Tensor Calculus For Engineers And Physicists
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Tensor Calculus For Engineers And Physicists
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Author : Emil de Souza Sánchez Filho
language : en
Publisher: Springer
Release Date : 2016-05-20
Tensor Calculus For Engineers And Physicists written by Emil de Souza Sánchez Filho and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-20 with Technology & Engineering categories.
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.
Tensor Analysis For Engineers And Physicists With Application To Continuum Mechanics Turbulence And Einstein S Special And General Theory Of Relativity
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Author : Meinhard T. Schobeiri
language : en
Publisher: Springer Nature
Release Date : 2021-12-13
Tensor Analysis For Engineers And Physicists With Application To Continuum Mechanics Turbulence And Einstein S Special And General Theory Of Relativity written by Meinhard T. Schobeiri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-13 with Science categories.
This book unies the common tensor analytical aspects in engineering and physics. Using tensor analysis enables the reader to understand complex physical phenomena from the basic principles in continuum mechanics including the turbulence, its correlations and modeling to the complex Einstein' tensor equation. The development of General Theory of Relativity and the introduction of spacetime geometry would not have been possible without the use of tensor analysis. This textbook is primarily aimed at students of mechanical, electrical, aerospace, civil and other engineering disciplines as well as of theoretical physics. It also covers the special needs of practicing professionals who perform CFD-simulation on a routine basis and would like to know more about the underlying physics of the commercial codes they use. Furthermore, it is suitable for self-study, provided that the reader has a sufficient knowledge of differential and integral calculus. Particular attention was paid to selecting the application examples. The transformation of Cartesian coordinate system into curvilinear one and the subsequent applications to conservation laws of continuum mechanics and the turbulence physics prepares the reader for fully understanding the Einstein tensor equations, which exhibits one of the most complex tensor equation in theoretical physics.
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.
Tensor Calculus And Differential Geometry For Engineers
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Author : Shahab Sahraee
language : en
Publisher: Springer Nature
Release Date : 2023-11-10
Tensor Calculus And Differential Geometry For Engineers written by Shahab Sahraee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-10 with Technology & Engineering categories.
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.
Tensor Analysis And Elementary Differential Geometry For Physicists And Engineers
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Author : Hung Nguyen-Schäfer
language : en
Publisher: Springer
Release Date : 2016-08-16
Tensor Analysis And Elementary Differential Geometry For Physicists And Engineers written by Hung Nguyen-Schäfer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-16 with Technology & Engineering categories.
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.
Tensor Calculus And Analytical Dynamics
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Author : John G. Papastavridis
language : en
Publisher: Routledge
Release Date : 2018-12-12
Tensor Calculus And Analytical Dynamics written by John G. Papastavridis and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Mathematics categories.
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.
Vectors And Tensors In Engineering And Physics
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Author : D. A. Danielson
language : en
Publisher: Westview Press
Release Date : 1997
Vectors And Tensors In Engineering And Physics written by D. A. Danielson and has been published by Westview Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
The second edition develops the calculus of tensor fields and uses this mathematics to model the physical world. This new edition includes expanded derivations and solutions, and new applications, to make this successful text an even more useful and user-friendly book than the first edition.
Vector And Tensor Analysis With Applications
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Author : A. I. Borisenko
language : en
Publisher: Courier Corporation
Release Date : 2012-08-28
Vector And Tensor Analysis With Applications written by A. I. Borisenko and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-28 with Mathematics categories.
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
Tensor Analysis And Elementary Differential Geometry For Physicists And Engineers
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Author : Hung Nguyen-Schafer
language : en
Publisher:
Release Date : 2014-07-31
Tensor Analysis And Elementary Differential Geometry For Physicists And Engineers written by Hung Nguyen-Schafer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-31 with categories.
Handbook Of Mathematics For Engineers And Scientists
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2006-11-27
Handbook Of Mathematics For Engineers And Scientists written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-27 with Mathematics categories.
Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific and engineering applications and present classical as well as newer solution methods for various mathematical equations. The book supplies numerous examples, graphs, figures, and diagrams and contains many results in tabular form, including finite sums and series and exact solutions of differential, integral, and functional equations.