Alexis Fontaine's integration of ordinary differential equations and the origins of the calculus of several variables

Greenberg, John L.

doi:10.1080/00033798200200101

Cited by 8 publications

(3 citation statements)

References 5 publications

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“…Ref. [46] cites [47] with the advent of the principle of virtual velocities and its use in Lagrange's Méchanique analytique in 1788. He shows how Lagrange uses these tools in astronomy.…”

Section: Integral Calculus Foundationmentioning

confidence: 99%

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Epistemic Complexity of the Mathematical Object “Integral”

Mateus-Nieves

Moll

2021

Mathematics

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The literature in mathematics education identifies a traditional formal mechanistic-type paradigm in Integral Calculus teaching which is focused on the content to be taught but not on how to teach it. Resorting to the history of the genesis of knowledge makes it possible to identify variables in the mathematical content of the curriculum that have a positive influence on the appropriation of the notions and procedures of calculus, enabling a particularised way of teaching. Objective: The objective of this research was to characterise the anthology of the integral seen from the epistemic complexity that composes it based on historiography. Design: The modelling of epistemic complexity for the definite integral was considered, based on the theoretical construct “epistemic configuration”. Analysis and results: Formalising this complexity revealed logical keys and epistemological elements in the process of the theoretical constitution that reflected epistemological ruptures which, in the organisation of the information, gave rise to three periods for the integral. The characterisation of this complexity and the connection of its components were used to design a process of teaching the integral that was applied to three groups of university students. The implementation showed that a paradigm shift in the teaching process is possible, allowing students to develop mathematical competencies.

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“…Ref. [46] cites [47] with the advent of the principle of virtual velocities and its use in Lagrange's Méchanique analytique in 1788. He shows how Lagrange uses these tools in astronomy.…”

Section: Integral Calculus Foundationmentioning

confidence: 99%

“…Ref. [47] (p. 250) mentions that "a feature of the French academy's growing commitment to analytical methods in physics in the course of the eighteenth century was to override the teleological metaphysics of rational mechanics" (p. 250).…”

Section: Integral Calculus Foundationmentioning

confidence: 99%

Epistemic Complexity of the Mathematical Object “Integral”

Mateus-Nieves

Moll

2021

Mathematics

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“…El descubrimiento del cálculo parcial diferencial, véaseGreenberg (1982).7 Profundizar consultando en Euler (1755).…”

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Epistemología de la integral como fundamento del cálculo integral

Mateus-Nieves

2021

Bolema

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Resumen Se realizó una historiografía a la integral, buscando identificar su ontología e implicaciones en el proceso de formalización del cálculo integral. Es una investigación cualitativa basada en la historiografía de un contenido matemático analizado con algunas herramientas del Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemática, desarrollado con estudiantes universitarios que toman la asignatura cálculo integral. El rastreo de la información permitió identificar algunas rupturas epistemológicas que direccionaron la investigación a identificar cambios en la concepción de la integral. La organización de la información permitió identificar tres periodos: 1) La integral como operador. 2) Evolución de la operación integración originando el cálculo integral. 3) Fundamentación del cálculo integral. Se identificó al cálculo integral como un ámbito poco explorado y normalmente considerado complejo. Esta propuesta permite pensar la integral no como un objeto complejo, sino como un ente matemático formado por diversos significados que deben descomponerse para su estudio. Los tres periodos aquí propuestos permiten: identificar la complejidad que la conforma, pensar en posibles maneras de relacionar, conectar o articular esa complejidad, en miras de lograr una articulación que redunde en comprensión y desarrollo de competencias matemáticas en aquellos que la estudian.

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Vibrating Strings and Eighteenth-Century Mechanics

Garber

1999

The Language of Physics

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Alexis Fontaine's integration of ordinary differential equations and the origins of the calculus of several variables

Cited by 8 publications

References 5 publications

Epistemic Complexity of the Mathematical Object “Integral”

Epistemic Complexity of the Mathematical Object “Integral”

Epistemología de la integral como fundamento del cálculo integral

Vibrating Strings and Eighteenth-Century Mechanics

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