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The introductory chapter contains notes to the history of variational problems, with a more detailed focus on contemporary situation, where the variational theories are is constructed as a calculus of vector fields and differential forms adapted to the fibred structure of fibred manifolds and their jet prolongations serving as underlying geometrical spaces for calculus of variations. The chapter also contains basic notations used throughout the book and references to renowned literature dealing with this issue in relation to physics. The content of the individual chapters is also characterized here very briefly.

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Introduction

  • 章节

  • 发表日期：

    2025年

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  • Jana Musilová,
  • Pavla Musilová,
  • Olga Rossi

摘要

The introductory chapter contains notes to the history of variational problems, with a more detailed focus on contemporary situation, where the variational theories are is constructed as a calculus of vector fields and differential forms adapted to the fibred structure of fibred manifolds and their jet prolongations serving as underlying geometrical spaces for calculus of variations. The chapter also contains basic notations used throughout the book and references to renowned literature dealing with this issue in relation to physics. The content of the individual chapters is also characterized here very briefly.