Mathematical Engineering

Differential Geometry

Basic Notions and Physical Examples

Authors: Epstein, Marcelo

  • 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
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eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-06920-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-06919-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 28, 2016
  • ISBN 978-3-319-35714-0
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
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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.

About the authors

Marcelo Epstein is Professor of Mechanical Engineering at the University of Calgary, where he has held the title of University Professor of Rational Mechanics. A Fellow of the American Academy of Mechanics and a recipient of the CANCAM award, he has published extensively in the field of the foundations and applications of continuum mechanics. He is the author or co-author of four books on various aspects of applied differential geometry, continuum mechanics and biomechanics.

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)

Table of contents (4 chapters)

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-06920-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-319-06919-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 28, 2016
  • ISBN 978-3-319-35714-0
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Differential Geometry
Book Subtitle
Basic Notions and Physical Examples
Authors
Series Title
Mathematical Engineering
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-06920-3
DOI
10.1007/978-3-319-06920-3
Hardcover ISBN
978-3-319-06919-7
Softcover ISBN
978-3-319-35714-0
Series ISSN
2192-4732
Edition Number
1
Number of Pages
XI, 139
Number of Illustrations and Tables
26 b/w illustrations
Topics