The Early Period of the Calculus of Variations

Nonfiction, Science & Nature, Mathematics, Calculus, History
Cover of the book The Early Period of the Calculus of Variations by Paolo Freguglia, Mariano Giaquinta, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Paolo Freguglia, Mariano Giaquinta ISBN: 9783319389455
Publisher: Springer International Publishing Publication: June 27, 2016
Imprint: Birkhäuser Language: English
Author: Paolo Freguglia, Mariano Giaquinta
ISBN: 9783319389455
Publisher: Springer International Publishing
Publication: June 27, 2016
Imprint: Birkhäuser
Language: English

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.

 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

 

More books from Springer International Publishing

Cover of the book African Perspectives of King Dingane kaSenzangakhona by Paolo Freguglia, Mariano Giaquinta
Cover of the book Muslim History and Social Theory by Paolo Freguglia, Mariano Giaquinta
Cover of the book Before Military Intervention by Paolo Freguglia, Mariano Giaquinta
Cover of the book Adaptive Sports Medicine by Paolo Freguglia, Mariano Giaquinta
Cover of the book Clinical Informatics Study Guide by Paolo Freguglia, Mariano Giaquinta
Cover of the book Dynamical Systems: Modelling by Paolo Freguglia, Mariano Giaquinta
Cover of the book Biomedical Applications of Acridines by Paolo Freguglia, Mariano Giaquinta
Cover of the book Eight Steps to Sustainable Organizational Learning by Paolo Freguglia, Mariano Giaquinta
Cover of the book Diagnosis of Blood and Bone Marrow Disorders by Paolo Freguglia, Mariano Giaquinta
Cover of the book Advanced Video Coding Systems by Paolo Freguglia, Mariano Giaquinta
Cover of the book Advanced Robotics for Medical Rehabilitation by Paolo Freguglia, Mariano Giaquinta
Cover of the book Multiscale Modelling in Sheet Metal Forming by Paolo Freguglia, Mariano Giaquinta
Cover of the book Ultrasonography in the ICU by Paolo Freguglia, Mariano Giaquinta
Cover of the book Digital Pathology by Paolo Freguglia, Mariano Giaquinta
Cover of the book Excel 2013 for Human Resource Management Statistics by Paolo Freguglia, Mariano Giaquinta
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy