Comparação de sistemas de programação

Este trabalho compara as soluções disponibilizadas pelos sistemas Derive 5.0, Maple 6 e Mathematica 4.0 para problemas que encontramos no ensino secundário e também nos primeiros anos da universidade. Procuramos destacar os aspectos distintos entre cada um dos programas ao mesmo tempo que fazemos referência aos pontos em que tudo se passa de forma semelhante. Esta dissertação aborda o cálculo numérico, o cálculo simbólico, a programação e os gráficos. Para cada um dos assuntos é estudada a forma como se podem resolver os problemas através dos três sistemas comparando-se estas soluções. Inicialmente, é feita uma abordagem que permite ao utilizador adquirir os conhecimentos básicos acerca dos diversos programas. Tratamos de seguida de algumas questões relacionadas com o cálculo numérico e com algumas funções nomeadamente da Teoria dos Números. Referimos listas e funções e são analisadas diversas formas de manipular listas e os seus elementos bem como algumas áreas da Análise Matemática das quais destacamos as equações, a derivação e a integração compreendendo cálculo numérico e cálculo simbólico. Examinamos um vasto conjunto de operações definidas sobre matrizes (representadas como listas de listas) e polinómios que abrangem as operações mais comuns de cada um dos campos. Analisamos também a programação recursiva, a programação imperativa, a programação funcional e a programação por regras de reescrita. A abordagem aqui adoptada foi a de fornecer ao utilizador as construções chave mais importantes que cada paradigma de programação utiliza bem como as informações básicas acerca do funcionamento de cada uma delas de modo a permitir a resolução dos problemas propostos. Por último os gráficos sobre os quais incidiu a nossa análise foram os de uma e de duas variáveis representados no referencial cartesiano, gráficos estes que são os mais utilizados quer ao nível do ensino superior quer ao nível do ensino secundário. A qualidade e a facilidade de obter rapidamente as representações dão outra dimensão ao estudo dos gráficos principalmente quando estamos a falar de gráficos a três dimensões. A ideia de animação gráfica é também aqui abordada sendo evidente os benefícios da utilização da mesma nos programas em que é possível efectuá-la. Concluímos que na programação o Mathematica destaca-se em relação aos demais o mesmo se passando no Maple no respeitante à representação gráfica. O Derive permite que durante o contacto inicial seja mais fácil trabalhar e aprender a linguagem própria.

Some experiments with high order compact methods using a computer algebra software - Part I

We consider a procedure for obtaining a compact fourth order method to the steady 2D Navier-Stokes equations in the streamfunction formulation using the computer algebra system Maple. The resulting code is short and from it we obtain the Fortran program for the method. To test the procedure we have solved many cavity-type problems which include one with an analytical solution and the results are compared with results obtained by second order central differences to moderate Reynolds numbers. (c) 2005 Elsevier B.V. All rights reserved.

Some experiments with high order compact methods using a computer algebra software - Part II (non-uniform grid)

We generalize a procedure proposed by Mancera and Hunt [P.F.A. Mancera, R. Hunt, Some experiments with high order compact methods using a computer algebra software-Part 1, Appl. Math. Comput., in press, doi: 10.1016/j.amc.2005.05.015] for obtaining a compact fourth-order method to the steady 2D Navier-Stokes equations in the streamfunction formulation-vorticity using the computer algebra system Maple, which includes conformal mappings and non-uniform grids. To analyse the procedure we have solved a constricted stepped channel problem, where a fine grid is placed near the re-entrant corner by transformation of the independent variables. (c) 2006 Elsevier B.V. All rights reserved.

Bayesian approximations in randomized response model

Practical Bayesian inference depends upon detailed examination of posterior distribution. When the prior and likelihood are conjugate, this is easily carried out; however, in general, one must resort to numerical approximation. In this paper, our aim is to solve, using MAPLE, the Bayesian paradigm, for a very special data collecting procedure, known as the randomized-response technique. This allows researchers to obtain sensitive information while guaranteeing privacy to respondents. This approach intends to reduce false responses on sensitive questions. Exact methods and approximations will be compared from the accuracy point of view as well as for the computational effort.

