Orientador: Renata Zotin Gomes de Oliveira / Banca: Sidineia Barrozo / Banca: Marta Cilene Gadotti / Resumo: Este trabalho tem como objetivo principal apresentar uma sugestão de como calcular áreas delimitadas por grá cos de funções para estudantes de Ensino Médio, utilizando o software Geogebra. Serão apresentadas atividades que exempli cam o desenvolvimento da proposta, que vao além do que, normalmente, os livros didáticos sugerem / Abstract: This work has as main objective to present a suggestion how to calculate areas bounded by graphs of functions to High School students, using the Geogebra software. It will be present activities to exemplify the development of the proposal, that go beyond what normally textbooks suggest / Mestre

Orientador: Wilson Massashiro Yonezawa / Banca: Patrícia Sandalo Pereira / Banca: João Coelho Neto / Banca: Luiz Antonio da Silva Vasconcellos / Banca: Andrea Carla Gonçalves Vianna / Resumo: O intuito desta pesquisa é investigar as formas que a disciplina de Cálculo Diferencial e Integral 1 na modalidade educação a distância (EaD) semipresencial pode auxiliar alunos em regime de dependência. Esta disciplina nos cursos de Engenharia é um ramo importante da matemática, porém com alta taxa de evasão. Em algumas universidades, chega a 55% dos ingressantes. Uma das ações realizada em uma Universidade Federal brasileira para flexibilizar a vida dos alunos que ficam em dependência nesta disciplina é sua oferta na modalidade EaD semipresencial. A execução do projeto, bem como a realização desta pesquisa só foi possível porque a legislação brasileira permite que os cursos superiores presenciais tenham até 20% de sua carga horária total na modalidade de educação a distância. Na fundamentação teórica abordamos as pesquisas sobre os problemas no ensino de Cálculo Diferencial e Integral 1, a educação a distância e suas possibilidades, as tecnologias na educação a distância, os ambientes virtuais de ensino e aprendizagem; o perfil esperado para os alunos da EaD e a aprendizagem colaborativa. A Análise Textual Discursiva foi a opção metodológica e apresentamos uma nova possibilidade de utilizar esta metodologia associada ao Software de análise qualitativa ATLAS.ti ®. Os resultados obtidos nesta pesquisa dão indícios de que os seus participantes se beneficiaram com esta proposta de utilizar as contribuições e as características da Modalidade EaD semipresencial, bem como os recur... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The purpose of this research is to investigate the forms that the subject of Differential and Integral Calculus 1 in the blended distance education modality can help students in a dependency regime. in Engineering courses such a subject in an important branch of mathematics, but with a high dropout rate. In some universities, it reaches 55% of the students. One of the actions which has been carried out in a Brazilian Federal University to make life flexible for the students who are dependent on the subject is its offering in the blended distance education modality. The execution of the project, as well as the realization of this research, was only possible because the Brazilian law allows the upper-level courses to have up to 20% of their total workload in the distance education modality. For the theoretical basis it was approached the researches on the problems in the teaching of Differential and Integral the researches on the problems in the teaching of Differential and Integral Calculus 1, the distance education and its possibilities, the technologies in the distance education, the virtual environments of teaching and learning, the expected profile for EaD (Distance Education) students and collaborative learning. The discursive textual analysis was the methodological option and it was presented a new possibility to use such a methodology associated to the qualitative analysis software ATLAD.ti. The results obtained in this research indicate that its participants have been benefited from the proposal to use the contributions and characteristics of the blended distance education modality, as well as the technological resources that have been available or aggregated by the students themselves. Furthermore, communicability as well as the sharing were of a great importance since the collaborative learning became one of the strong factors: In conclusion, it was emphasized that the... (Complete abstract electronic access below) / Doutor

