Overview
- Gives a unique integrated presentation of algebraic, analytic and geometric tools
- Provides a progressive introduction of concepts
- Includes a wide variety of exercises and historical comments
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (11 chapters)
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Front Matter
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THE CALCULUS OF VARIATIONS
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Front Matter
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Back Matter
Keywords
About this book
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 subject’s 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 École polytechnique in 1987. It will be accessible to graduate students and advanced undergraduates.
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Authors and Affiliations
About the author
Jean-Pierre Bourguignon is the Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France, where he was director from 1994 to 2013. His research interests are in differential geometry, in particular its relations with partial differential equations and mathematical physics. He was president of the Société Mathématique de France (1990–1992) and of the European Mathematical Society (1995–1998). He received the Paul Langevin prize from the Académie des Sciences de Paris in 1987 and the Physical Sciences and Mathematics Prize from the Comité du Rayonnement Français in 1997.
Bibliographic Information
Book Title: Variational Calculus
Authors: Jean-Pierre Bourguignon
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-031-18307-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-18306-5Published: 13 November 2022
Softcover ISBN: 978-3-031-18309-6Published: 14 November 2023
eBook ISBN: 978-3-031-18307-2Published: 12 November 2022
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XIX, 274
Number of Illustrations: 1 b/w illustrations
Topics: Differential Geometry, Global Analysis and Analysis on Manifolds, Mathematical Physics