in Taching of Mathematic
Molnárová, Petronela ; Robová, Jarmila (referee) ; Kašpar, Jan (advisor)
Nazov prace: Grafickc kalkulacky vo vyucbe matemaliky Autor: Pctronela Molnarova Katcdra: Didakliky matematiky Veduci bakalarskcj pracc: KNDr. Jan Kaspar, CSc. e-mail vcduceho: Jan.Kaspar.WmlT.cuni.c/ Touto pracou som chcela ukaxaf, ako jo mozne vyuzif graflcku kalkulacku pri vyucbe na /akladnej skole. Na zaeiatku pracc som sa zamcrala na obsah grafickcj kalkulacky. V kratkosti som popisala nieklorc zaplikacii. V zostavajucej casti pracc som sa venovala konkretnym castiam matematiky, v ktorych podTa inojho nazoru graficka kalkulacka najde uplatnenie. Boli to ticto parlie: lincarne rovnice, funkcic - linearnc a kvadralickc, statistika. Kazda lema jc najskor tcorcticky spracovana. Uvicdla som definicic odpovedajuce urovni /akladnej skoly. Teoria je doplnena ulohami a ich ricscnim na grafickcj kalkulacke. Kl'ucove slova: graficka kalkulacka, xakladna skola, funkcie, statistika Title: Graphing Calculators in Teaching of Mathematics Author: Pctronela Molnarova Department: Didactics mathematics Supervisor: RNDr. Jan Kaspar, CSc. Supervisor's e-mail address: Jan.Kaspanfrmff.cuni.c/ The aim of this work was to find out the practical application ofthc graphing calculator in the elementary school education. At the beginning of this work I discuss about the content of the graphing calculator. Some of its applications...
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Solver of Mathematical Equations for Android
Janičko, Adam ; Herout, Adam (referee) ; Zachariáš, Michal (advisor)
This thesis aims at creating equation solver application for Android platform. The thesis includes graphical user interface (GUI), save and edit options for equations, the actual equation solving and widget for quickly evaluating already stored equations. When creating equations, user is able to use selected mathematical functions, constants and custom variables that user can define right before evaluation. The equation in the standard infix notation inappropriate for further processing is transferred to the prefix notation using modified Shunting Yard algorithm. Final expression is put together once. That means the evaluation is faster, when the values of user-defined variables changes.
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Building credit scoring models using selected statistical methods in R
Jánoš, Andrej ; Bašta, Milan (advisor) ; Pecáková, Iva (referee)
Credit scoring is important and rapidly developing discipline. The aim of this thesis is to describe basic methods used for building and interpretation of the credit scoring models with an example of application of these methods for designing such models using statistical software R. This thesis is organized into five chapters. In chapter one, the term of credit scoring is explained with main examples of its application and motivation for studying this topic. In the next chapters, three in financial practice most often used methods for building credit scoring models are introduced. In chapter two, the most developed one, logistic regression is discussed. The main emphasis is put on the logistic regression model, which is characterized from a mathematical point of view and also various ways to assess the quality of the model are presented. The other two methods presented in this thesis are decision trees and Random forests, these methods are covered by chapters three and four. An important part of this thesis is a detailed application of the described models to a specific data set Default using the R program. The final fifth chapter is a practical demonstration of building credit scoring models, their diagnostics and subsequent evaluation of their applicability in practice using R. The appendices include used R code and also functions developed for testing of the final model and code used through the thesis. The key aspect of the work is to provide enough theoretical knowledge and practical skills for a reader to fully understand the mentioned models and to be able to apply them in practice.
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