The Geometry Of Jet Bundles
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The Geometry Of Jet Bundles
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Author : D. J. Saunders
language : en
Publisher: Cambridge University Press
Release Date : 1989-03-09
The Geometry Of Jet Bundles written by D. J. Saunders and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-03-09 with Mathematics categories.
The purpose of this book is to , particularly those associated with the calculus of variations, in a modern geometric way.
The Geometry Of Jet Bundles
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Author : D. J. Saunders
language : en
Publisher: Cambridge University Press
Release Date : 1989-03-09
The Geometry Of Jet Bundles written by D. J. Saunders and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-03-09 with Mathematics categories.
The purpose of this book is to provide an introduction to the theory of jet bundles for mathematicians and physicists who wish to study differential equations, particularly those associated with the calculus of variations, in a modern geometric way. One of the themes of the book is that first-order jets may be considered as the natural generalisation of vector fields for studying variational problems in field theory, and so many of the constructions are introduced in the context of first- or second-order jets, before being described in their full generality. The book includes a proof of the local exactness of the variational bicomplex. A knowledge of differential geometry is assumed by the author, although introductory chapters include the necessary background of fibred manifolds, and on vector and affine bundles. Coordinate-free techniques are used throughout, although coordinate representations are often used in proofs and when considering applications.
Geometry Of Jet Bundles And The Structure Of Lagrangian And Hamiltonian Formalisms
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Author : Boris A. Kupershmidt
language : en
Publisher:
Release Date : 1979
Geometry Of Jet Bundles And The Structure Of Lagrangian And Hamiltonian Formalisms written by Boris A. Kupershmidt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Field theory (Physics) categories.
Natural Operations In Differential Geometry
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Author : Ivan Kolar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Natural Operations In Differential Geometry written by Ivan Kolar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M.
Handbook Of Global Analysis
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Author : Demeter Krupka
language : en
Publisher: Elsevier
Release Date : 2011-08-11
Handbook Of Global Analysis written by Demeter Krupka and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.
This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents
Applied Differential Geometry
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Author : William L. Burke
language : en
Publisher: Cambridge University Press
Release Date : 1985-05-31
Applied Differential Geometry written by William L. Burke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-05-31 with Mathematics categories.
This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.
Smooth Manifolds And Observables
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Author : Jet Nestruev
language : en
Publisher: Springer Nature
Release Date : 2020-09-10
Smooth Manifolds And Observables written by Jet Nestruev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-10 with Mathematics categories.
This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.
Smooth Manifolds And Fibre Bundles With Applications To Theoretical Physics
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Author : Steinar Johannesen
language : en
Publisher: CRC Press
Release Date : 2016-12-08
Smooth Manifolds And Fibre Bundles With Applications To Theoretical Physics written by Steinar Johannesen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-08 with Mathematics categories.
This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics provides complete and rigorous proofs of all the results presented within. Among the themes illustrated in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. It can be used as a textbook for a pure mathematics course in differential geometry, assuming the reader has a good understanding of basic analysis, linear algebra and point set topology. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories.
Synthetic Geometry Of Manifolds
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Author : Anders Kock
language : en
Publisher: Cambridge University Press
Release Date : 2010
Synthetic Geometry Of Manifolds written by Anders Kock and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighborhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.
The Convenient Setting Of Global Analysis
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Author : Andreas Kriegl
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
The Convenient Setting Of Global Analysis written by Andreas Kriegl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Global analysis (Mathematics). categories.
For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR