| 书目名称 | Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds | | 编辑 | Uwe Mühlich | | 视频video | | | 概述 | 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 in | | 丛书名称 | Solid Mechanics and Its Applications | | 图书封面 |  | | 描述 | .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 t | | 出版日期 | Book 2017 | | 关键词 | Tensor Calculus; Differentiable manifolds; Continuum mechanics; Affine space; Euclidean space | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-56264-3 | | isbn_softcover | 978-3-319-85869-2 | | isbn_ebook | 978-3-319-56264-3Series ISSN 0925-0042 Series E-ISSN 2214-7764 | | issn_series | 0925-0042 | | copyright | Springer International Publishing AG 2017 |
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发表于 2025-3-21 19:17:41