Esta tese estuda a geometria de problemas variacionais através da linearização e projetivização das suas equações de Euler - Lagrange. O processo de linearização fornece a passagem das equações de Euler - Lagrange para as equações de Jacobi; a minimalidade (local) de extremais está determinada pelo conceito de ponto conjugado, que tem natureza projetiva. Propriedades de minimalidade local são transformadas em propriedades de auto-interseção de uma curva na variedade de Grassmann adequada. Desenvolvemos este processo em duas aplicações: 1) O estudo da minimalidade local de extremais de problemas variacionais de ordem superior. Neste caso, encontramos uma curva não degenerada de planos isotrópicos num espaço vetorial simplético, que, após prolongamento por derivadas, fornece uma curva degenerada de planos Lagrangeanos cujas auto-interseções determinam a minimalidade. 2) No caso mais clássico de problemas de ordem um, estudamos a versão linear - projetiva do problema inverso: dada uma equação diferencial de ordem dois, quando ela é a equação de Euler - Lagrange de um problema variacional? Veremos que as condições do problema inverso linear - projetivo fornecem informações sobre os possíveis Lagrangianos, por exemplo a assinatura. / In this work we study the geometry of high order calculus of variations through the linearization and projectivization of their Euler Lagrange equations. The linearization process provides the passage from the Euler Lagrange equations to the Jacobi equations; the (local) minimality properties of the extremal is determined by conjugate points, which is a projective concept. Minimaltiy properties of the extremals are transformed into self-intersection propertie of curves in the appropriate Grassmann manifold. We develop this process in two instances: 1) The study of minimality properties of extremals of higher-order variational problems. In this case, we find a non-degenerate curve of isotropic subspaces, that, after prolongation by derivatives, gives a degenerate curve of Lagrangian planes whose self-intersections determine minimality. 2) In the classical case of order one variational problems, we study a projective-linear version of the inverse problem: given a second order differential equation, when is it the Euler-Lagrange equation of a variational problem? We will see that the conditions given by the linear projective inverse problem provides information about the possible Lagrangians, for example, its signature.

O método das matrizes operacionais é expandido para o corpo complexo a ordens arbitrárias pela abordagem de Riemann-Liouville e Caputo com ênfase nas séries de Fourier complexas. Elabora-se uma adaptação do formalismo bra-ket de Dirac à linguagem tensorial no espaço de Hilbert de funções com expansões finitas para uso específico na teoria de equações diferenciais e matrizes operacionais, denominado \\Formalismo Coadjunto\". Estende-se o tratamento aos operadores fracionais de Weyl para períodos genéricos a fim de determinar as matrizes operacionais de derivação e integração de ordem arbitrária na base complexa de Fourier. Introduz-se um novo método de resolução de equações diferenciais ordinárias lineares e fracionais não-homogêneas, denominado \\Modelagem Operacional\", que permite a obtenção de soluções de equações de alta ordem com grande precisão sem a necessidade de imposição de condições iniciais ou de contorno. O método apresentado é aperfeiçoado por meio de um novo tipo de expansão, que denominamos \"Séries Associadas de Fourier\", a qual apresenta convergência mais rápida que a série de Fourier original numa restrição de domínio, possibilitando soluções de EDOs e EDFs de alta ordem com maior precis~ao e ampliando a esfera de casos passíveis de resolução. / Operational matrices method is expanded to complex field and arbitrary orders by using the Riemann-Liouville and Caputo approach with emphasis on complex Fourier series. Dirac\'s bra-ket notation is associated to tensor procedures in Hilbert spaces for finite function expansions to be applied specifically to dfferential equations and operational matrices, being called \\Coadjoint Formalism\". This treatment is extended to Weyl fractional operators for generic periods in order to establish the integral and derivative operational matrices of fractional order to complex Fourier basis. A new method to solve linear non-homogeneous ODEs and FDEs, called \\Operational Modelling\"is introduced. It yields high precision solutions on high order dfferential equations without assumption of boundary or initial conditions. The presented method is improved by a new kind of function expansion, called \\Fourier Associated Series\", which yields a faster convergence than original Fourier in a restrict domain, enabling to obtain solutions of high order ODEs and FDEs with excellent precision and broadening the set of solvable equations.

O ponto central dessa dissertação é expor categorialmente as funções de verdade do cálculo proposicional clássico, assim como provar, também categorialmente, que a definição dada se comporta tal como as tabelas de verdade dos operadores. Para tanto é feita uma exposição axiomática de teoria de categorias, salientando as construções e conceitos que servirão para o propósito principal da dissertação. É dada uma maior atenção ao conceito de Topos, estrutura onde as funções de verdade são em princípio construídas. Tal exposição é precedida de uma breve exposição da história de teoria de categorias. Por fim é apresentada uma possível nova estrutra, mais simples que Topos, onde também se constrói as funções de verdade. / The main purpose of this dissertation is to give a categorial account of the truth functions from the classic propositional calculus, as well as to prove, also categorially, that the definition given behave as the truth tables of the operators. For this end, an axiomatic exposition of category theory is made, focusing on constructions and concepts which will be used for the main purpose of the dissertation. More attention is given to the concept of Topos, structure where the truth functions are primarily constructed. Preceded by a brief exposition of Category Theory history. At the end, a new possible structure in which truth functions may be constructed, simpler than a Topos, is presented.

