The Early Period of the Calculus of Variations - Softcover

Freguglia, Paolo; Giaquinta, Mariano

Softcover

ISBN 10: 3319817795 ISBN 13: 9783319817798

Verlag: Birkhäuser, 2018

Inhaltsangabe

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 Additamenta

Finally, 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.

 

Über diesen Titel

Über die Autorin bzw. den Autor

Esistono ormai da tempo molti articoli, in particolar modo su riviste di biomatematica, di (bio)fisica e di biologia, che presentano proposte e risultati di modellistica matematica relativi direttamente e indirettamente alla teoria dell'evoluzione. Sicuramente questi studi sono da considerarsi cruciali per la stessa costituzione della biologia teorica. E non solo. Il tentativo di applicare metodi matematici alla teoria dell'evoluzione s'inserisce altresì nell'ambito delle problematiche relative alla trattazione della complessità. Si tratta infatti di proporre una metodologia di "controllo" per una fenomenologia complessa come è la teoria dell'evoluzione (e comunque in generale l'oggetto di studio della biologia). Si propone, cioè, l'impiego di strumenti matematici (logici, geometrici, di dinamica stocastica e computazionali) con lo scopo di dare una risposta alle difficili esigenze delle problematiche evoluzionistiche. Con contributi specifici di Vincenzo Capasso, Cristiano Bocci, Lucia Pusillo e Enrico Rogora.

Von der hinteren Coverseite

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 Additamenta

Finally, 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.

 

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2018
• Sprache: Englisch
• ISBN 10: 3319817795
• ISBN 13: 9783319817798
• Einband: Taschenbuch
• Anzahl der Seiten: 308
• Kontakt zum Hersteller: preigu GmbH & Co. KG; mail@preigu.de; ; Lengericher Landstr. 19; Osnabrück; Niedersachsen; 49078; Deutschland