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商品詳細
Calculus of Variations on Fibred Manifolds and Variational Physics: A Geometrical Approach to Variational Problems in Physics. 2025 ed.
・ISBN 978-3-031-77407-2 paper EUR 74.99
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| 著者・編者 | Musilova, Jana / Musilova, Pavla / Rossi, Olga, |
|---|---|
| シリーズ | (Lecture Notes in Physics) |
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2025 |
| ページ数 | 331 pp. |
| 言語 | ENG |
| ニュース番号 | ＜A03-76796＞ |
解説
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.