Solid Mechanics and Its Applications

Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds

Authors: Mühlich, Uwe

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  • 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
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eBook 101,14 €
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  • ISBN 978-3-319-56264-3
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Hardcover 124,79 €
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  • ISBN 978-3-319-56263-6
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  • Usually dispatched within 3 to 5 business days.
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Softcover 124,79 €
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  • ISBN 978-3-319-85869-2
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  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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.



Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook 101,14 €
price for Spain (gross)
  • ISBN 978-3-319-56264-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-3-319-56263-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
price for Spain (gross)
  • ISBN 978-3-319-85869-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds
Authors
Series Title
Solid Mechanics and Its Applications
Series Volume
230
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-56264-3
DOI
10.1007/978-3-319-56264-3
Hardcover ISBN
978-3-319-56263-6
Softcover ISBN
978-3-319-85869-2
Series ISSN
0925-0042
Edition Number
1
Number of Pages
XII, 125
Number of Illustrations
23 b/w illustrations
Topics