published_or_final_version / Mathematics / Master / Master of Philosophy

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Thesis (Ph. D.)--University of Michigan, 1936. / "Lithoprinted." Bibliography: p. 119-135: "Sources of information concerning works included in the bibliography": p. 2; bibliographical foot-notes.

Thesis (Ph. D.)--Missouri University of Science and Technology, 2009. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed August 31, 2009) Includes bibliographical references (p. 146-149).

Thesis (Ph. D.)--University of Michigan, 1936. / "Lithoprinted." Bibliography: p. 119-135: "Sources of information concerning works included in the bibliography": p. 2; bibliographical foot-notes.

We present an abstract framework for state space formulation and a generalized theorem on well-posedness which can be applied to a class of partial functional differential equations which arise in the modeling of viscoelastic and certain thermo-viscoelastic systems. Examples to which the theory applies include both second- and fourth-order equations with a variety of boundary conditions. The theory presented here allows for singular kernels as well as flexibility in the choice of state space. We discuss an approximation scheme using spline in the spatial variable and an averaging scheme in the delay variable. We compare a uniform mesh to a nonuniform mesh and give numerical results which indicate that the non-uniform mesh, which gives a better approximation of the kernel near the singularity, yields faster convergence. We give a proof of convergence of the simulation problem for singular kernels and of the control problem for bounded kernels. We use techniques of semigroup theory to establish the results on well-posedness and convergence. / Ph. D.

Orientador: Lourdes de la Rosa Onuchic / Banca: Miriam Godoy Penteado / Banca: Regina M.S.P. Tancredi / Resumo: O objetivo desta pesquisa é o de analisar o ensino-aprendizagem de equações polinomiais do 2º grau. Para esta pesquisa adotamos a Metodologia de Pesquisa de Romberg. Definido o Fenômeno de Interesse, o Ensino-Aprendizagem de Equações Polinomiais do 2º grau, foi criado um Modelo Preliminar e apoiado em ideias de outros sobre os eixos norteadores do desenvolvimento da pesquisa: a Álgebra Escolar, a Produção de Significados e a Resolução de Problemas, nos conduziram à seguinte questão Quais os significados produzidos, pelos alunos, no processo de ensino-aprendizagem-avaliação de equações polinomiais do 2º grau? Para resolver esse problema, estratégias (o quê?) e procedimentos (como?) foram criados gerando o Procedimento Geral - a criação de um projeto de ensino-aprendizagemavaliação para trabalhar as equações polinomiais de 2º grau. Esse Procedimento Geral foi posto em ação, em sala de aula, fazendo uso da Metodologia de Ensino-Aprendizagem- Avaliação de Matemática através da Resolução de Problemas, na qual os alunos devem ser co-construtores de seu próprio conhecimento durante o processo da resolução do problema proposto, levando-os à construção de novos conceitos, conteúdos e técnicas operatórias matemáticos. Para a coleta de dados utilizamos algumas técnicas: observação participante, seguida de registros (notas de campo, registros de trabalhos de alunos em diferentes momentos e vídeos de algumas aulas). A análise da produção de significados dos alunos foi realizada a partir das atividades trabalhadas em sala de aula. Esta análise apresentou uma abordagem qualitativa que nos possibilitou múltiplas interpretações dos dados coletados segundo nossas crenças, experiências e concepções / Abstract: The aim of this research is to analyze the processes involved on the teaching and learning of 2nd grade polynomial equations. To pursue this objective, we adopted Romberg's Research Methodology. Once the Phenomenon of Interest was defined, the Teaching-Learning of 2nd grade Polynomial Equations, we developed a Preliminary Model and, based on ideas from others about the main aspects related with this research: Elementary Algebra, the Production of Meanings and the Problem Solving, we were conducted to the question What are the meanings produced by students in the teaching-learning-assessment process of 2nd grade polynomial equations? To solve this problem, strategies (what?) and procedures (how?) were created generating the General Procedure - the creation of a project of teaching-learning-assessment to work with 2nd grade polynomial equations . This General Procedure was put into action, in the classroom, using the Methodology of Teaching-Learning-Assessment of Mathematics through Problem Solving, in which students must be co-constructors of their own knowledge during the resolution process of the proposed problem, guiding them in the construction of new concepts, mathematical subjects and techniques. To collect data we used some techniques: participant observation, followed by records (field notes, records of students work at different times and videos of some classes). The analysis of the meanings production of students was held from the activities worked on in the classroom. This analysis produced a qualitative approach that allowed us multiple interpretations of the data collected according to our beliefs, experiences and ideas / Mestre

