Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds (Solid Mechanics and Its Applications #230)

Synopsis

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.

Copyright:

2017

Book Details

Book Quality:

Publisher Quality

ISBN-13:

9783319562643

Related ISBNs:

9783319562636

Publisher:

Springer International Publishing

Date of Addition:

10/07/18

Copyrighted By:

Springer International Publishing, Cham

Adult content:

No

Language:

English

Has Image Descriptions:

No

Categories:

Nonfiction, Science, Technology, Earth Sciences, Mathematics and Statistics

Submitted By:

Bookshare Staff

Usage Restrictions:

This is a copyrighted book.