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

Description: Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds by Uwe MÜhlich 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. FORMAT Paperback LANGUAGE English CONDITION Brand New 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. Table of Contents 1 Introduction.- 2 Notes on point set topology.- 3 The nite dimensional real vector space.- 4 Tensor Algebra.- 5 Afne space and euclidean space.- 6 Tensor analysis in euclidean space.- 7 A primer on smooth manifolds.- B Further Reading. Feature 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 Details ISBN3319858696 Series Solid Mechanics and Its Applications ISBN-10 3319858696 ISBN-13 9783319858692 Format Paperback DEWEY 519 Pages 125 Publisher Springer International Publishing AG Year 2018 Publication Date 2018-07-25 Imprint Springer International Publishing AG Place of Publication Cham Country of Publication Switzerland Language English Series Number 230 UK Release Date 2018-07-25 Edited by Kwang-Leong Choy Birth 1945 Affiliation Univ Of Illinois At Urbana-champaign, Usa Position Professor Qualifications University of Virginia Author Uwe MÜhlich Edition Description Softcover reprint of the original 1st ed. 2017 Alternative 9783319562636 Audience Professional & Vocational Illustrations 23 Illustrations, black and white; XII, 125 p. 23 illus. We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:118812350;

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