Página 1 dos resultados de 216 itens digitais encontrados em 0.126 segundos

## A tensão entre o discreto e o contínuo na história da matemática e no ensino de matemática.; The discrete and the continuous in the history of mathematics and in mathematics education

Brolezzi, Antonio Carlos
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
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Discreto e contínuo são termos que se referem respectivamente a duas das ações básicas na elaboração da Matemática: contar e medir. Neste trabalho examinamos o problema pedagógico que surge da tendência de se abordar os temas de Matemática elementar optando por um ou outro aspecto, sem explorar a interação entre eles. Nossa ideia é que isso se resolve através da administração da tensão conceitual entre essas noções. Trata-se de caminhar com ambas as pernas, a da ideia do discreto e a da continuidade, na construção dos conceitos matemáticos. Este trabalho é baseado na pesquisa em História da Matemática, justificada pela visão do conhecimento como uma rede conceitual, uma rede de significações em permanente transformação. Procuramos assim fazer uso da História para repensar aspectos do ensino de Matemática elementar, especialmente relacionados ao nosso tema: a construção da ideia de Número; o nascimento do Cálculo Diferencial e Integral; as relações entre qualidade/quantidade. Ao final, mostramos exemplos de Oficinas Temáticas para a formação de professores, nas quais procuramos aplicar a abordagem histórica visando administrar o par conceitual discreto/contínuo dentro de assuntos do currículo elementar de matemática.; Discrete and continuous are concepts related respectively to two basic actions in Mathematics: to count and to measure. In this work we examine the pedagogical problem originated in the tendency of approaching elementary Mathematics by making an option between either one or other feature...

## O ensino de cálculo: dificuldades de natureza epistemológica; The teaching of calculus: difficulties of an epistemological nature

Rezende, Wanderley Moura
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
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São notórias e bem evidentes as dificuldades de aprendizagem no ensino de Cálculo. Algumas tentativas de resolver, ou pelo menos, amenizar, este problema têm sido realizadas tanto no campo pedagógico quanto no âmbito da pesquisa. Muitas dessas ações, inseridas no próprio contexto do ensino superior de Cálculo, partem do pressuposto que essas dificuldades de aprendizagem são de natureza psicológica, internas ao sujeito aprendiz. No entanto, contrariando esta tendência, esta pesquisa pretende mostrar que parte significativa dos problemas de aprendizagem do atual ensino de Cálculo é de natureza essencialmente epistemológica, está além dos métodos e das técnicas de ensino, sendo inclusive anterior ao seu próprio tempo de realização. Diante disto, foram imaginadas duas ações inter-relacionadas, dois mapeamentos que visam ao levantamento e entendimento dessas dificuldades de natureza epistemológica no ensino de Cálculo: um mapeamento conceitual do Cálculo e de suas idéias e procedimentos básicos; em seguida, munido desses elementos, realizou-se efetivamente o mapeamento das dificuldades supracitadas. Assim, a partir do entrelaçamento dos fatos históricos e pedagógicos, e tendo como pano de fundo as dualidades essenciais e os mapas conceituais do Cálculo...

## O ensino do conceito de integral, em sala de aula, com recursos da história da matemática e da resolução de problemas

Ribeiro, Marcos Vinícius
Tipo: Dissertação de Mestrado Formato: 324 f. : il.
POR
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## Case of Urethral Foreign Body: IUD Perforation of the Bladder with Calculus Formation

Gillis, E; Chhiv, N; Kang, S; Sayegh, R; Lotfipour, S
Fonte: California Chapter of the American Academy of Emergency Medicine Publicador: California Chapter of the American Academy of Emergency Medicine
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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A 28-year-old female presented to the Emergency Department (ED) with a chief complaint of strings protruding from her vagina. The patient also complained of recurrent symptoms of cystitis and occasional hematuria over the past five months without resolution after treatment. The patient underwent ED evaluation and was noted to have strings coated in calculus protruding from her urethral meatus. On AP abdominal film a T-shaped intrauterine device (IUD) with calculus was noted in the pelvis. By computed tomography (CT) scan the object was shown to be extruding from the vagina into the bladder. Of note the patient had a history of IUD use with supposed removal five years prior to presentation. The diagnosis of IUD perforation of the bladder with calculus formation was confirmed by cystoscopy, and the IUD and calculi were successfully removed without complication.

