Freguglia, Paolo (Author)
Mariano Giaquinta (Author)
This monograph explores the early development of the calculus of variations in continental Europe during the Eighteenth Century by illustrating the mathematics of its founders. Closely following the original papers and correspondences of Euler, Lagrange, the Bernoullis, and others, the reader is immersed in the challenge of theory building. We see what the founders were doing, the difficulties they faced, the mistakes they made, and their triumphs. The authors guide the reader through these works with instructive commentaries and complements to the original proofs, as well as offering a modern perspective where useful. The authors begin in 1697 with Johann Bernoulli’s work on the brachystochrone problem and the events leading up to it, marking the dawn of the calculus of variations. From there, they cover key advances in the theory up to the development of Lagrange’s δ-calculus, including: • The isoperimetrical problems• Shortest lines and geodesics• Euler’s Methodus Inveniendi and the two AdditamentaFinally, the authors give the readers a sense of how vast the calculus of variations has become in centuries hence, providing some idea of what lies outside the scope of the book as well as the current state of affairs in the field. This book will be of interest to anyone studying the calculus of variations who wants a deeper intuition for the techniques and ideas that are used, as well as historians of science and mathematics interested in the development and evolution of modern calculus and analysis.
...MoreReview Ronald Calinger (2018) Review of "The Early Period of the Calculus of Variations". British Journal for the History of Mathematics (pp. 138-139).
Article
Peiffer, Jeanne;
(2006)
Jacob Bernoulli, maître et rival de son frère Johann
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Elisa Patergnani;
Luigi Pepe;
(2021)
Les mathématiciens français et italiens du «siècle long»: 1700-1814
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Parker, Adam E.;
(2013)
Who Solved the Bernoulli Differential Equation and How Did They Do It?
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Guillame Jouve;
(2017)
The First Works of D'Alembert and Euler About the Problem of Vibrating Strings from the Perspective of Their Correspondence
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Demidov, Serge S.;
(2008)
D'Alembert et la notion de solution des équations différentielles aux dérivées partielles
(/isis/citation/CBB000933173/)
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Jia, Xiaoyong;
Li, Yuewu;
(2009)
The Calculus of Variations from Euler to Lagrange: As a Result of Formalized Improvement
(/isis/citation/CBB000933767/)
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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/)
Book
Bernoulli, Jakob;
Bernoulli, Johann;
(1991)
Die Streitschriften von Jacob und Johann Bernoulli: Variationsrechnung. Bearbeitet und kommentiert von Goldstine, Herman H., mit historischen Anmerkungen von Radelet-de Grave, Patricia
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Article
Nauenberg, M.;
(2010)
The Early Application of the Calculus to the Inverse Square Force Problem
(/isis/citation/CBB001021999/)
Article
Charlotte Wahl;
(2014)
Between Cosmopolitanism and Nationalism. the Role of Expatriates in the Dissemination of Leibniz’s Differential Calculus
(/isis/citation/CBB567158444/)
Book
Brummelen, Glen Van;
Kinyon, Michael;
(2005)
Mathematics and the Historian's Craft: The Kenneth O. May Lectures
(/isis/citation/CBB001023435/)
Book
Davide Gullotto;
(2023)
La Repubblica dei Matematici. Storia dell’analisi matematica nell’età di Euler e Leibniz
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Book
Ferraro, Giovanni;
Palladino, Franco;
(1995)
Il calcolo sublime di Eulero e Lagrange: Esposto col metodo sintetico nel progetto di Nicolò Fergola
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Article
Fraser, Craig G.;
(1992)
Isoperimetric problems in the variation calculus of Euler and Lagrange
(/isis/citation/CBB000049830/)
Article
Erik R. Tou;
(2019)
Bernoullian Influences on Leonhard Euler’s Early Fluid Mechanics
(/isis/citation/CBB776843735/)
Chapter
Feigenbaum, Lenore;
(1992)
The fragmentation of the European mathematical community
(/isis/citation/CBB000056505/)
Article
Bradleya, Robert E.;
(2013)
De l'Hôpital, Bernoulli, and the Genesis of Analyse des infiniment petits
(/isis/citation/CBB001212296/)
Article
Clero, Jean-Pierre;
(2006)
La révolution des témoignages dans le calcul des probabilités
(/isis/citation/CBB001021372/)
Article
Blanco Abellán, Mónica;
(2001)
Análisis de la discusión L'Hôpital-Bernoulli
(/isis/citation/CBB000300736/)
Chapter
Blanco Abellan, Mónica;
(2008)
On How Johann Bernoulli's Lessons on Differential Calculus Were Communicated in Eighteenth-Century France and Italy
(/isis/citation/CBB000760625/)
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