Overview

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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9783031183096

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Reviews

“The present book … can be considered as an advanced book including important notions, results and methods from analysis and geometry. … We consider that the book is an excellent pedagogical work, containing the essential elements of Variational Calculus. It is addressed to advanced students and researchers in the field.” (Gheorghe Moroşanu, zbMATH 1505.49002, 2023)

Author Information

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.

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