Solutions Of Exercises Of Principles Of Tensor Calculus
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Solutions Of Exercises Of Principles Of Tensor Calculus
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Author : Taha Sochi
language : en
Publisher: Taha Sochi
Release Date : 2022-10-10
Solutions Of Exercises Of Principles Of Tensor Calculus written by Taha Sochi and has been published by Taha Sochi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-10 with Mathematics categories.
This book contains the solutions of all the exercises of my book: Principles of Tensor Calculus. These solutions are sufficiently simplified and detailed for the benefit of readers of all levels particularly those at introductory levels.
Solutions Of Exercises Of Tensor Calculus Made Simple
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Author : Taha Sochi
language : en
Publisher: Taha Sochi
Release Date :
Solutions Of Exercises Of Tensor Calculus Made Simple written by Taha Sochi and has been published by Taha Sochi this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
This book contains the detailed solutions of all the exercises of my book: Tensor Calculus Made Simple. The solutions are generally very detailed and hence they are supposed to provide some sort of revision for the subject topic.
Tensor Calculus Made Simple
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Author : Taha Sochi
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2016-12-09
Tensor Calculus Made Simple written by Taha Sochi and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-09 with categories.
This book is about tensor analysis. It consists of 169 pages. The language and method used in presenting the ideas and techniques of tensors make it very suitable as a textbook or as a reference for an introductory course on tensor algebra and calculus or as a guide for self-studying and learning.
Principles Of Tensor Calculus
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Author : Taha Sochi
language : en
Publisher: Taha Sochi
Release Date : 2022-08-23
Principles Of Tensor Calculus written by Taha Sochi and has been published by Taha Sochi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-23 with Mathematics categories.
This book is based on my previous book: Tensor Calculus Made Simple, where the development of tensor calculus concepts and techniques are continued at a higher level. Unlike the previous book which is largely based on a Cartesian approach, the formulation in the present book is based on a general coordinate system. The book is furnished with an index as well as detailed sets of exercises to provide useful revision and practice. To facilitate linking related concepts and sections, cross referencing is used extensively throughout the book. The book also contains a number of graphic illustrations to help the readers to visualize the ideas and understand the subtle concepts. The book can be used as a text for an introductory or an intermediate level course on tensor calculus.
Principles Of
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Author : Taha Sochi
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-08-08
Principles Of written by Taha Sochi and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-08 with Calculus of tensors categories.
This book is based on my previous book: Tensor Calculus Made Simple, where the development of tensor calculus concepts and techniques are continued at a higher level. Unlike the previous book which is largely based on a Cartesian approach, the formulation in the present book is based on a general coordinate system. The book is furnished with an index as well as detailed sets of exercises to provide useful revision and practice. To facilitate linking related concepts and sections, cross referencing is used extensively throughout the book. The book also contains a number of graphic illustrations to help the readers to visualize the ideas and understand the subtle concepts. The book can be used as a text for an introductory or an intermediate level course on tensor calculus.
Applications Of Tensor Analysis In Continuum Mechanics
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Author : Michael J Cloud
language : en
Publisher: World Scientific
Release Date : 2018-07-10
Applications Of Tensor Analysis In Continuum Mechanics written by Michael J Cloud and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-10 with Technology & Engineering categories.
'A strong point of this book is its coverage of tensor theory, which is herein deemed both more readable and more substantial than many other historic continuum mechanics books. The book is self-contained. It serves admirably as a reference resource on fundamental principles and equations of tensor mathematics applied to continuum mechanics. Exercises and problem sets are useful for teaching … The book is highly recommended as both a graduate textbook and a reference work for students and more senior researchers involved in theoretical and mathematical modelling of continuum mechanics of materials. Key concepts are well described in the text and are supplemented by informative exercises and problem sets with solutions, and comprehensive Appendices provide important equations for ease of reference.'Contemporary PhysicsA tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions.This book provides a clear, concise, and self-contained treatment of tensors and tensor fields. It covers the foundations of linear elasticity, shell theory, and generalized continuum media, offers hints, answers, and full solutions for many of the problems and exercises, and Includes a handbook-style summary of important tensor formulas.The book can be useful for beginners who are interested in the basics of tensor calculus. It also can be used by experienced readers who seek a comprehensive review on applications of the tensor calculus in mechanics.
Solutions Of Exercises Of Introduction To Differential Geometry Of Space Curves And Surfaces
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Author : Taha Sochi
language : en
Publisher: Independently Published
Release Date : 2019-01-21
Solutions Of Exercises Of Introduction To Differential Geometry Of Space Curves And Surfaces written by Taha Sochi and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-21 with Mathematics categories.
This book contains the solutions of the exercises of my book: Introduction to Differential Geometry of Space Curves and Surfaces. These solutions are sufficiently simplified and detailed for the benefit of readers of all levels particularly those at introductory level.
General Relativity Simplified Assessed
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Author : Taha Sochi
language : en
Publisher: Taha Sochi
Release Date : 2022-08-17
General Relativity Simplified Assessed written by Taha Sochi and has been published by Taha Sochi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-17 with Science categories.
This book is about the general theory of relativity which is concisely labeled as general relativity. The book is the result of a rather extensive view to the literature of this theory over most of its lifetime reflecting various stages of its development. The book contains 129 solved problems as well as 606 exercises whose detailed solutions are published in another book that accompanies the present book. The book also includes a detailed index and many cross references. The book can be used as an introduction to general relativity at undergraduate and graduate levels. Unlike most other books on general relativity which are mostly dedicated to the presentation, justification, application and validation of the formalism of the theory (and hence rather minor attention is usually paid to the interpretation and epistemology of the theory), this book is primarily interested in the interpretative and epistemological aspects of the theory.
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
Principles And Applications Of Tensor Analysis
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Author : Matthew S Smith
language : en
Publisher:
Release Date : 2012-03-01
Principles And Applications Of Tensor Analysis written by Matthew S Smith and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-01 with categories.