Authors:
- Provides a comprehensive description of the geometric constructs that form the backbone of modern differential geometry
- Demonstrates the close correspondence between geometrical objects and physically meaningful counterparts in engineering and physics
- Treatment is not overly technical from the mathematical point of view, thus allowing for a comfortable mastery of the essential ideas
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Engineering (MATHENGIN)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
“The book under review has grown out of lecture notes for a mini-course given at a workshop on differential geometry and continuum mechanics at the International Centre for Mathematical Sciences in 2013. … addressing researchers and engineers in particular, Epstein’s book provides a … quick way to appreciate modern differential geometry and topology and get to their essential ideas and usefulness. Surely, Epstein manages to give the reader a motivation to delve into the deep waters of these two fields.” (Theophanes Grammenos, Mathematical Reviews, June, 2015)
“This book is based on a short course on ‘Differential Geometry and Continuum Mechanics’ given by Marcelo Epstein at the International Centre of Mathematical Sciences in Edinburgh in June 2013. The course provided a guided tour of differential geometry for researchers and graduate students in science and engineering — many of whom had a particular interest in continuum mechanics. … this book is a gold mine of aesthetically pleasing mathematical ideas, the presentation of which is highly inspirational.” (P. N. Ruane, MAA Reviews, December, 2014)Authors and Affiliations
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Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Canada
Marcelo Epstein
About the author
Bibliographic Information
Book Title: Differential Geometry
Book Subtitle: Basic Notions and Physical Examples
Authors: Marcelo Epstein
Series Title: Mathematical Engineering
DOI: https://doi.org/10.1007/978-3-319-06920-3
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-06919-7Published: 15 July 2014
Softcover ISBN: 978-3-319-35714-0Published: 10 September 2016
eBook ISBN: 978-3-319-06920-3Published: 02 July 2014
Series ISSN: 2192-4732
Series E-ISSN: 2192-4740
Edition Number: 1
Number of Pages: XI, 139
Number of Illustrations: 26 b/w illustrations
Topics: Differential Geometry, Solid Mechanics, Classical Mechanics, Mathematical Methods in Physics