Ferraro, Giovanni (Author)
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.
...MoreArticle 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).
Article Lusa Monforte, Guillermo (2008) Congrés Internacional “300 Aniversari Leonhard Euler (1707--2007)”. Una presentación informal. Quaderns d'Història de l'Enginyeria (p. 3).
Article
Yuan, Min;
Jia, Xiaoyong;
(2008)
A Historical Survey: Why Did Lagrange Redefine the Complete Integral of a First-Order Partial Differential Equation
(/isis/citation/CBB000933545/)
Article
Delshams, Amadeu;
Massa Esteve, Maria Rosa;
(2008)
Consideracions al voltant de la Funció Beta a l'obra de Leonhard Euler (1707--1783)
(/isis/citation/CBB000933316/)
Article
Marc Parmentier;
(2015)
Leibniz et le virtuel
(/isis/citation/CBB764317706/)
Article
Navarro Loidi, Juan Miguel;
(2008)
El número e en los textos matemáticos españoles del siglo XVIII
(/isis/citation/CBB000933319/)
Book
Paolo Freguglia;
Mariano Giaquinta;
(2016)
The Early Period of the Calculus of Variations
(/isis/citation/CBB578052686/)
Article
Jouve, Guillaume;
(2008)
Le rôle de d'Alembert dans les débuts d'une étude programmatique des équations aux dérivées partielles (1760--1783)
(/isis/citation/CBB000933174/)
Article
Ferraro, Giovanni;
(2004)
Differentials and Differential Coefficients in the Eulerian Foundations of the Calculus
(/isis/citation/CBB000410838/)
Book
Brummelen, Glen Van;
Kinyon, Michael;
(2005)
Mathematics and the Historian's Craft: The Kenneth O. May Lectures
(/isis/citation/CBB001023435/)
Article
Maria Rosaria Enea;
Giovanni Ferraro;
Giovanni Capobianco;
(2017)
Geometry and Analysis in Euler’s Integral Calculus
(/isis/citation/CBB172886959/)
Article
Ferraro, Giovanni;
(2007)
Convergence and Formal Manipulation in the Theory of Series from 1730 to 1815
(/isis/citation/CBB000771368/)
Book
Bradley, Robert E.;
Sandifer, Charles Edward;
(2007)
Leonhard Euler: Life, Work and Legacy
(/isis/citation/CBB000773345/)
Article
Demidov, Serge S.;
(2008)
D'Alembert et la notion de solution des équations différentielles aux dérivées partielles
(/isis/citation/CBB000933173/)
Article
Guillame Jouve;
(2017)
The First Works of D'Alembert and Euler About the Problem of Vibrating Strings from the Perspective of Their Correspondence
(/isis/citation/CBB238196040/)
Article
Jia, Xiaoyong;
Li, Yuewu;
(2009)
The Calculus of Variations from Euler to Lagrange: As a Result of Formalized Improvement
(/isis/citation/CBB000933767/)
Book
Davide Gullotto;
(2023)
La Repubblica dei Matematici. Storia dell’analisi matematica nell’età di Euler e Leibniz
(/isis/citation/CBB269641386/)
Article
Frédéric Jaëck;
(2019)
Calcul différentiel et intégral adapté aux substitutions par Volterra
(/isis/citation/CBB042003689/)
Article
Siegmund-Schultze, Reinhard;
(2007)
Philipp Frank, Richard von Mises, and the Frank-Mises
(/isis/citation/CBB000780198/)
Article
Cogliati, Alberto;
(2014)
Early History of Infinite Continuous Groups, 1883--1898
(/isis/citation/CBB001420738/)
Chapter
Archibald, Tom;
(2003)
Differential equations: A historical overview to circa 1900
(/isis/citation/CBB000355275/)
Chapter
Fellmann, Emil A.;
(1996)
Partielle Differentiation im Briefwechsel Eulers mit Niklaus I Bernoulli: Eine Miszelle
(/isis/citation/CBB000070674/)
Be the first to comment!