An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Relatório de estágio de qualificação profissional (fase intercalar do estágio)

No âmbito do Mestrado em Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico e da Prática Pedagógica Supervisionada, realizada em contexto de Creche, foi desenvolvido o presente relatório de estágio de qualificação profissional na Educação Pré-Escolar. A prática educativa sustentou-se num quadro teórico-concetual de referência, com vista à construção de saberes para a Educação de Infância, pelo compromisso e responsabilização progressiva da ação docente, tendo sido encarado como um momento de singular importância. Desta forma, este documento procura ilustrar o processo de desenvolvimento de competências profissionais pela estudante para este nível de educação. Nesta linha de pensamento, importa referenciar a metodologia de investigação-ação, que fundamentou a prática pedagógica da estudante ao longo das várias etapas do processo educativo: Observação, Planificação, Ação, Avaliação, Comunicação e Articulação. Assim, apoiada em estratégias e atitudes investigativas e reflexivas, esta metodologia potenciou a transformação, melhoria e adequação das suas práticas. O contexto de formação assumiu-se, portanto, como um lugar privilegiado de articulação entre teoria e prática, onde o processo de ensino e aprendizagem ficou pautado por intencionalidades educativas com vista ao desenvolvimento integral de cada criança, bem como pela construção de saberes e competências profissionais pela estagiária, elencadas nos Decretos-Lei n.º 240 e 241 de 2001. Tomando em consideração o processo desenvolvido, importa realçar a importância de uma formação profissional ao longo da vida, de modo a potenciar o desenvolvimento de uma atitude perante a Educação cada vez mais crítica, problematizadora, indagadora, reflexiva e investigativa, em prol do desenvolvimento holístico de cada criança.

Introducing numerical analysis tools in engineering: a Scilab user case in electronics course

Software tools in education became popular since the widespread of personal computers. Engineering courses lead the way in this development and these tools became almost a standard. Engineering graduates are familiar with numerical analysis tools but also with simulators (e.g. electronic circuits), computer assisted design tools and others, depending on the degree. One of the main problems with these tools is when and how to start use them so that they can be beneficial to students and not mere substitutes for potentially difficult calculations or design. In this paper a software tool to be used by first year students in electronics/electricity courses is presented. The growing acknowledgement and acceptance of open source software lead to the choice of an open source software tool – Scilab, which is a numerical analysis tool – to develop a toolbox. The toolbox was developed to be used as standalone or integrated in an e-learning platform. The e-learning platform used was Moodle. The first approach was to assess the mathematical skills necessary to solve all the problems related to electronics and electricity courses. Analysing the existing circuit simulators software tools, it is clear that even though they are very helpful by showing the end result they are not so effective in the process of the students studying and self learning since they show results but not intermediate steps which are crucial in problems that involve derivatives or integrals. Also, they are not very effective in obtaining graphical results that could be used to elaborate reports and for an overall better comprehension of the results. The developed tool was based on the numerical analysis software Scilab and is a toolbox that gives their users the opportunity to obtain the end results of a circuit analysis but also the expressions obtained when derivative and integrals calculations, plot signals, obtain vector diagrams, etc. The toolbox runs entirely in the Moodle web platform and provides the same results as the standalone application. The students can use the toolbox through the web platform (in computers where they don't have installation privileges) or in their personal computers by installing both the Scilab software and the toolbox. This approach was designed for first year students from all engineering degrees that have electronics/electricity courses in their curricula.

A Insolvência de Ambos os Cônjuges

Dissertação de Mestrado em Solicitaria