The Very Basics Of Tensors
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The Very Basics Of Tensors
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Author : Nils K. Oeijord
language : en
Publisher: iUniverse
Release Date : 2005-05-25
The Very Basics Of Tensors written by Nils K. Oeijord and has been published by iUniverse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-25 with Mathematics categories.
Tensor calculus is a generalization of vector calculus, and comes near of being a universal language in physics. Physical laws must be independent of any particular coordinate system used in describing them. This requirement leads to tensor calculus. The only prerequisites for reading this book are a familiarity with calculus (including vector calculus) and linear algebra, and some knowledge of differential equations.
The Very Basics Of Tensors
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Author : Nils K. Oeijord
language : en
Publisher: iUniverse
Release Date : 2005
The Very Basics Of Tensors written by Nils K. Oeijord and has been published by iUniverse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Tensor calculus is a generalization of vector calculus, and comes near of being a universal language in physics. Physical laws must be independent of any particular coordinate system used in describing them. This requirement leads to tensor calculus. The only prerequisites for reading this book are a familiarity with calculus (including vector calculus) and linear algebra, and some knowledge of differential equations.
Tensors For Physics
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Author : Siegfried Hess
language : en
Publisher: Springer
Release Date : 2015-04-25
Tensors For Physics written by Siegfried Hess and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-25 with Science categories.
This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with. The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic by external orienting fields. The dynamics of tensors deals with phenomena of current research. In the last section, the 3D Maxwell equations are reformulated in their 4D version, in accord with special relativity.
What Are Tensors Exactly
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Author : Hongyu Guo
language : en
Publisher:
Release Date : 2021-06-08
What Are Tensors Exactly written by Hongyu Guo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-08 with Engineering categories.
The Association of Southeast Asian Nations (ASEAN) has been one of the world's most dynamic and fastest-growing regions over the years. Its average combined GDP growth rate is more than 6% and the total combined GDP was valued at US$3.0 trillion in 2018. ASEAN countries have managed to significantly reduce their national poverty over the last few decades. Although a correlation exists between economic growth and poverty reduction, millions of people in ASEAN countries still do not have sufficient incomes to fulfill their basic needs including food, shelter, clothes and sanitation. This book is a collection of working group papers contributed by members of Network of ASEAN-China Think-tanks (NACT) and covers best practices on poverty alleviation in ASEAN member states as well as in China, and ASEAN-China cooperation. It discusses experiences of ASEAN member states and China such as with regard to national policies, principles, definitions, approaches, progress, and challenges in poverty reduction. It reviews and evaluates the way forward including existing joint projects, opportunities, and challenges in the future cooperation and offers policy recommendations from both national and regional perspectives to help policymakers better cope with the daunting poverty challenges.
Fundamentals Of Tensor Calculus For Engineers With A Primer On Smooth Manifolds
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Author : Uwe Mühlich
language : en
Publisher: Springer
Release Date : 2017-04-18
Fundamentals Of Tensor Calculus For Engineers With A Primer On Smooth Manifolds written by Uwe Mühlich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-18 with Science categories.
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.
Introduction To Tensor Analysis And The Calculus Of Moving Surfaces
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Author : Pavel Grinfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-24
Introduction To Tensor Analysis And The Calculus Of Moving Surfaces written by Pavel Grinfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-24 with Mathematics categories.
This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.
Tensors
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Author : Anadi Jiban Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-05
Tensors written by Anadi Jiban Das and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-05 with Science categories.
Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.
An Introduction To Tensors And Group Theory For Physicists
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Author : Nadir Jeevanjee
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-26
An Introduction To Tensors And Group Theory For Physicists written by Nadir Jeevanjee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-26 with Science categories.
An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Advanced undergraduate and graduate students in physics and applied mathematics will find clarity and insight into the subject in this textbook.
Manifolds Tensors And Forms
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Author : Paul Renteln
language : en
Publisher: Cambridge University Press
Release Date : 2014
Manifolds Tensors And Forms written by Paul Renteln and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.