Overview
- Takes a concept beyond the math approach
- Written by an engineer for engineers and students in engineering and applied physics
- Includes various didactical exercises to help the reader to gain deeper insights
- Includes supplementary material: sn.pub/extras
Part of the book series: Solid Mechanics and Its Applications (SMIA, volume 230)
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Table of contents (7 chapters)
Keywords
About this book
This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept.
After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters.
It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms.
The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out.
Authors and Affiliations
Bibliographic Information
Book Title: Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds
Authors: Uwe Mühlich
Series Title: Solid Mechanics and Its Applications
DOI: https://doi.org/10.1007/978-3-319-56264-3
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-56263-6Published: 25 April 2017
Softcover ISBN: 978-3-319-85869-2Published: 25 July 2018
eBook ISBN: 978-3-319-56264-3Published: 18 April 2017
Series ISSN: 0925-0042
Series E-ISSN: 2214-7764
Edition Number: 1
Number of Pages: XII, 125
Number of Illustrations: 23 b/w illustrations
Topics: Solid Mechanics, Classical and Continuum Physics, Mathematical Applications in the Physical Sciences, Mathematical Methods in Physics