Embora os indivíduos construtores dos sambaquis constituam o grupo pré-histórico brasileiro melhor estudado, várias questões continuam em aberto. Algumas delas estão ligadas a estratégias de subsistência. Sabe-se que a economia desses indivíduos era baseada na pesca e que a coleta de moluscos teria papel complementar na alimentação. Mas, atualmente, estudos antracológicos e de cálculo dentário vêm demonstrando a grande importância da utilização de plantas pelos sambaquieiros. Entretanto, pouco se conhece sobre as espécies consumidas e o modo de preparo dos alimentos. O sambaqui Jabuticabeira II, localizado na região sul de Santa Catarina, apresenta indícios da utilização de plantas que incluem: artefatos líticos que se acredita que tenham sido usados para raspar, moer e quebrar vegetais; sementes de famílias de plantas que produzem frutos comestíveis; coquinhos; e restos carbonizados de lenho de uma grande diversidade de espécies. Além disso, notou-se grande número e variedade de grãos de amido no cálculo dentário dos indivíduos sepultados nesse sambaqui, sugerindo que o consumo de vegetais ricos em amido teria sido grande. O presente estudo trata, portanto, da análise de 119 microvestígios vegetais de cálculo dentário de 19 adultos de Jabuticabeira II, objetivando avaliar se ocorria, de fato, um consumo de grande variedade de vegetais amiláceos, bem como identificar quais plantas foram consumidas. Para possibilitar tal identificação, foi iniciada a elaboração de uma coleção de referência de grãos de amido de plantas nativas da região. A partir dos resultados obtidos sugere-se que os sambaquieiros de Jabuticabeira II consumiam uma grande variedade de plantas ricas em amido. Embora o número de microrrestos vegetais variasse bastante entre os indivíduos, aparentemente, não ocorria diferença quanto a dieta vegetal de acordo com sexo, classe etária ou lócus de enterramento. A presença de diatomáceas de ambientes de água salobra indicam que os recursos faunísticos consumidos eram obtidos a partir da paleolaguna. Eram consumidos órgãos de reserva subterrâneos de aráceas (inhames), Dioscorea sp. (carás), Calathea SP. (ariá) e Ipomoea batatas (batata-doce) e, possivelmente, frutos das famílias Myrtaceae (incluindo Eugenia uniflora - pitanga) e Arecaceae (palmeiras). Acredita-se que o milho (Zea mays) também fazia parte da dieta, embora não tenha sido possível discernir se era cultivado nesse sitio, ou se foi obtido através de troca com grupos cultivadores de outras regiões. Ainda que fitólitos de gramíneas possam ter sido acidentalmente incorporados ao cálculo dentário dos indivíduos de Jabuticabeira II, sugere-se que algumas gramíneas poderiam ter sido utilizadas, não somente como alimento, mas também com fins medicinais ou de higiene oral. O alimento de origem vegetal parece ter sido processado através de moagem ou maceração, assado em brasas ou cinzas ou, ainda, preparado em fornos escavados. As evidências obtidas neste trabalho não apontam para o cultivo intensivo das plantas que eram utilizadas na dieta desse grupo, mas não corroboram, nem descartam a hipótese de que o manejo ou horticultura de alguns taxa florísticos importantes tenha ocorrido / The sambaqui (shellmound) builders are the best studied ancient human group from Brazil. However, much has still to be discovered about them. It is very well known that their subsistence was based on fishing and that molluscs\' gathering was a complement to their diet. Recently, anthracology and dental calculus studies have shown the importance of plants, but very little is known about the species eaten and the processes that were used for food preparation. The Jabuticabeira II sambaqui, located in southern Santa Catarina, shows evidences of plant use that include: lithic artifacts related to food processing; seeds from plant families that produce edible fruits; palm nuts; and remains from carbonized wood from a variety of species. Besides that, a high number and variety of starch grains were recovered from the dental calculus of some skeletons, suggesting that the consumption of starchy plants was important. For the present study, plant microfossils (n=119) recovered from the dental calculus from 19 adults exhumed from Jabuticabeira II shellmound were analysed, in order to identify the species consumed and to test if, in fact, their diet consisted of a high variety of starchy plants. To allow identification, the construction of a starch reference collection from plants from the studied region was initiated. The results suggest that the individuals buried at Jabuticabeira II indeed ate a high variety of starchy plants. Despite the inter- individual variation in the number of microfossils, there seems to be no difference in the plant intake according to sex, age class and burial site. The diatoms from brackish water that were also found indicate that the faunal resources consumed were obtained from the paleolagoon nearby. Underground storage organs from the Araceae family (arum family), Dioscorea sp. (yams), Calathea sp. (llerén), Ipomoea batatas (sweet potato), and possibly fruits from the Myrtaceae family, including Eugenia uniflora (pitanga), and Arecaceae family (palm trees) were eaten. Although corn starch (Zea mays) grains were also identified, it is not yet clear if it was cultivated in Jabuticabeira II, or if it was obtained through exchange with cultivators from other sites. The grass leaf phytoliths that were also recovered suggest that plants from the Poaceae family could have been used as medicine or for oral hygiene. Plant food seems to have been processed through grinding, toasting in ashes, and maybe in underground ovens. Finally, there is no evidence that suggests that plants were cultivated in Jabuticabeira II, but the management of some botanical taxa cannot be excluded

