Jean-Pierre Bourguignon: Variational Calculus

Cover: 9783031183096 | Variational Calculus | Jean-Pierre Bourguignon | Taschenbuch | xix

Rückseite: 9783031183096 | Variational Calculus | Jean-Pierre Bourguignon | Taschenbuch | xix

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2023
Fachbereich:	Geometrie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xix 274 S. 1 s/w Illustr. 274 p. 1 illus.
ISBN-13:	9783031183096
ISBN-10:	3031183096
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Bourguignon, Jean-Pierre
Auflage:	1st edition 2022
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 17 mm
Von/Mit:	Jean-Pierre Bourguignon
Erscheinungsdatum:	14.11.2023
Gewicht:	0,452 kg

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