Computational Aspects of the Calculation of Isometry Groups in General Relativity

We describe the ideas behind the package 'isometry', implemented in Maple to calculate isometry groups of dimensions 2, 3 and 4 in General Relativity. The package extends the functionality of previous programs written to perform invariant classification of space-times in General Relativity. Programming solutions used to surmount problems encountered with the calculation of eigenvectors and the determination of the signs of expressions are described. We also show how the package can be used to find the Killing vectors of a space-time.

Ensaio sobre o fluxo de Ricci e os buracos negros: fundamentação e estudo computacional

Pós-graduação em Ciência da Computação - IBILCE

Aplicativo computacional para utilização de componentes principais em experimentação agronômica

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Compreensões de conceitos de cálculo diferencial no primeiro ano de matemática: uma abordagem integrando oralidade, escrita e informática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Abordagem geométrica: possibilidades para o ensino e aprendizagem de Introdução às Equações Diferenciais Ordinárias

Pós-graduação em Educação Matemática - IGCE

Aprendizagem de eletromagnetismo via programação e computação simbólica

Relatamos a experiência de utilizar programação em Maple como ferramenta de aprendizagem do estudante num curso básico de teoria eletromagnética. Acreditamos que este relato possa ser útil a quem desejar utilizar o computador como instrumento pedagógico no ensino de Física.

Aplicação da computação simbólica na resolução de problemas de condução de calor em cilindros vazados com condições de contorno convectivas

Pós-graduação em Engenharia Mecânica - FEG

Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Algorithmische Methoden zur Berechnung von Vierbeinfunktionen

Die vorliegende Arbeit beschäftigt sich mit derAutomatisierung von Berechnungen virtuellerStrahlungskorrekturen in perturbativen Quantenfeldtheorien.Die Berücksichtigung solcher Korrekturen aufMehrschleifen-Ebene in der Störungsreihenentwicklung istheute unabdingbar, um mit der wachsenden Präzisionexperimenteller Resultate Schritt zu halten. Im allgemeinen kinematischen Fall können heute nur dieEinschleifen-Korrekturen als theoretisch gelöst angesehenwerden -- für höhere Ordnungen liegen nur Teilergebnissevor. In Mainz sind in den letzten Jahren einige neuartigeMethoden zur Integration von Zweischleifen-Feynmandiagrammenentwickelt und im xloops-Paket in algorithmischer Formteilweise erfolgreich implementiert worden. Die verwendetenVerfahren sind eine Kombination exakter symbolischerRechenmethoden mit numerischen. DieZweischleifen-Vierbeinfunktionen stellen in diesem Rahmenein neues Kapitel dar, das durch seine große Anzahl vonfreien kinematischen Parametern einerseits leichtunüberschaubar wird und andererseits auch auf symbolischerEbene die bisherigen Anforderungen übersteigt. Sie sind ausexperimenteller Sicht aber für manche Streuprozesse vongroßem Interesse. In dieser Arbeit wurde, basierend auf einer Idee von DirkKreimer, ein Verfahren untersucht, welches die skalarenVierbeinfunktionen auf Zweischleifen-Niveau ganz ohneRandbedingungen an den Parameterraum zu integrierenversucht. Die Struktur der nach vier Residuenintegrationenauftretenden Terme konnte dabei weitgehend geklärt und dieKomplexität der auftretenden Ausdrücke soweit verkleinertwerden, dass sie von heutigen Rechnern darstellbar sind.Allerdings ist man noch nicht bei einer vollständigautomatisierten Implementierung angelangt. All dies ist dasThema von Kapitel 2. Die Weiterentwicklung von xloops über Zweibeinfunktionenhinaus erschien aus vielfältigen Gründen allerdings nichtmehr sinnvoll. Im Rahmen dieser Arbeit wurde daher einradikaler Bruch vollzogen und zusammen mit C. Bauer und A.Frink eine Programmbibliothek entworfen, die als Vehikel fürsymbolische Manipulationen dient und es uns ermöglicht,übliche symbolische Sprachen wie Maple durch C++ zuersetzen. Im dritten Kapitel wird auf die Gründeeingegangen, warum diese Umstellung sinnvoll ist, und dabeidie Bibliothek GiNaC vorgestellt. Im vierten Kapitel werdenDetails der Implementierung dann im Einzelnen vorgestelltund im fünften wird sie auf ihre Praxistauglichkeituntersucht. Anhang A bietet eine Übersicht über dieverwendeten Hilfsmittel komplexer Analysis und Anhang Bbeschreibt ein bewährtes numerisches Instrument.

