Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions

Grabiner, Judith V.

doi:10.2307/2974733

Cited by 13 publications

(9 citation statements)

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“…The above results are rigorously derived and, as Wallace claimed in the letter to Herschel quoted above, "new at least in their form." Though the final results resemble special cases of Lagrange's remainder formula-and also a much earlier geometrical one of Maclaurin [33,399]-Wallace's approach via his "Fundamental Problem" is his own. There is just one fly in the ointment.…”

Section: Wallace On Fluxionsmentioning

confidence: 67%

“…Though the Scottish universities needed structural reform [57], the proposals were considered insensitive to the distinctive nature of Scottish education. Many sectors of Scottish life, including the Church of Scotland, town councils, universities, and professional bodies, strongly opposed the bill, and it had to be withdrawn [27,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

Section: Wallace and The Reviewersmentioning

confidence: 99%

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Calculus and Analysis in Early 19th-Century Britain: The Work of William Wallace

Craik

1999

Historia Mathematica

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Scottish-born William Wallace (1768-1843) was an early exponent of the differential calculus in Britain and translator of French mathematical works. Encyclopaedias published during the early 19th century provided a valuable educational resource, to which Wallace and his colleague, James Ivory, contributed. Wallace's encyclopaedia articles on "Fluxions" and his other analytical writings are examined here, as are his relations with James Ivory, John Herschel, and others. Wallace's long 1815 article on "Fluxions" in the Edinburgh Encyclopaedia was the first complete account of calculus, using differential notation, to be published in English. There, he attempted an original and rigorous "doctrine of limits," which deserved more attention than it received. In 1832, while professor of mathematics in Edinburgh, he applied analysis to support the reform of taxation proposed in the Reform Bill. It is suggested that the later neglect of Wallace's achievements is attributable to a mix of personal, institutional, political, and national rivalries. C 1999 Academic Press William Wallace né enÉcosse (1768-1843) fut un interprète précoce du calcul différentiel en Grande Bretagne et traduisit des ouvrages mathématiques de langue française. Les encyclopédies publiées au début du XIXe siècle fournirent une précieuse ressource pédagogiqueà laquelle contribuèrent Wallace et son collègue James Ivory. Les articles encyclopédiques de Wallace sur les "Fluxions" et d'autreś ecrits analytiques font l'objet du présent article; et aussi ses relations avec James Ivory, John Herschel et d'autres mathématiciens. Le long article de Wallace sur les "Fluxions" paru dans l'Edinburgh Encyclopaedia de 1815 fut le premier exposé complet du calcul, utilisant la notation différentielle,à etre publié en anglais. Dans cet article, il mit en oeuvre une "doctrine des limites" originale et rigoureuse, qui méritait plus d'attention qu'elle ne reçut. En 1832, alors qu'ilétait professeur de mathématiquesà Edimbourg, il utilisa l'analyse pour soutenir la réforme fiscale proposée dans le Projet de loi de Réforme. Cet article suggère que l'oubli postérieur de l'oeuvre accomplie par Wallace doitêtre attribuéà un mélange de rivalités personnelles, institutionnelles, politiques et nationales. C

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Section: Wallace On Fluxionsmentioning

confidence: 67%

Section: Wallace and The Reviewersmentioning

confidence: 99%

Calculus and Analysis in Early 19th-Century Britain: The Work of William Wallace

Craik

1999

Historia Mathematica

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“…see [8]. In [9], the author obtained another way of proving the Weierstrass inequality by applying AGM inequality and also, extended the Weierstrass inequalities by the use of majorization.…”

Section: Introductionmentioning

confidence: 99%

The Proofs of Product Inequalities in Vector Spaces

Barnes

Owusu-Ansah²,

Amponsah³

et al. 2018

Eur. J. Pure Appl. Math.

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In this paper, we introduce the proofs of product inequalities:u v ≤ u + v , for all u, v ∈ [0, 2], and u + v ≤ u v , for allu, v ∈ [2, ∞). The first product inequality u v ≤ u + v holds forany two vectors in the interval [0, 1] in Holder’s space and also valid anytwo vectors in the interval [1, 2] in the Euclidean space. On the otherhand, the second product inequality u + v ≤ u v ∀u, v ∈ [2, ∞)only in Euclidean space. By applying the first product inequality to theL p spaces, we observed that if f : Ω → [0, 1], and g : Ω → R, thenf p g p ≤ f p + g p . Also, if f, g : Ω → R, then f p + g p ≤f p g p .

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“…The AGM inequality was first introduced by Lagrange (as cited in [1]). Since then the AGM inequality has used to establish the relationships between the areas and perimeters of geometrical plane figures, the so-called isoperimetric inequalities, for example, see authors in [2,3]. However, a substantial progress has been made to increase the understanding of the AGM inequality by the researchers across the globe.…”

Section: Introductionmentioning

confidence: 99%

The Proofs of the Arithmetic-Geometric Mean Inequality Through Both the Product and Binomial Inequalities

Barnes

Harris²,

Darquah³

et al. 2018

Eur. J. Pure Appl. Math.

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Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions

Cited by 13 publications

References 0 publications

Calculus and Analysis in Early 19th-Century Britain: The Work of William Wallace

Calculus and Analysis in Early 19th-Century Britain: The Work of William Wallace

The Proofs of Product Inequalities in Vector Spaces

The Proofs of the Arithmetic-Geometric Mean Inequality Through Both the Product and Binomial Inequalities

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