by Chan Kwan Leung. / Parallel title in Chinese characters. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 168-169). / by Chan Kwan Leung. / Acknowledgement --- p.i / Abstract --- p.ii / Chapter 1. --- Introduction / Chapter 1.1 --- Objective of our variational method --- p.2 / Chapter 1.2 --- Outline of the content --- p.5 / Chapter 2. --- Formulation of the new variational method / Chapter 2.1 --- Formulation --- p.14 / Chapter 2.2 --- Motivation --- p.15 / Chapter 3. --- The variational method applied to the anharmonic oscillator problem / Chapter 3.1 --- Formalism --- p.18 / Chapter 3.2 --- Relationship with usual variational method --- p.32 / Chapter 3.3 --- Relationship with W.K.B. approximation --- p.37 / Chapter 3.4 --- Perturbative corrections --- p.45 / Chapter 3.5 --- Diagonalization of non-orthogonal basis --- p.57 / Chapter 3.6 --- Perturbative corrections using the non-orthogonal basis --- p.72 / Chapter 3.7 --- Some previous works on the anharmonic oscillator problem --- p.85 / Chapter 4. --- The variational method applied to the helium-like atomic problem / Chapter 4.1 --- Previous work on the problem --- p.90 / Chapter 4.2 --- Formulation of the variational method on the problem --- p.95 / Chapter 4.3 --- Zeroth order results for atomic helium --- p.103 / Chapter 4.4 --- Diagonalization using the non-orthogonal basis --- p.109 / Chapter 4.5 --- Results for some helium-like ions --- p.136 / Chapter 4.6 --- Possibility of generalization to systems with more electrons --- p.140 / Chapter 5 --- Concluding remarks / Chapter 5.1 --- Range of applicability of our variational method --- p.164 / Chapter 5.2 --- Ground state problem --- p.165 / Chapter 5.3 --- Completeness of our 'basis' --- p.166 / References --- p.168

Exact solutions to the Einstein field equations are notoriously difficult to find. Most known solutions describe systems with unrealistically high degrees of symmetry. A notable example is the FLRW metric underlying modern cosmology: the universe is assumed to be perfectly homogeneous and isotropic, but in the late universe, this is only true on average and only at large scales. Where an exact solution is not available, discrete gravitational approaches can approximate the system instead. This thesis investigates several cosmological systems using two distinct discrete approaches. Closed, flat, and open ‘lattice universes’ are first considered where matter is distributed as a regular lattice of identical point masses in constant-time hypersurfaces. Lindquist and Wheeler’s Schwarzschild–cell method is applied where the lattice cell around each mass is approximated by a perfectly spherical cell with Schwarzschild space–time inside. The resulting dynamics and cosmological redshifts closely resemble those of the dust-filled FLRW universes, but with certain differences in redshift behaviour attributable to the lattice universe’s lumpiness. The application of Regge calculus to cosmology is considered next. We focus exclusively on the closed models developed by Collins, Williams, and Brewin. Their approach is first applied to a universe where an exact solution is already well-established, the vacuum Λ-FLRW model. The resulting models are found to closely reproduce the dynamics of the continuum model being approximated, though certain constraints on the applicability of the approach are also uncovered. Then using this knowledge, we next model the closed lattice universe. The resulting evolution closely resembles that of the closed dust-filled FLRW universe. Constraints on the placement of the masses in the Regge skeleton are also uncovered. Finally, a ‘lattice universe’ with one perturbed mass is modelled. The evolution is still stable and similar to that of the unperturbed model. The thesis concludes by discussing possible extensions of our work.