Abandoned Coal Mine Drainage and Its Remediation: Impacts on Stream Ecosystem Structure and Function

The effects of abandoned mine drainage (AMD) on streams and responses to remediation efforts were studied using three streams (AMD-impacted, remediated, reference) in both the anthracite and the bituminous coal mining regions of Pennsylvania (USA). Response variables included ecosystem function as well as water chemistry and macroinvertebrate community composition. The bituminous AMD stream was extremely acidic with high dissolved metals concentrations, a prolific mid-summer growth of the filamentous alga, Mougeotia, and .10-fold more chlorophyll than the reference stream. The anthracite AMD stream had a higher pH, substrata coated with iron hydroxide(s), and negligible chlorophyll. Macroinvertebrate communities in the AMD streams were different from the reference streams, the remediated streams, and each other. Relative to the reference stream, the AMD stream(s) had (1) greater gross primary productivity (GPP) in the bituminous region and undetectable GPP in the anthracite region, (2) greater ecosystem respiration in both regions, (3) greatly reduced ammonium uptake and nitrification in both regions, (4) lower nitrate uptake in the bituminous (but not the anthracite) region, (5) more rapid phosphorus removal from the water column in both regions, (6) activities of phosphorus-acquiring, nitrogenacquiring, and hydrolytic-carbon-acquiring enzymes that indicated extreme phosphorus limitation in both regions, and (7) slower oak and maple leaf decomposition in the bituminous region and slower oak decomposition in the anthracite region. Remediation brought chlorophyll concentrations and GPP nearer to values for respective reference streams, depressed ecosystem respiration, restored ammonium uptake, and partially restored nitrification in the bituminous (but not the anthracite) region, reduced nitrate uptake to an undetectable level, restored phosphorus uptake to near normal rates, and brought enzyme activities more in line with the reference stream in the bituminous (but not the anthracite) region. Denitrification was not detected in any stream. Water chemistry and macroinvertebrate community structure analyses capture the impact of AMD at the local reach scale, but functional measures revealed that AMD has ramifications that can cascade to downstream reaches and perhaps to receiving estuaries.

A VEGETATION RECONSTRUCTION OF UNION COUNTY, PENNSYLVANIA DURING THE EARLY HISTORICAL PERIOD (1755-1855)

This thesis assesses relationships between vegetation and topography and the impact of human tree-cutting on the vegetation of Union County during the early historical era (1755-1855). I use early warrant maps and forestry maps from the Pennsylvania historical archives and a warrantee map from the Union County courthouse depicting the distribution of witness trees and non-tree surveyed markers (posts and stones) in early European settlement land surveys to reconstruct the vegetation and compare vegetation by broad scale (mountains and valleys) and local scale (topographic classes with mountains and valleys) topography. I calculated marker density based on 2 km x 2 km grid cells to assess tree-cutting impacts. Valleys were mostly forests dominated by white oak (Quercus alba) with abundant hickory (Carya spp.), pine (Pinus spp.), and black oak (Quercus velutina), while pine dominated what were mostly pine-oak forests in the mountains. Within the valleys, pine was strongly associated with hilltops, eastern hemlock (Tsuga canadensis) was abundant on north slopes, hickory was associated with south slopes, and riparian zones had high frequencies of ash (Fraxinus spp.) and hickory. In the mountains, white oak was infrequent on south slopes, chestnut (Castanea dentata) was more abundant on south slopes and ridgetops than north slopes and mountain coves, and white oak and maple (Acer spp.) were common in riparian zones. Marker density analysis suggests that trees were still common over most of the landscape by 1855. The findings suggest there were large differences in vegetation between valleys and mountains due in part to differences in elevation, and vegetation differed more by topographic classes in the valleys than in the mountains. Possible areas of tree-cutting were evenly distributed by topographic classes, suggesting Europeans settlers were clearing land and harvesting timber in most areas of Union County.