Article ID: CBB000933315

The Integral as an Anti-Differential. An Aspect of Euler's Attempt to Transform the Calculus into an Algebraic Calculus (2008)

unapi

Ferraro, Giovanni (Author)


Quaderns d'Història de l'Enginyeria
Volume: 9
Pages: 25--58

ISSN: 1135-934X

Publication Date: 2008
Edition Details: Part of a special issue: 300 Aniversari de Leonhard Euler (1707--2007)
Language: English

The integration of differential formulas was one of the main fields of Euler's activity. He wrote many papers on the subject. In this article, I will dwell upon an important aspect of Euler's work on integration: the notion of integration as anti-differentiation. I will show that this notion requires examination within the context of Euler's strategy, which was aimed at transforming integral calculus into an exclusively algebraic theory and which gave rise to several problems, the most important of which concerned the existence of the anti-differential and the nature of the functions involved in the operation of integration. I will also consider the role of general and particular integrals in Euler's theory and stress that the importance attributed to indefinite integration and general integrals was linked to the conception of analysis as the science that investigated mathematical objects in an abstract and general way. Finally, I will discuss the implication of Euler's concept in his treatment of elliptic integrals.

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Article Massa Esteve, Maria Rosa (2008) Congrés Internacional “300 Aniversari Leonhard Euler (1707--2007)”. Barcelona, 20--21 de setembre de 2007. Quaderns d'Història de l'Enginyeria (p. 307). unapi

Article Lusa Monforte, Guillermo (2008) Congrés Internacional “300 Aniversari Leonhard Euler (1707--2007)”. Una presentación informal. Quaderns d'Història de l'Enginyeria (p. 3). unapi

Citation URI
https://data.isiscb.org/isis/citation/CBB000933315/

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Authors & Contributors
Ferraro, Giovanni
Jia, Xiaoyong
Jouve, Guillame
Giovanni Capobianco
Enea, Maria Rosaria
Davide Gullotto
Concepts
Mathematics
Calculus
Differential and integral equations
Differential equations
Infinitesimals
Physics
Time Periods
18th century
19th century
17th century
20th century, early
Places
Spain
Russia
Europe
Institutions
St. Petersburg Academy of Sciences
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