Made available in DSpace on 2014-12-17T15:04:47Z (GMT). No. of bitstreams: 1 MariaSueliFF.pdf: 1053990 bytes, checksum: e1b0f752b300ce7232435cab9e0841a9 (MD5) Previous issue date: 2006-05-19 / This work presents a contribution for the studies reffering to the use of the History of Mathematics focusing on the improvement of the Teaching and Learning Process. It considers that the History of Matematics, as a way of giving meaning to the discipline and improve the quality of the Teaching and Learning Process. This research focuses on the questions of the students, classified in three categories of whys: the chronological, the logical and the pedagogical ones. Therefore, it is investigated the teaching of the Complex Numbers, from the questions of the students of the Centro Federal de Educa??o Tecnol?gica do Rio Grande do Norte (Educational Institution of Professional and Technology Education from Rio Grande do Norte). The work has the following goals: To classify and to analyse the questions of the students about the Complex Numbers in the classes of second grade of the High School, and to collate with the pointed categories used by Jones; To disccus what are the possible guidings that teachers of Mathematics can give to these questions; To present the resources needed to give support to the teacher in all things involving the History of Mathematics. Finally, to present a bibliographic research, trying to reveal supporting material to the teacher, with contents that articulate the Teaching of Mathematics with the History of Mathematics. It was found that the questionings of the pupils reffers more to the pedagogical whys, and the didatic books little contemplate other aspects of the history and little say about the sprouting and the evolution of methods of calculations used by us as well / Este trabalho busca apresentar uma contribui??o para os estudos referentes ao uso da Hist?ria da Matem?tica visando ? melhoria do processo ensino-aprendizagem. Prop?e que a Hist?ria da Matem?tica seja articulada ao Ensino da Matem?tica, como forma de dar significado ? disciplina e melhorar a qualidade do processo de ensino-aprendizagem. Nesta investiga??o, o foco est? nas indaga??es dos alunos, classificadas em tr?s categorias de porqu?s: o cronol?gico, o l?gico e o pedag?gico. Para tanto, investiga-se o ensino dos n?meros complexos, a partir das quest?es levantadas pelos alunos do Centro Federal de Educa??o Tecnol?gica do Rio Grande do Norte, em Natal. O trabalho tem como objetivos: classificar e analisar os questionamentos dos alunos nas aulas de n?meros complexos, da segunda s?rie do Ensino M?dio, e confront?-los com as categorias apontadas por Jones; discutir quais os poss?veis encaminhamentos que o professor de Matem?tica pode dar a estas quest?es; apresentar os recursos de apoio ao professor no que se refere ? Hist?ria da Matem?tica. Em seguida, apresenta uma pesquisa bibliogr?fica, buscando revelar material de apoio ao professor, com conte?dos que articulassem o Ensino da Matem?tica com a Hist?ria da Matem?tica. Descobrimos que os questionamentos dos alunos referem-se mais aos porqu?s pedag?gicos e que os livros did?ticos pouco contemplam outros aspectos da hist?ria e pouco dizem sobre o surgimento e a evolu??o dos m?todos de c?lculos utilizados por n?s

