Basic Concepts Of Synthetic Differential Geometry
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Basic Concepts Of Synthetic Differential Geometry
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Author : R. Lavendhomme
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Basic Concepts Of Synthetic Differential Geometry written by R. Lavendhomme 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.
Starting at an introductory level, the book leads rapidly to important and often new results in synthetic differential geometry. From rudimentary analysis the book moves to such important results as: a new proof of De Rham's theorem; the synthetic view of global action, going as far as the Weil characteristic homomorphism; the systematic account of structured Lie objects, such as Riemannian, symplectic, or Poisson Lie objects; the view of global Lie algebras as Lie algebras of a Lie group in the synthetic sense; and lastly the synthetic construction of symplectic structure on the cotangent bundle in general. Thus while the book is limited to a naive point of view developing synthetic differential geometry as a theory in itself, the author nevertheless treats somewhat advanced topics, which are classic in classical differential geometry but new in the synthetic context. Audience: The book is suitable as an introduction to synthetic differential geometry for students as well as more qualified mathematicians.
Synthetic Geometry Of Manifolds
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Author : Anders Kock
language : en
Publisher:
Release Date : 2014-05-14
Synthetic Geometry Of Manifolds written by Anders Kock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 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.
Differential Geometry
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Author : Marcelo Epstein
language : en
Publisher: Springer
Release Date : 2014-07-02
Differential Geometry written by Marcelo Epstein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-02 with Mathematics categories.
Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics. Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constitutive response of continuous media. Once these ideas have been grasped at the topological level, the differential structure needed for the description of physical fields is introduced in terms of differentiable manifolds and principal frame bundles. These mathematical concepts are then illustrated with examples from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy fluxes and dislocation theory. This book will be useful for researchers and graduate students in science and engineering.
Synthetic Differential Geometry
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Author : Anders Kock
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-22
Synthetic Differential Geometry 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 2006-06-22 with Mathematics categories.
This book, first published in 2006, details how limit processes can be represented algebraically.
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.
Introduction To Differential Geometry For Engineers
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Author : Brian F. Doolin
language : en
Publisher: Courier Corporation
Release Date : 2012-01-01
Introduction To Differential Geometry For Engineers written by Brian F. Doolin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-01 with Mathematics categories.
This outstanding guide supplies important mathematical tools for diverse engineering applications, offering engineers the basic concepts and terminology of modern global differential geometry. Suitable for independent study as well as a supplementary text for advanced undergraduate and graduate courses, this volume also constitutes a valuable reference for control, systems, aeronautical, electrical, and mechanical engineers. The treatment's ideas are applied mainly as an introduction to the Lie theory of differential equations and to examine the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, vector fields, exterior algebra, and Lie algebras. An appendix reviews concepts related to vector calculus, including open and closed sets, compactness, continuity, and derivative.
Synthetic Differential Geometry Models
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Author : Anders Kock
language : en
Publisher:
Release Date : 2006
Synthetic Differential Geometry Models written by Anders Kock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Geometry, Differential categories.
Second edition of this book detailing how limit processes can be represented algebraically.
Synthetic Differential Topology
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Author : Marta Bunge
language : en
Publisher: Cambridge University Press
Release Date : 2018-03-29
Synthetic Differential Topology written by Marta Bunge 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 2018-03-29 with Mathematics categories.
This book formally introduces synthetic differential topology, a natural extension of the theory of synthetic differential geometry which captures classical concepts of differential geometry and topology by means of the rich categorical structure of a necessarily non-Boolean topos and of the systematic use of logical infinitesimal objects in it. Beginning with an introduction to those parts of topos theory and synthetic differential geometry necessary for the remainder, this clear and comprehensive text covers the general theory of synthetic differential topology and several applications of it to classical mathematics, including the calculus of variations, Mather's theorem, and Morse theory on the classification of singularities. The book represents the state of the art in synthetic differential topology and will be of interest to researchers in topos theory and to mathematicians interested in the categorical foundations of differential geometry and topology.
Aspects Of Differential Geometry I
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Author : Peter Gilkey
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Aspects Of Differential Geometry I written by Peter Gilkey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries. Chapter 1 provides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bundles, and Stokes' Theorem. Chapter 3 is an introduction to Riemannian geometry. The Levi-Civita connection is presented, geodesics introduced, the Jacobi operator is discussed, and the Gauss-Bonnet Theorem is proved. The material is appropriate for an undergraduate course in the subject. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new. Table of Contents: Preface / Acknowledgments / Basic Notions and Concepts / Manifolds / Riemannian and Pseudo-Riemannian Geometry / Bibliography / Authors' Biographies / Index
Geometry
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Author : R. V. Gamkrelidze
language : en
Publisher:
Release Date : 1993
Geometry written by R. V. Gamkrelidze and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.