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This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups.

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.

The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics

Featured topics - Analysis on manifolds

- Analysis on manifolds - Differential forms on jet spaces

- Differential forms on jet spaces - Global variational functionals

- Global variational functionals - Euler-Lagrange mapping

- Euler-Lagrange mapping - Helmholtz form and the inverse problem

- Helmholtz form and the inverse problem - Symmetries and the Noether's theory of conservation laws

- Symmetries and the Noether's theory of conservation laws - Regularity and the Hamilton theory

- Regularity and the Hamilton theory - Variational sequences

- Variational sequences - Differential invariants and natural variational principles

- Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures

- First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals

- New ideas on global variational functionals - Complete proofs of all theorems

- Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity

- Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces

- Basic structures and tools: global analysis, smooth manifolds, fibred spaces