Variational Calculus
Buch in deiner Nähe kaufen
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.
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.
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
Autor*in
Jean-Pierre Bourguignon
Themen in »Variational Calculus«
Differential Calculus Calculus of Variations Manifolds Euler-Lagrange equations Hamiltonian systems Modelling for mechanics and physics
Stimmen zu »Variational Calculus«
“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)
()