published_or_final_version / Education / Master / Master of Education

Made available in DSpace on 2014-06-11T19:24:52Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-11-17Bitstream added on 2014-06-13T20:52:42Z : No. of bitstreams: 1 puti_tc_me_rcla.pdf: 1308914 bytes, checksum: f8b18c88c3d90dd27e02db6a5bc88658 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo desta pesquisa é o de analisar o ensino-aprendizagem de equações polinomiais do 2º grau. Para esta pesquisa adotamos a Metodologia de Pesquisa de Romberg. Definido o Fenômeno de Interesse, o Ensino-Aprendizagem de Equações Polinomiais do 2º grau, foi criado um Modelo Preliminar e apoiado em ideias de outros sobre os eixos norteadores do desenvolvimento da pesquisa: a Álgebra Escolar, a Produção de Significados e a Resolução de Problemas, nos conduziram à seguinte questão Quais os significados produzidos, pelos alunos, no processo de ensino-aprendizagem-avaliação de equações polinomiais do 2º grau? Para resolver esse problema, estratégias (o quê?) e procedimentos (como?) foram criados gerando o Procedimento Geral – a criação de um projeto de ensino-aprendizagemavaliação para trabalhar as equações polinomiais de 2º grau. Esse Procedimento Geral foi posto em ação, em sala de aula, fazendo uso da Metodologia de Ensino-Aprendizagem- Avaliação de Matemática através da Resolução de Problemas, na qual os alunos devem ser co-construtores de seu próprio conhecimento durante o processo da resolução do problema proposto, levando-os à construção de novos conceitos, conteúdos e técnicas operatórias matemáticos. Para a coleta de dados utilizamos algumas técnicas: observação participante, seguida de registros (notas de campo, registros de trabalhos de alunos em diferentes momentos e vídeos de algumas aulas). A análise da produção de significados dos alunos foi realizada a partir das atividades trabalhadas em sala de aula. Esta análise apresentou uma abordagem qualitativa que nos possibilitou múltiplas interpretações dos dados coletados segundo nossas crenças, experiências e concepções / The aim of this research is to analyze the processes involved on the teaching and learning of 2nd grade polynomial equations. To pursue this objective, we adopted Romberg’s Research Methodology. Once the Phenomenon of Interest was defined, the Teaching-Learning of 2nd grade Polynomial Equations, we developed a Preliminary Model and, based on ideas from others about the main aspects related with this research: Elementary Algebra, the Production of Meanings and the Problem Solving, we were conducted to the question What are the meanings produced by students in the teaching-learning-assessment process of 2nd grade polynomial equations? To solve this problem, strategies (what?) and procedures (how?) were created generating the General Procedure – the creation of a project of teaching-learning-assessment to work with 2nd grade polynomial equations . This General Procedure was put into action, in the classroom, using the Methodology of Teaching-Learning-Assessment of Mathematics through Problem Solving, in which students must be co-constructors of their own knowledge during the resolution process of the proposed problem, guiding them in the construction of new concepts, mathematical subjects and techniques. To collect data we used some techniques: participant observation, followed by records (field notes, records of students work at different times and videos of some classes). The analysis of the meanings production of students was held from the activities worked on in the classroom. This analysis produced a qualitative approach that allowed us multiple interpretations of the data collected according to our beliefs, experiences and ideas

This study investigates wave propagation in an elastic half-space with quadratic nonlinearity due to a line load on the surface. The consideration of this problem is one of the well known Lamb problems. Even since Lamb's original solution, numerous investigators have obtained solutions to many different variants of the Lamb problem. However, most of the solutions existing in the current literature are limited to wave propagation in a linear elastic half-space. In this work, the Lamb problem in an elastic half-space with quadratic nonlinearity is considered. For this, the problem is first formulated as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. The accuracy of the numerical method is first studied by comparing the numerical solution with the analytical solution for a half-space with linear response (the original Lamb's problem). The numerical results for the half-space with quadratic nonlinearity are than studied using signal-processing tools such as the fast Fourier transform (FFT) in order to analyze and interpret any nonlinear effects. This in particular gives the possibility to evaluate the excitation of higher order harmonics whose amplitude is used to infer material properties. To quantify and compare the nonlinearity of different materials, two parameters are introduced; these parameters are similar to the acoustical nonlinearity parameter for plane waves.