A Brief On Tensor Analysis

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A Brief On Tensor Analysis

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Author : James G. Simmonds
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-31

A Brief On Tensor Analysis written by James G. Simmonds 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 2012-10-31 with Mathematics categories.

There are three changes in the second edition. First, with the help of readers and colleagues-thanks to all-I have corrected typographical errors and made minor changes in substance and style. Second, I have added a fewmore Exercises,especially at the end ofChapter4.Third, I have appended a section on Differential Geometry, the essential mathematical tool in the study of two-dimensional structural shells and four-dimensional general relativity. JAMES G. SIMMONDS vii Preface to the First Edition When I was an undergraduate, working as a co-op student at North Ameri can Aviation, I tried to learn something about tensors. In the Aeronautical Engineering Department at MIT, I had just finished an introductory course in classical mechanics that so impressed me that to this day I cannot watch a plane in flight-especially in a turn-without imaging it bristling with vec tors. Near the end of the course the professor showed that, if an airplane is treated as a rigid body, there arises a mysterious collection of rather simple looking integrals called the components of the moment of inertia tensor.

A Brief On Tensor Analysis

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Author : James G. Simmonds
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-31

A Brief On Tensor Analysis written by James G. Simmonds 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 1997-07-31 with Mathematics categories.

In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.

A Brief On Tensor Analysis

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Author : Springer
language : en
Publisher:
Release Date : 2012-10-29

A Brief On Tensor Analysis written by Springer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-29 with categories.

A Brief On Tensor Analysis

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Author : J. G. Simmonds
language : en
Publisher:
Release Date : 1982-04-13

A Brief On Tensor Analysis written by J. G. Simmonds and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-04-13 with categories.

Tensor Algebra And Tensor Analysis For Engineers

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Author : Mikhail Itskov
language : en
Publisher: Springer Nature
Release Date : 2025-09-26

Tensor Algebra And Tensor Analysis For Engineers written by Mikhail Itskov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-09-26 with Science categories.

This is the sixth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. In accordance with the contemporary way of scientific publication, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In particular, the book discusses such multi-physical topics of solid mechanics as electro- and magnetoelasticity. In addition, advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics are included. This new edition also focuses on numerical aspects of tensor calculus and shows how modern methods of machine learning can be applied to the calculation of tensor functions. Hence, these textbook addresses graduate students as well as scientists working in this field and in particular dealing with interdisciplinary problems. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

An Introduction To Tensor Analysis

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Author : Bipin Singh Koranga
language : en
Publisher: CRC Press
Release Date : 2022-09-01

An Introduction To Tensor Analysis written by Bipin Singh Koranga and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-01 with Science categories.

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.

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.

Introduction To Vector And Tensor Analysis

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Author : Robert C. Wrede
language : en
Publisher: Courier Corporation
Release Date : 2013-01-30

Introduction To Vector And Tensor Analysis written by Robert C. Wrede and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-30 with Mathematics categories.

Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.

Tensor Algebra And Tensor Analysis For Engineers

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Author : Mikhail Itskov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-04

Tensor Algebra And Tensor Analysis For Engineers written by Mikhail Itskov 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 2007-05-04 with Technology & Engineering categories.

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.

Tensor Analysis With Applications In Mechanics

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Author : L. P. Lebedev
language : en
Publisher: World Scientific
Release Date : 2010

Tensor Analysis With Applications In Mechanics written by L. P. Lebedev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

1. Preliminaries. 1.1. The vector concept revisited. 1.2. A first look at tensors. 1.3. Assumed background. 1.4. More on the notion of a vector. 1.5. Problems -- 2. Transformations and vectors. 2.1. Change of basis. 2.2. Dual bases. 2.3. Transformation to the reciprocal frame. 2.4. Transformation between general frames. 2.5. Covariant and contravariant components. 2.6. The cross product in index notation. 2.7. Norms on the space of vectors. 2.8. Closing remarks. 2.9. Problems -- 3. Tensors. 3.1. Dyadic quantities and tensors. 3.2. Tensors from an operator viewpoint. 3.3. Dyadic components under transformation. 3.4. More dyadic operations. 3.5. Properties of second-order tensors. 3.6. Eigenvalues and eigenvectors of a second-order symmetric tensor. 3.7. The Cayley-Hamilton theorem. 3.8. Other properties of second-order tensors. 3.9. Extending the Dyad idea. 3.10. Tensors of the fourth and higher orders. 3.11. Functions of tensorial arguments. 3.12. Norms for tensors, and some spaces. 3.13. Differentiation of tensorial functions. 3.14. Problems -- 4. Tensor fields. 4.1. Vector fields. 4.2. Differentials and the nabla operator. 4.3. Differentiation of a vector function. 4.4. Derivatives of the frame vectors. 4.5. Christoffel coefficients and their properties. 4.6. Covariant differentiation. 4.7. Covariant derivative of a second-order tensor. 4.8. Differential operations. 4.9. Orthogonal coordinate systems. 4.10. Some formulas of integration. 4.11. Problems -- 5. Elements of differential geometry. 5.1. Elementary facts from the theory of curves. 5.2. The torsion of a curve. 5.3. Frenet-Serret equations. 5.4. Elements of the theory of surfaces. 5.5. The second fundamental form of a surface. 5.6. Derivation formulas. 5.7. Implicit representation of a curve; contact of curves. 5.8. Osculating paraboloid. 5.9. The principal curvatures of a surface. 5.10. Surfaces of revolution. 5.11. Natural equations of a curve. 5.12. A word about rigor. 5.13. Conclusion. 5.14. Problems -- 6. Linear elasticity. 6.1. Stress tensor. 6.2. Strain tensor. 6.3. Equation of motion. 6.4. Hooke's law. 6.5. Equilibrium equations in displacements. 6.6. Boundary conditions and boundary value problems. 6.7. Equilibrium equations in stresses. 6.8. Uniqueness of solution for the boundary value problems of elasticity. 6.9. Betti's reciprocity theorem. 6.10. Minimum total energy principle. 6.11. Ritz's method. 6.12. Rayleigh's variational principle. 6.13. Plane waves. 6.14. Plane problems of elasticity. 6.15. Problems -- 7. Linear elastic shells. 7.1. Some useful formulas of surface theory. 7.2. Kinematics in a neighborhood of [symbol]. 7.3. Shell equilibrium equations. 7.4. Shell deformation and strains; Kirchhoff's hypotheses. 7.5. Shell energy. 7.6. Boundary conditions. 7.7. A few remarks on the Kirchhoff-Love theory. 7.8. Plate theory. 7.9. On Non-classical theories of plates and shells