## A regra de L´Hopital : analise historica da regra de L´Hopital : a importancia da historia da matematica na disciplina de calculo; The hule of L´Hopital : Historical analysis of the hule of L´Hopital : impotance of the history of mathematics in the discipline of calculation

Everaldo Fernandes Barbosa
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
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O trabalho apresenta uma biografia do marquês de L'Hôpital e de Johann Bernoulli e as discussões sobre o cálculo do limite de uma função racional cujo numerador e denominador tendem a zero (conhecida como Regra de L'Hôpital), publicado no livro Análise dos Infinitamente Pequenos por Linhas Curvas pelo Marquês de L'Hôpital. Apresentamos a demonstração de ambos, L'Hôpital e Bernoulli e a demonstração rigorosa de Cauchy. Discutimos as controvérsias com relação à autoria da regra e as reivindicações de Johann Bernoulli pela sua autoria, pois Bernoulli foi pago para produzir e desvendar os mistérios, que para L'Hôpital, existiam na matemática de Leibniz. Incluímos também a interpretação geométrica que sugere a veracidade da regra e outras variantes que dependem dela. Além disso, são apresentadas discussões com relação ao uso da História da Matemática como material pedagógico para ensino de Cálculo Diferencial e Integral I e a altercação feita nos livros brasileiros e estrangeiros de cálculo sobre a aplicação da regra; The work presents Marquis de L'Hôpital and Johann Bernoulli's biographies and discussions on the calculation of the limit of a rational function whose numerator and denominator tend to zero (known as L'Hôpital's Rule)...

## Fundamental Theorem of Calculus

Sobczyk, Garret; Sanchez, Omar Leon
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been explained. Various classical examples of this theorem, such as the Green's and Stokes' theorem are discussed, as well as the new theory of monogenic functions, which generalizes the concept of an analytic function of a complex variable to higher dimensions.; Comment: 11 pages, 2 figures

## Excursus into the History of Calculus

Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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This is a brief overview of some turning points in the history of infinitesimals.

## Reconstructing the Star Formation History of the Galaxy

Hernandez, X.; Valls-Gabaud, D.; Gilmore, G.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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The evolution of the star formation rate in the Galaxy is one of the key ingredients quantifying the formation and determining the chemical and luminosity evolution of galaxies. Many complementary methods exist to infer the star formation history of the components of the Galaxy, from indirect methods for analysis of low-precision data, to new exact analytic methods for analysis of sufficiently high quality data. We summarise available general constraints on star formation histories, showing that derived star formation rates are in general comparable to those seen today. We then show how colour-magnitude diagrams of volume- and absolute magnitude-limited samples of the solar neighbourhood observed by Hipparcos may be analysed, using variational calculus techniques, to reconstruct the local star formation history. The remarkable accuracy of the data coupled to our maximum-likelihood variational method allows objective quantification of the local star formation history with a time resolution of ~ 50 Myr. Over the past 3Gyr, the solar neighbourhood star formation rate has varied by a factor of ~ 4, with characteristic timescale about 0.5Gyr, possibly triggered by interactions with spiral arms.; Comment: 12 pages, Proc. of the Sept. 20-24...

