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Variational calculus

Bourguignon, J.-P.

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Variational calculus

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Variational calculus/ by Jean-Pierre Bourguignon.
作者:	Bourguignon, J.-P.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xix, 274 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Variational inequalities (Mathematics) -
電子資源:	https://doi.org/10.1007/978-3-031-18307-2
ISBN:	9783031183072

Variational calculus
Bourguignon, J.-P.

Variational calculus[electronic resource] /by Jean-Pierre Bourguignon. - Cham :Springer International Publishing :2022. - xix, 274 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

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.

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.

ISBN: 9783031183072

Standard No.: 10.1007/978-3-031-18307-2doiSubjects--Topical Terms:

712918
Variational inequalities (Mathematics)

LC Class. No.: QA316

Dewey Class. No.: 515.64

Variational calculus
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505 0 $a 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.
520 $a 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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