Fundamentals Of Tensor Calculus For Engineers With A Primer On Smooth Manifolds

Author : Uwe Mühlich
Publisher : Springer
Page : 125 pages
File Size : 40,5 Mb
Release : 2017-04-18
Category : Science
ISBN : 9783319562643

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Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds by Uwe Mühlich Pdf

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.

Author : Emil de Souza Sánchez Filho
Publisher : Springer
Page : 345 pages
File Size : 53,7 Mb
Release : 2016-05-20
Category : Technology & Engineering
ISBN : 9783319315201

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Tensor Calculus for Engineers and Physicists by Emil de Souza Sánchez Filho Pdf

This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without needing to resort to other bibliographical sources on tensors. Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.

Author : Mikhail Itskov
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 44,8 Mb
Release : 2009-04-30
Category : Technology & Engineering
ISBN : 9783540939078

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Tensor Algebra and Tensor Analysis for Engineers by Mikhail Itskov Pdf

There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.

Author : Shahab Sahraee,Peter Wriggers
Publisher : Springer Nature
Page : 684 pages
File Size : 41,6 Mb
Release : 2023-12-12
Category : Technology & Engineering
ISBN : 9783031339530

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Tensor Calculus and Differential Geometry for Engineers by Shahab Sahraee,Peter Wriggers Pdf

The book contains the basics of tensor algebra as well as a comprehensive description of tensor calculus, both in Cartesian and curvilinear coordinates. Some recent developments in representation theorems and differential forms are included. The last part of the book presents a detailed introduction to differential geometry of surfaces and curves which is based on tensor calculus. By solving numerous exercises, the reader is equipped to properly understand the theoretical background and derivations. Many solved problems are provided at the end of each chapter for in-depth learning. All derivations in this text are carried out line by line which will help the reader to understand the basic ideas. Each figure in the book includes descriptive text that corresponds with the theoretical derivations to facilitate rapid learning.

Author : John R. Tyldesley
Publisher : Longman Publishing Group
Page : 136 pages
File Size : 53,7 Mb
Release : 1975
Category : Mathematics
ISBN : PSU:000030140875

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An Introduction to Tensor Analysis for Engineers and Applied Scientists by John R. Tyldesley Pdf

Author : John G. Papastavridis
Publisher : Routledge
Page : 444 pages
File Size : 53,7 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781351411615

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Tensor Calculus and Analytical Dynamics by John G. Papastavridis Pdf

Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.

Author : Hung Nguyen-Schäfer,Jan-Philip Schmidt
Publisher : Springer
Page : 389 pages
File Size : 52,9 Mb
Release : 2016-08-16
Category : Technology & Engineering
ISBN : 9783662484975

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Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers by Hung Nguyen-Schäfer,Jan-Philip Schmidt Pdf

This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation • Tensor Analysis • Elementary Differential Geometry • Differential Forms • Applications of Tensors and Differential Geometry • Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.

Author : Bipin Singh Koranga,Sanjay Kumar Padaliya
Publisher : CRC Press
Page : 127 pages
File Size : 40,9 Mb
Release : 2022-09-01
Category : Mathematics
ISBN : 9781000795912

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An Introduction to Tensor Analysis by Bipin Singh Koranga,Sanjay Kumar Padaliya Pdf

The subject of Tensor Analysis deals with the problem of the formulation of the relation between various entities in forms which remain invariant when we pass from one system of coordinates to another. The invariant form of equation is necessarily related to the possible system of coordinates with reference to which the equation remains invariant. The primary purpose of this book is the study of the invariance form of equation relative to the totally of the rectangular co-ordinate system in the three-dimensional Euclidean space. We start with the consideration of the way the sets representing various entities are transformed when we pass from one system of rectangular co-ordinates to another. A Tensor may be a physical entity that can be described as a Tensor only with respect to the manner of its representation by means of multi-sux sets associated with different system of axes such that the sets associated with different system of co-ordinate obey the transformation law for Tensor. We have employed sux notation for tensors of any order, we could also employ single letter such A,B to denote Tensors.

Author : Ralph Abraham,J.E. Marsden,Tudor Ratiu
Publisher : Springer Science & Business Media
Page : 672 pages
File Size : 49,7 Mb
Release : 1993-08-13
Category : Mathematics
ISBN : 9780387967905

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Manifolds, Tensor Analysis, and Applications by Ralph Abraham,J.E. Marsden,Tudor Ratiu Pdf

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.

Author : Goldberg Vladislav V,Akivis Maks A
Publisher : World Scientific Publishing Company
Page : 380 pages
File Size : 54,8 Mb
Release : 2003-09-29
Category : Science
ISBN : 9789813102255

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Tensor Calculus With Applications by Goldberg Vladislav V,Akivis Maks A Pdf

This textbook presents the foundations of tensor calculus and the elements of tensor analysis. In addition, the authors consider numerous applications of tensors to geometry, mechanics and physics.While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, since such tensors are important in applications to physics and engineering.With regard to applications, the authors construct the general theory of second-degree surfaces, study the inertia tensor as well as the stress and strain tensors, and consider some problems of crystallophysics. The last chapter introduces the elements of tensor analysis.All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book presents problems (a total over 300 problems are given). Examples and problems are intended to illustrate, reinforce and deepen the presented material. There are answers to most of the problems, as well as hints and solutions to selected problems at the end of the book.

Author : Tracy Yerkes Thomas
Publisher : Unknown
Page : 126 pages
File Size : 50,6 Mb
Release : 2013-08
Category : Electronic
ISBN : 1258790874

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Concepts from Tensor Analysis and Differential Geometry by Tracy Yerkes Thomas Pdf

Author : Tracy Y. Thomas
Publisher : Elsevier
Page : 128 pages
File Size : 48,9 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483263717

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Concepts from Tensor Analysis and Differential Geometry by Tracy Y. Thomas Pdf

Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.

Author : Hung Nguyen-Schafer,Jan-Philip Schmidt
Publisher : Unknown
Page : 256 pages
File Size : 43,5 Mb
Release : 2014-07-31
Category : Electronic
ISBN : 3662434458

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Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers by Hung Nguyen-Schafer,Jan-Philip Schmidt Pdf

Author : Ralph Abraham
Publisher : Unknown
Page : 654 pages
File Size : 53,7 Mb
Release : 1988
Category : Calculus of tensors
ISBN : 7506205475

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Manifolds, Tensor Analysis, and Applications by Ralph Abraham Pdf

Author : Y.R. Talpaert
Publisher : Springer
Page : 591 pages
File Size : 40,8 Mb
Release : 2013-01-17
Category : Mathematics
ISBN : 9401599890

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Tensor Analysis and Continuum Mechanics by Y.R. Talpaert Pdf

This book is designed for students in engineering, physics and mathematics. The material can be taught from the beginning of the third academic year. It could also be used for self study, given its pedagogical structure and the numerous solved problems which prepare for modem physics and technology. One of the original aspects of this work is the development together of the basic theory of tensors and the foundations of continuum mechanics. Why two books in one? Firstly, Tensor Analysis provides a thorough introduction of intrinsic mathematical entities, called tensors, which is essential for continuum mechanics. This way of proceeding greatly unifies the various subjects. Only some basic knowledge of linear algebra is necessary to start out on the topic of tensors. The essence of the mathematical foundations is introduced in a practical way. Tensor developments are often too abstract, since they are either aimed at algebraists only, or too quickly applied to physicists and engineers. Here a good balance has been found which allows these extremes to be brought closer together. Though the exposition of tensor theory forms a subject in itself, it is viewed not only as an autonomous mathematical discipline, but as a preparation for theories of physics and engineering. More specifically, because this part of the work deals with tensors in general coordinates and not solely in Cartesian coordinates, it will greatly help with many different disciplines such as differential geometry, analytical mechanics, continuum mechanics, special relativity, general relativity, cosmology, electromagnetism, quantum mechanics, etc ..