Differential Geometry (eBook)

Basic Notions and Physical Examples

Marcelo Epstein (Autor)

eBook Download: PDF

2014 | 2014
XI, 139 Seiten
Springer International Publishing (Verlag)
978-3-319-06920-3 (ISBN)

Infos

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.

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.

Inhalt

Topological constructs.- Physical illustrations.- Differential constructs.- Physical illustrations.

Produkt-Details

• Erscheint lt. Verlag: 2.7.2014
• Reihe/Serie: Mathematical Engineering
• Reihe/Serie: Mathematical Engineering
• Zusatzinfo: XI, 139 p. 26 illus.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Schlagworte: Continuum Mechanics • de Rham Currents • differential forms • dislocations • fibre bundles • Groupoids • Lie groups • Parallel Transport • Topological and Differentiable Manifolds
• ISBN-10: 3-319-06920-9 / 3319069209
• ISBN-13: 978-3-319-06920-3 / 9783319069203