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 The Cognitive Foundations of Group Attitudes and Social Interaction by Paolo Freguglia, Mariano Giaquinta
Cover of the book Sample Path Analysis and Distributions of Boundary Crossing Times by Paolo Freguglia, Mariano Giaquinta
Cover of the book Advanced Computing in Industrial Mathematics by Paolo Freguglia, Mariano Giaquinta
Cover of the book Religion and Volunteering by Paolo Freguglia, Mariano Giaquinta
Cover of the book Balanced and Cyclical Growth in Models of Decentralized Economy by Paolo Freguglia, Mariano Giaquinta
Cover of the book Advances in Human Factors in Sports, Injury Prevention and Outdoor Recreation by Paolo Freguglia, Mariano Giaquinta
Cover of the book Entrepreneurship, Business and Economics - Vol. 2 by Paolo Freguglia, Mariano Giaquinta
Cover of the book Springer Series in Light Scattering by Paolo Freguglia, Mariano Giaquinta
Cover of the book Computational Science and Its Applications – ICCSA 2016 by Paolo Freguglia, Mariano Giaquinta
Cover of the book Recognition and Enforcement of Foreign Arbitral Awards by Paolo Freguglia, Mariano Giaquinta
Cover of the book Fixed Point of the Parabolic Renormalization Operator by Paolo Freguglia, Mariano Giaquinta
Cover of the book An Introduction to the Mathematical Theory of Dynamic Materials by Paolo Freguglia, Mariano Giaquinta
Cover of the book Nanomaterials and Plant Potential by Paolo Freguglia, Mariano Giaquinta
Cover of the book Resilience-Oriented Urban Planning by Paolo Freguglia, Mariano Giaquinta
Cover of the book Managing Sustainable Stakeholder Relationships 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