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.
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. That is, the distance a particle travelsthe arclength of its trajectoryis the integral of its speed. Clearly developed arguments and proofs, colour illustrations, and over 100 exercises and solutions make this book ideal for courses and self-study. The section on cartography demonstrates the concrete importance of elementary dif-ferential geometry in applications. If Wa b R3 is a parametrized curve, then for any a t b, we dene its arclength from ato tto be s.t/ D Zt a k0.u/kdu. geometry, the divergence theorem, triangulations, and the Gauss Bonnet theorem. multi-dimensional spaces that locally (on a small scale) look like Euclidean n-dimensional space Rn, but globally (on a large scale) may have an interesting shape (topology). … 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. The fundamental concept underlying the geometry of curves is the arclength of a parametrized curve. It wouldnt be a good first book in differential geometry, though. Overview Differential Geometry is the study of (smooth) manifolds. “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.
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