## Klein's double discontinuity revisited: what use is university mathematics to high school calculus?

Winsløw, Carl; Grønbæk, Niels
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Much effort and research has been invested into understanding and bridging the gaps which many students experience in terms of contents and expectations as they begin university studies with a heavy component of mathematics, typically in the form of calculus courses. We have several studies of bridging measures, success rates and many other aspects of these entrance transition problems. In this paper, we consider the inverse transition, experienced by university students as they revisit core parts of high school mathematics (in particular, calculus) after completing the mandatory undergraduate mathematics courses. To what extent does the advanced experience enable them to approach the high school calculus in a deeper and more autonomous way? To what extent can capstone courses support such an approach? How could it be hindered by deficiencies in the students' advanced experience? In this paper, we present a theoretical framework for an analysis of these questions, as well as a number of critical observations and reflections on how they appear in our own institutional context.; Comment: Will appear in "Recherches en Didactique des Math\'ematiques" vol. 34 no. 1

## Completeness of the Leibniz Field and Rigorousness of Infinitesimal Calculus

Hall, James F.; Todorov, Todor D.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of ten equivalent statements} borrowed from algebra, real analysis, general topology and non-standard analysis. We also discuss the completeness of non-Archimedean fields and present several examples of such fields. As an application we exploit one of our results to argue that the Leibniz infinitesimal calculus in the $18^\textrm{th}$ century was already a rigorous branch of mathematics -- at least much more rigorous than most contemporary mathematicians prefer to believe. By advocating our particular historical point of view, we hope to provoke a discussion on the importance of mathematical rigor in mathematics and science in general. We believe that our article will be of interest for those readers who teach courses on abstract algebra, real analysis, general topology, logic and the history of mathematics.; Comment: 32

## The Road to Stueckelberg's Covariant Perturbation Theory as Illustrated by Successive Treatments of Compton Scattering

Lacki, J.; Ruegg, H.; Telegdi, V.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We review the history of the road to a manifestly covariant perturbative calculus within quantum electrodynamics from the early semi-classical results of the mid-twenties to the complete formalism of Stueckelberg in 1934. We chose as our case study the calculation of the cross-section of the Compton effect. We analyse Stueckelberg's paper extensively. This is our first contribution to a study of his fundamental contributions to the theoretical physics of twentieth century.; Comment: This paper is a "working-physicist" version of a paper to be published in Studies in History and Philosophy of Modern Physics

## DD Calculus

Shen, Samuel S. P.; Lin, Qun
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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This paper introduces DD calculus and describes the basic calculus concepts of derivative and integral in a direct and non-traditional way, without limit definition: Derivative is computed from the point-slope equation of a tangent line and integral is defined as the height increment of a curve. This direct approach to calculus has three distinct features: (i) it defines derivative and (definite) integral without using limits, (ii) it defines derivative and antiderivative simultaneously via a derivative-antiderivative (DA) pair, and (iii) it posits the fundamental theorem of calculus as a natural corollary of the definitions of derivative and integral. The first D in DD calculus attributes to Descartes for his method of tangents and the second D to DA-pair. The DD calculus, or simply direct calculus, makes many traditional notations and procedures unnecessary, a plus when introducing calculus to the non-mathematics majors. It has few intermediate procedures, which can help dispel the mystery of calculus as perceived by the general public. The materials in this paper are intended for use in a two-hour introductory lecture on calculus.; Comment: 19 pages, 11 figures

## History of the formulas and algorithms for pi

Guillera, Jesus
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.54%
Throughout more than two millennia many formulas have been obtained, some of them beautiful, to calculate the number pi. Among them, we can find series, infinite products, expansions as continued fractions and expansions using radicals. Some expressions which are (amazingly) related to pi have been evaluated. In addition, a continual battle has been waged just to break the records computing digits of this number; records have been set using rapidly converging series, ultra fast algorithms and really surprising ones, calculating isolated digits. The development of powerful computers has played a fundamental role in these achievements of calculus.; Comment: Translated from the original Spanish by Luis Sanchez Lajusticia. Updated by the author. Some mistakes corrected

## A Brief Survey of the History of the Calculus of Variations and its Applications

Ferguson, James
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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In this paper, we trace the development of the theory of the calculus of variations. From its roots in the work of Greek thinkers and continuing through to the Renaissance, we see that advances in physics serve as a catalyst for developments in the mathematical theory. From the 18th century onwards, the task of establishing a rigourous framework of the calculus of variations is studied, culminating in Hilbert's work on the Dirichlet problem and the development of optimal control theory. Finally, we make a brief tour of some applications of the theory to diverse problems.; Comment: 26 pages, no figures