Made available in DSpace on 2014-12-17T15:04:51Z (GMT). No. of bitstreams: 1 RobsonOS.pdf: 527706 bytes, checksum: 215f631ef1e4979b7dcc88ec12d7b013 (MD5) Previous issue date: 2008-02-25 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The aim of the present work is to contribute to the teaching-learning process in Mathematics through an alternative which tries to motivate the student so that he/she will learn the basic concepts of Complex Numbers and realize that they are not pointless. Therefore, this work s general objective is to construct a didactic sequence which contains structured activities that intends to build up, in each student s thought, the concept of Complex Numbers. The didactic sequence is initially based on a review of the main historical aspects which begot the construction of those numbers. Based on these aspects, and the theories of Richard Skemp, was elaborated a sequence of structured activities linked with Maths history, having the solution of quadratic equations as a main starting point. This should make learning more accessible, because this concept permeates the students previous work and, thus, they should be more familiar with it. The methodological intervention began with the application of that sequence of activities with grade students in public schools who did not yet know the concept of Complex Numbers. It was performed in three phases: a draft study, a draft study II and the final study. Each phase was applied in a different institution, where the classes were randomly divided into groups and each group would discuss and write down the concepts they had developed about Complex Numbers. We also use of another instrument of analysis which consisted of a recorded interview of a semi-structured type, trying to find out the ways the students thought in order to construct their own concepts, i.e. the solutions of the previous activity. Their ideas about Complex Numbers were categorized according to their similarities and then analyzed. The results of the analysis show that the concepts constructed by the students were pertinent and that they complemented each other this supports the conclusion that the use of structured activities is an efficient alternative for the teaching of mathematics / O presente estudo visa apresentar uma contribui??o para o processo de ensino-aprendizagem em matem?tica atrav?s de uma alternativa que se prop?e a trazer uma nova motiva??o ao aluno para que este adquira as primeiras id?ias relacionadas ao conceito de n?meros complexos percebendo que estes n?o s?o destitu?dos de sentido. Para tanto, o estudo tem como objetivo geral a constru??o de uma seq??ncia did?tica contendo atividades estruturadas, visando a forma??o dessas id?ias importantes para aquisi??o do conceito pelo aluno. O estudo baseia-se inicialmente em um resgate dos principais aspectos hist?ricos que deram origem ? constru??o desses n?meros. Diante desses aspectos, buscamos nos fundamentar em Richard Skemp na elabora??o de uma seq??ncia de atividades estruturadas onde incorporaremos a hist?ria da matem?tica e tendo como ponto de partida a resolu??o de equa??es quadr?ticas, entendendo que, dessa forma, estar?amos tornando a aprendizagem mais acess?vel, uma vez que esse conceito permeia as s?ries anteriores e, consequentemente, os alunos deveriam estar mais familiarizados a ele. A interven??o metodol?gica iniciou-se com a aplica??o dessa seq??ncia de atividades com alunos de terceiros anos do ensino m?dio de escolas p?blicas que ainda n?o conheciam o conceito de n?meros complexos e foi realizada em tr?s etapas que denominamos: estudo piloto I, estudo piloto II e estudo definitivo, cada uma delas em uma institui??o diferente; as turmas foram divididas aleatoriamente em grupos onde cada grupo escreveria as id?ias que haviam desenvolvido acerca dos n?meros complexos. Isso precedeu o uso de um outro instrumento de an?lise que se trata de uma entrevista gravada do tipo semiestruturada com o objetivo de apurar os caminhos tra?ados pelos alunos durante a resolu??o das atividades desenvolvidas. As id?ias adquiridas foram categorizadas por similaridades e, em seguida, analisadas. Os resultados das an?lises nos mostram que as id?ias formadas foram pertinentes, se completam entre si e fomentam a discuss?o de que o uso de atividades estruturadas com esse fim ? uma alternativa eficiente e poss?vel de ser aplicada, mesmo em realidades escolares mais desfavorecidas

Die Verwendung von Mathcad an der TU Chemnitz hat sich sowohl im Bereich der Forschung und Entwicklung als auch der Lehre und Bearbeitung studentischer Projekte etabliert. Im Rahmen dieser Entwicklung ist das Expertenwissen entstanden, Lehrveranstaltungen zur gezielten Nutzung von Mathcad bei der Lösung technischer Berechnungsprobleme zu halten. Der erste Teil des Vortrags stellt Bemühungen zur Einführung dieser Software bereits in der Sekundarstufe II des Gymnasiums Einsiedel Chemnitz vor. Im zweiten Teil des Vortrags wird die intuitive Verwendung von Mathcad auch bei aufwendigeren Berechnungen an Beispielen der Getriebekinematik gezeigt. Mittels der Exponentialschreibweise werden eine Kurbelschwinge und ein Roboterarm beschrieben.

Η παρούσα διδακτορική διατριβή αποτελεί μια συμβολή στην ανάλυση του ηλεκτρικού πεδίου στο περιβάλλον εναέριων γραμμών απλού και διπλού κυκλώματος. Αναπτύσσονται αναλυτικές σχέσεις για τον ακριβή υπολογισμό της έντασης του ηλεκτρικού πεδίου καθώς και απλούστερες προσεγγιστικές σχέσεις. Η προτεινόμενη μέθοδος υπολογισμού προέκυψε από τον συνδυασμό της ανάλυσης των φορτίων των αγωγών σε συμμετρικές συνιστώσες, της περιγραφής της έντασης του ηλεκτρικού πεδίου με διπλούς μιγαδικούς αριθμούς και της χρήσης του αναπτύγματος πολυπόλων για την έκφραση της έντασης του ηλεκτρικού πεδίου. Με τους διπλούς μιγαδικούς αριθμούς επιτυγχάνεται η παράσταση με μιγαδικούς αριθμούς τόσο των χρονικά ημιτονοειδώς μεταβαλλόμενων μεγεθών (τάσεων και φορτίων) όσο και των γεωμετρικών αποστάσεων. Το ανάπτυγμα πολυπόλων είναι μια σειρά απείρων όρων, όπου ο κάθε επόμενος όρος είναι αντιστρόφως ανάλογος της αυξανόμενης δύναμης της απόστασης. Αναπτύσσονται επίσης ακριβείς αναλυτικές σχέσεις, καθώς και απλούστερες προσεγγιστικές σχέσεις, για τον υπολογισμό της μαγνητικής επαγωγής γραμμών διπλού κυκλώματος. Για την ανάπτυξη των σχέσεων αυτών συνδυάζεται η χρήση των διπλών μιγαδικών αριθμών με το ανάπτυγμα πολυπόλων για την έκφραση της μαγνητικής επαγωγής. / This thesis is a contribution to the analysis of the electric field in the vicinity of single-circuit and double-circuit overhead power lines. Analytical formulas are developed for the accurate calculation of the intensity of the electric field as well as simpler approximate formulas. The proposed calculation method has arisen from the combination of the analysis of the conductors’ charges in their symmetrical components, the description of the intensity of the electric field using double complex numbers and the use of multipole expansions to express the intensity of the electric field. The use of double complex numbers allows the simultaneous representation of sinusoidal varying quantities (voltages and charges) and geometrical distances with complex numbers. The multipole expansion is a series of infinite terms, where each term is inversely proportional to an increasing power of the distance. Accurate analytical formulas are also developed as well as simpler approximate formulas for the calculation of the magnetic flux density produced by double-circuit lines. For the development of those formulas the use of double complex numbers is combined with the multipole expansion to express the magnetic flux density.

