Topics In Differential Geometry A New Approach Using D Differentiation
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Topics In Differential Geometry A New Approach Using D Differentiation
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Author : Donal J. Hurley
language : en
Publisher: Springer Science & Business Media
Release Date : 2002
Topics In Differential Geometry A New Approach Using D Differentiation written by Donal J. Hurley 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 2002 with Mathematics categories.
D-differentiation is a unified operation that enables aspects of differential geometry to be developed and presented from a new perspective. This book is the first comprehensive and self-contained treatment of this new method. It demonstrates, concisely but without sacrificing rigour or intelligibility, how even elementary concepts in differential geometry can be reformulated to obtain new and valuable insights. In addition, D-differentiation has applications in several areas of physics, such as classical mechanics, solid-state physics and general relativity. This book will prove useful to all users of D-differentiation - from advanced graduate students onwards - and to those researching into new approaches to some branches of physics and mathematics.
A Geometric Approach To Differential Forms
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Author : David Bachman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-02
A Geometric Approach To Differential Forms written by David Bachman 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 2012-02-02 with Mathematics categories.
This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.
A New Approach To Differential Geometry Using Clifford S Geometric Algebra
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Author :
language : en
Publisher:
Release Date : 2011-12-01
A New Approach To Differential Geometry Using Clifford S Geometric Algebra written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-01 with categories.
Elementary Topics In Differential Geometry
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Author : J. A. Thorpe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Elementary Topics In Differential Geometry written by J. A. Thorpe 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 2012-12-06 with Mathematics categories.
In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Several textbooks adopting this point of view are now available and have been widely adopted. Students completing the sophomore year now have a fair preliminary under standing of spaces of many dimensions. It should be apparent that courses on the junior level should draw upon and reinforce the concepts and skills learned during the previous year. Unfortunately, in differential geometry at least, this is usually not the case. Textbooks directed to students at this level generally restrict attention to 2-dimensional surfaces in 3-space rather than to surfaces of arbitrary dimension. Although most of the recent books do use linear algebra, it is only the algebra of ~3. The student's preliminary understanding of higher dimensions is not cultivated.
Topics In Modern Differential Geometry
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Author : Stefan Haesen
language : en
Publisher: Springer
Release Date : 2016-12-21
Topics In Modern Differential Geometry written by Stefan Haesen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-21 with Mathematics categories.
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
A First Course In Differential Geometry
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Author : Izu Vaisman
language : en
Publisher: CRC Press
Release Date : 2020-11-26
A First Course In Differential Geometry written by Izu Vaisman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.
This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.
Topics In Differential Geometry
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Author : Peter W. Michor
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Topics In Differential Geometry written by Peter W. Michor 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 2008 with Geometry, Differential categories.
"This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra."--BOOK JACKET.
New Problems In Differential Geometry
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Author : M. Rahula
language : en
Publisher: World Scientific
Release Date : 1993
New Problems In Differential Geometry written by M. Rahula and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The main theme of this book is the geometrical interpretation of phenomena taking place in Jet spaces in connection with differential equations. This concise volume caters to all mathematicians who wish to deepen their acquaintance with the mathematics of differential geometry.
Differential Geometry And Topology
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Author : Keith Burns
language : en
Publisher: CRC Press
Release Date : 2005-05-27
Differential Geometry And Topology written by Keith Burns and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-27 with Mathematics categories.
Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow. Smooth manifolds, Riemannian metrics
Differential Geometry And Lie Groups
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Author : Jean Gallier
language : en
Publisher: Springer
Release Date : 2021-08-19
Differential Geometry And Lie Groups written by Jean Gallier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-19 with Mathematics categories.
This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.