Variational calculus / Jean-Pierre Bourguignon.
Bourguignon, J.-P. (Jean-Pierre), 1947- author.
2022
QA316
Available Online

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Title Variational calculus / Jean-Pierre Bourguignon.
Author Bourguignon, J.-P. (Jean-Pierre), 1947- author.
ISBN 9783031183072 (electronic bk.)
303118307X (electronic bk.)
9783031183065
3031183061
DOI https://doi.org/10.1007/978-3-031-18307-2
Published Cham : Springer, [2022]
Copyright ©2022
Language English
Language Note Translated from the French.
Description 1 online resource (xix, 274 pages) : illustrations.
Item Number 10.1007/978-3-031-18307-2 doi
Call Number QA316
Dewey Decimal Classification 515/.64
Summary This book provides a comprehensive introduction to the Calculus of Variations and its use in modelling mechanics and physics problems. Presenting a geometric approach to the subject, it progressively guides the reader through this very active branch of mathematics, accompanying key statements with a huge variety of exercises, some of them solved. Stressing the need to overcome limitations of the initial point of view, and emphasising the interconnectivity of various branches of mathematics (algebra, analysis and geometry), the book includes some advanced material to challenge the most motivated students. Systematic, short historical notes provide details on the subjects odyssey, and how new tools have been developed over the last two centuries. This English translation updates a set of notes for a course first given at the Ecole polytechnique in 1987. It will be accessible to graduate students and advanced undergraduates.
Bibliography, etc. Note Includes bibliographical references and indexes.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Series Springer monographs in mathematics.
Available in Other Form Variational calculus.
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Part I The Analytic Setting
A First Generalisation of the Notion of Space: Spaces of Infinite Dimension
Banach Spaces and Hilbert Spaces
Linearisation and Local Inversion of Differentiable Maps
Part II The Geometric Setting
Some Applications of Differential Calculus
New Generalisation of the Notion of a Space: Configuration Spaces
Tangent Vectors and Vector Fields on Configuration Spaces
Regular Points and Critical Points of Numerical Functions
Part III The Calculus of Variations
Configuration Spaces of Geometric Objects
The Euler-Lagrange Equations
The Hamiltonian Viewpoint
Symmetries and Conversation Laws
Appendix: Basic Elements of Topology
References
Notation Index
Subject Index.

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