Orientador: Maria Cristina Dias Tavares / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e Computação / Made available in DSpace on 2018-08-07T13:37:43Z (GMT). No. of bitstreams: 1 Paz_MarcosdeAraujo_D.pdf: 6127820 bytes, checksum: 21f6dc485bcf097846769f086c2362ad (MD5) Previous issue date: 2005 / Resumo: O objetivo deste trabalho é contribuir para o estudo de linhas de transmissão e o desenvolvimento de modelos de linhas voltados a programas do tipo EMTP. O trabalho desenvolvido consiste em aproveitar as propriedades e semelhanças dos modos não homopolares de propagação das linhas de transmissão, sejam elas idealmente transpostas ou que apresentem plano de simetria vertical. Por meio de manipulações da matriz de transformação fase-modo-fase através do uso de vetores ortogonais e elementos complexos no domínio modal, pode-se reduzir a dimensão dos vetores de estado. O procedimento proposto é direcionado às modelagens que utilizam transformação fase-modo-fase na determinação das variáveis de estado (corrente e tensão) nas linhas de transmissão. Os recursos usados levam a uma redução tanto em número de operações por iteração quanto em alocação de estados, otimizando o procedimento de cá1culo e aumentando a velocidade de simulação no processamento. A economia computacional que o procedimento proposto proporciona pode ser usada em ferramentas de simulação em tempo real / Abstract: The research objective is to contribute with the study of the transmission line and the development of line models in EMTP-type programs. The proposed model takes advantage of some similarities between non homopolar modes, applying orthogonal vectors and complex number theory to manipulate the state vectors in modal domain reducing the state vectors dimension. The proposed procedure is aimed to the modelling that use phase-mode-phase transformation in the determination of state variables (current and voltage) in transmission lines. The resources used lead to a reduction both in the number of operations per iteration and state allocation, optimizing the procedure and increasing the processing simulation speed. The computational economy, which the proposed procedure provide, can be applied to real-time simulation tools / Doutorado / Energia Eletrica / Doutor em Engenharia Elétrica

In this thesis I present new insights into aspects of Peter Guthrie Tait's life and work, derived principally from largely-unexplored primary source material: Tait's scrapbook, the Tait–Maxwell school-book and Tait's pocket notebook. By way of associated historical insights, I also come to discuss the innovative and far-reaching mathematics of the elusive Frenchman, C.-V. Mourey. P. G. Tait (1831–1901) F.R.S.E., Professor of Mathematics at the Queen's College, Belfast (1854–1860) and of Natural Philosophy at the University of Edinburgh (1860–1901), was one of the leading physicists and mathematicians in Europe in the nineteenth century. His expertise encompassed the breadth of physical science and mathematics. However, since the nineteenth century he has been unfortunately overlooked—overshadowed, perhaps, by the brilliance of his personal friends, James Clerk Maxwell (1831–1879), Sir William Rowan Hamilton (1805–1865) and William Thomson (1824–1907), later Lord Kelvin. Here I present the results of extensive research into the Tait family history. I explore the spiritual aspect of Tait's life in connection with The Unseen Universe (1875) which Tait co-authored with Balfour Stewart (1828–1887). I also reveal Tait's surprising involvement in statistics and give an account of his introduction to complex numbers, as a schoolboy at the Edinburgh Academy. A highlight of the thesis is a re-evaluation of C.-V. Mourey's 1828 work, La Vraie Théorie des quantités négatives et des quantités prétendues imaginaires, which I consider from the perspective of algebraic reform. The thesis also contains: (i) a transcription of an unpublished paper by Hamilton on the fundamental theorem of algebra which was inspired by Mourey and (ii) new biographical information on Mourey.