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Calculus of variations on fibred manifolds and variational physicsa geometrical approach to variational problems in physics /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Calculus of variations on fibred manifolds and variational physicsby Jana Musilová, Pavla Musilová, Olga Rossi.
其他題名:	a geometrical approach to variational problems in physics /
作者:	Musilová, Jana.
其他作者:	Musilová, Pavla.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	xiii, 331 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Calculus of variations.
電子資源:	https://doi.org/10.1007/978-3-031-77408-9
ISBN:	9783031774089$q(electronic bk.)

Calculus of variations on fibred manifolds and variational physicsa geometrical approach to variational problems in physics /
Musilová, Jana.

Calculus of variations on fibred manifolds and variational physicsa geometrical approach to variational problems in physics /[electronic resource] :by Jana Musilová, Pavla Musilová, Olga Rossi. - Cham :Springer Nature Switzerland :2025. - xiii, 331 p. :ill., digital ;24 cm. - Lecture notes in physics,v. 10331616-6361 ;. - Lecture notes in physics ;650..

Chapter 1. Introduction -- Chapter 2. Fibred manifolds -- Chapter 3. Vector fields and differential forms -- Chapter 4. Calculus of variations -- Chapter 5. Dynamical forms and the inverse problem -- Chapter 6. Hamiltonian systems -- Chapter 7. Elements of the variational sequences -- Chapter 8. Extension: Geometrical structures for field theories -- Chapter 9. Variational physics -- Chapter 10. Appendix.

This book presents modern variational calculus in mechanics and field theories with applications to theoretical physics. It is based on modern mathematical tools, specifically fibred spaces and their jet prolongations, which operate with vector fields and differential forms on foundational structures. The book systematically explains Lagrangian and Hamiltonian mechanics and field theory, with a focused exploration of the underlying structures. Additionally, it addresses the well-known inverse problem of calculus of variations and provides examples illustrating key variational physical theories. The text is complemented by solved examples from physics and includes exercises designed to help readers master the subject. Aimed at PhD students, postdocs, and interested researchers, this book assumes prior knowledge of mathematical analysis, linear and multilinear algebra, as well as elements of general and theoretical physics for effective engagement with the discussion.

ISBN: 9783031774089$q(electronic bk.)

Standard No.: 10.1007/978-3-031-77408-9doiSubjects--Topical Terms:

191127
Calculus of variations.

LC Class. No.: QC20.7.C3

Dewey Class. No.: 530.15564

Calculus of variations on fibred manifolds and variational physicsa geometrical approach to variational problems in physics /
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505 0 $a Chapter 1. Introduction -- Chapter 2. Fibred manifolds -- Chapter 3. Vector fields and differential forms -- Chapter 4. Calculus of variations -- Chapter 5. Dynamical forms and the inverse problem -- Chapter 6. Hamiltonian systems -- Chapter 7. Elements of the variational sequences -- Chapter 8. Extension: Geometrical structures for field theories -- Chapter 9. Variational physics -- Chapter 10. Appendix.
520 $a This book presents modern variational calculus in mechanics and field theories with applications to theoretical physics. It is based on modern mathematical tools, specifically fibred spaces and their jet prolongations, which operate with vector fields and differential forms on foundational structures. The book systematically explains Lagrangian and Hamiltonian mechanics and field theory, with a focused exploration of the underlying structures. Additionally, it addresses the well-known inverse problem of calculus of variations and provides examples illustrating key variational physical theories. The text is complemented by solved examples from physics and includes exercises designed to help readers master the subject. Aimed at PhD students, postdocs, and interested researchers, this book assumes prior knowledge of mathematical analysis, linear and multilinear algebra, as well as elements of general and theoretical physics for effective engagement with the discussion.
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