## The Birth of Calculus: Towards a More Leibnizian View

Kollerstrom, Nicholas
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We re-evaluate the great Leibniz-Newton calculus debate, exactly three hundred years after it culminated, in 1712. We reflect upon the concept of invention, and to what extent there were indeed two independent inventors of this new mathematical method. We are to a considerable extent agreeing with the mathematics historians Tom Whiteside in the 20th century and Augustus de Morgan in the 19th. By way of introduction we recall two apposite quotations: "After two and a half centuries the Newton-Leibniz disputes continue to inflame the passions. Only the very learned (or the very foolish) dare to enter this great killing ground of the history of ideas" from Stephen Shapin and "When de l'Hopital, in 1696, published at Paris a treatise so systematic, and so much resembling one of modern times, that it might be used even now, he could find nothing English to quote, except a slight treatise of Craig on quadratures, published in 1693" from Augustus de Morgan.; Comment: 21 Pages, 5 Colour Figures

## Differential Calculus, Tensor Products and the Importance of Notation

Manton, Jonathan H.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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An efficient coordinate-free notation is elucidated for differentiating matrix expressions and other functions between higher-dimensional vector spaces. This method of differentiation is known, but not explained well, in the literature. Teaching it early in the curriculum would avoid the tedium of element-wise differentiation and provide a better footing for understanding more advanced applications of calculus. Additionally, it is shown to lead naturally to tensor products, a topic previously considered too difficult to motivate quickly in elementary ways.; Comment: 9 pages

## You could simplify calculus

Livshits, Michael
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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I explain a direct approach to differentiation and integration. Instead of relying on the general notions of real numbers, limits and continuity, we treat functions as the primary objects of our theory, and view differentiation as division of f(x)-f(a) by x-a in a certain class of functions. When f is a polynomial the division can be carried out explicitly. To see why a polynomial with a positive derivative is increasing (the monotonicity theorem), we use the estimate |f(x)-f(a)-f'(a)(x-a)|<=K(x-a)^2. By making it into a definition we arrive at the notion of uniform Lipschitz differentiability (ULD), and see that the derivative of a ULD function is Lipschitz. Taking different moduli of continuity instead of |.|, we get different flavors of calculus, each rather elementary, but all together covering the total range of continuously differentiable functions. Using functions continuous at a, we recapture the classical definition of differentiability at a point. We also see that ULD is equivalent to divisibility of f(x)-f(a) by x-a in the class of Lipschitz functions of two variables, x and a. The analogous fact is true for any subadditive modulus of continuity. In this bottom-up, computational, one modulus of continuity at a time approach...

## Unthinkable: Mathematics and the Rise of the West

Welsh, Whitney
Tipo: Dissertação
Relevância na Pesquisa
55.73%

This dissertation explores the ideational underpinnings of the rise of the west through a comparison of ancient Greek geometry, medieval Arabic algebra, and early modern European calculus. Blending insights from Thomas Kuhn, Michel Foucault, and William H. Sewell, I assert that there is an underlying logic, however clouded, to the unfolding of a given civilization, governed by a cultural episteme that delineates the boundaries of rational thought and the accepted domain of human endeavor. Amid a certain conceptual configuration, the rise of the west happens; under other circumstances, it does not. Mathematics, as an explicit exhibition of logic premised on culturally determined axioms, presents an outward manifestation of the lens through which a civilization surveys the world, and as such offers a window on the fundamental assumptions from which a civilization's trajectory proceeds. To identify the epistemological conditions favorable to the rise of the west, I focus specifically on three mathematical divergences that were integral to the development of calculus, namely analytic geometry, trigonometry, and the fundamental theorem of calculus. Through a comparative/historical analysis of original source documents in mathematics...

## A gênese da causalidade física; The genesis of physical causality

Paty, Michel
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; ; ; ; ; ; Formato: application/pdf