Li, Ming Hin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 42-46). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Inference for Fractional Cointegration --- p.5 / Chapter 2.1 --- Concept of Fractional Cointegration --- p.5 / Chapter 2.1.1 --- Fractional Integration --- p.5 / Chapter 2.1.2 --- Fractional Cointegration --- p.8 / Chapter 2.2 --- Fractional Cointegration Modeling --- p.9 / Chapter 2.2.1 --- Engle-Granger's Methodology --- p.9 / Chapter 2.2.2 --- Johansen's Methodology --- p.10 / Chapter 2.2.2.1 --- Maximum Likelihood Estimators --- p.12 / Chapter 2.2.2.2 --- Cofractional Rank Test --- p.16 / Chapter 3 --- Pairs Trading Strategy --- p.19 / Chapter 3.1 --- Statistical Arbitrage --- p.19 / Chapter 3.2 --- Fractional Cointegration Pairs Trading --- p.20 / Chapter 3.2.1 --- Trading Procedures --- p.22 / Chapter 4 --- Empirical Study --- p.27 / Chapter 4.1 --- Backgrounds --- p.27 / Chapter 4.2 --- Settings --- p.28 / Chapter 4.3 --- Empirical Results --- p.29 / Chapter 5 --- Conclusions and Further Research --- p.39 / Bibliography --- p.42

Made available in DSpace on 2016-04-27T16:57:35Z (GMT). No. of bitstreams: 1 Wagner Marini.pdf: 979138 bytes, checksum: f3882bd2078421c09e44be2c9f6d6645 (MD5) Previous issue date: 2015-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The objective of this dissertation is to carry out a study focused on the research of Teaching and Learning of Calculus in Exact initial courses, produced in Brazil from 2003 to 2013. This study involves survey, categorization, and synthesis of the results and it was organized through a Panorama that includes dissertations, theses and articles focused on this theme. Methodological procedures that lead to the analysis of the collected material are those appropriate to qualitative research theorist related to state of the art. The analysis of the work constituents of Panorama aimed to highlight the relationship between the theories of sustaining, methodologies adopted and philosophical conceptions with the approach and development of work itself, having as reference, especially what is indicated by the English (2010). Furthermore, the analysis guided by the quest to answer the four questions drawn up for this purpose, has allowed the observation that there is a diversity of theories used as support of the work and a profusion of outcomes that allow the desirable bridge between the theory and the practice of Teaching and Learning the Differential and Integral Calculus. Results are highlighted based on the need of the area to establish consensus / O objetivo desta dissertação é o de realizar um estudo focado nas pesquisas, sobre o Ensino e de Aprendizagem do Cálculo em cursos iniciais de Exatas, produzidas no Brasil no período de 2003 e 2013. Esse estudo envolve levantamento, categorização e síntese dos resultados e foi organizado por meio de um Panorama que inclui dissertações teses e artigos com foco nesse tema. Os procedimentos metodológicos que conduzem a análise do material coletado são aqueles adequados às pesquisas qualitativas teóricas assemelhadas ao estado da arte. A análise dos trabalhos constituintes do Panorama visou destacar a relação das teorias de sustentação, das metodologias adotadas e das concepções filosóficas, com a abordagem e desenvolvimento dos trabalhos propriamente dito, tendo como referência, especialmente o que é indicado por English (2010). Além disso, a análise, norteada pela busca de respostas a quatro perguntas elaboradas para esse fim, permitiu a constatação de que há uma diversidade de teorias utilizadas como sustentação desses trabalhos e uma profusão de resultados que fazem a ponte desejável entre a teoria e a prática do Ensino e Aprendizagem do Cálculo Diferencial e Integral. Resultados são destacados atendendo a necessidade da área no estabelecimento de consensos