Fundamentals of Tensor Calculus for Engineers With a Primer on Smooth Manifolds
Language: English
Published by Springer, 2018
Series: Book 122 of 151 - Solid Mechanics and Its Applications
- Softcover
- New
Seller: Majestic Books, Hounslow, United KingdomMajestic Books
AbeBooks seller since January 19, 2007
Condition: New
£ 190.06
Quantity: 4 available
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Print on Demand pp. XII, 125 23 illus.
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- Title
- Fundamentals of Tensor Calculus for Engineers With a Primer on Smooth Manifolds
- Author
- Mühlich, Uwe
- Publisher
- Springer
- Publication year
- 2018
- Condition
- New
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 3319858696
- ISBN 13
- 9783319858692
- Series
- Book 122 of 151: Solid Mechanics and Its Applications
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.
"Synopsis" may belong to another edition of this title.
From the Back Cover
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.
"About the title" may belong to another edition of this title.
Majestic Books
Hounslow, United Kingdom
AbeBooks seller since January 19, 2007
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