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Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics

31 May 2013

**Mikhail Itskov - Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics (3rd edition)**

Published: 2012-08-13 | ISBN: 3642308783 | PDF | 284 pages | 3 MB

There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the co

31 May 2013

Published: 2012-08-13 | ISBN: 3642308783 | PDF | 284 pages | 3 MB

There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the co

Ricci and Levi-Civita's Tensor Analysis Paper

12 June 2011

**Ricci and Levi-Civita's Tensor Analysis Paper**

This is a translation of "Methodes de calcul differential absoluetleurs applications," by G. Ricci and T. Levi-Civita, Mathematische Annalen, vol. 54 A900). This memoire is one of the most influential and important in the history of both differential geometry and mathematical physics. For example, it seems to have been the basic document from which Einstein learned the tensor analysis that he used in the creation of General Relativity. My immediate aim is, of course, to make this key paper - which is still very readable and informative - available to the scientific community. To enhance its usefulness, I have added Remarks which link the material with contemporary differential geometry and physics. I have also modernized the notations and terminology, e.g. using the summation convention, and substituting the term "Tensor Analysis" for "Absolute Differential Calculus." I have also added a few topics to the main text, e.g. the notion of "mixed tensor," which seemed useful....

12 June 2011

1975 | 261 | ISBN: 0915692112 | DJVU | 1 Mb

This is a translation of "Methodes de calcul differential absoluetleurs applications," by G. Ricci and T. Levi-Civita, Mathematische Annalen, vol. 54 A900). This memoire is one of the most influential and important in the history of both differential geometry and mathematical physics. For example, it seems to have been the basic document from which Einstein learned the tensor analysis that he used in the creation of General Relativity. My immediate aim is, of course, to make this key paper - which is still very readable and informative - available to the scientific community. To enhance its usefulness, I have added Remarks which link the material with contemporary differential geometry and physics. I have also modernized the notations and terminology, e.g. using the summation convention, and substituting the term "Tensor Analysis" for "Absolute Differential Calculus." I have also added a few topics to the main text, e.g. the notion of "mixed tensor," which seemed useful....

Tensor Analysis with Applications in Mechanics

30 January 2011**Tensor Analysis with Applications in Mechanics** by Leonid P. Lebedev, Michael J. Cloud
World Scientific Publishing Company | 2010 | ISBN: 9814313122 | 380 pages | PDF | 12 MB
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.

30 January 2011

Manifolds, Tensor Analysis and Applications

23 July 2010**Manifolds, Tensor Analysis and Applications**

23 July 2010

Springer 2001 | 617 | ISBN: 0201101688 | PDF | 5

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 mechanics, electromagnetism, plasma dynamics and control theory are given using both invariant and index notation. The prerequisites required are solid undergraduate courses in linear algebra and advanced calculus. ...Tensor Calculus: A Concise Course

6 June 2011

**Tensor Calculus: A Concise Course**

425 pages | Aug 31 2010 |ISBN:0486428311 | PDF | 5.5 Mb

This book will prove to be a good introduction, both for the physicist who wishes to make applications and for the mathematician who prefers to have a short survey before taking up one of the more voluminous textbooks on differential geometry."--MathSciNet (Mathematical Reviews on the Web), American Mathematical Society A compact exposition of the fundamental results in the theory of tensors, this text also illustrates the power of the tensor technique by its applications to differential geometry, elasticity, and relativity

6 June 2011

425 pages | Aug 31 2010 |ISBN:0486428311 | PDF | 5.5 Mb

This book will prove to be a good introduction, both for the physicist who wishes to make applications and for the mathematician who prefers to have a short survey before taking up one of the more voluminous textbooks on differential geometry."--MathSciNet (Mathematical Reviews on the Web), American Mathematical Society A compact exposition of the fundamental results in the theory of tensors, this text also illustrates the power of the tensor technique by its applications to differential geometry, elasticity, and relativity

Ralph Abraham, Jerrold E. Marsden, Manifolds, Tensor Analysis, and Applications

6 May 2013

**Ralph Abraham, Jerrold E. Marsden, Manifolds, Tensor Analysis, and Applications**

ISBN: 0387967907 | edition 1993 | PDF | 617 pages | 8 mb

6 May 2013

ISBN: 0387967907 | edition 1993 | PDF | 617 pages | 8 mb

Applied Elasticity: Matrix and Tensor Analysis of Elastic Continua

13 May 2013

**Applied Elasticity: Matrix and Tensor Analysis of Elastic Continua**

John D. Renton,

2003 | 203 Pages | ISBN: 1898563853 | PDF | 11 MB

13 May 2013

John D. Renton,

2003 | 203 Pages | ISBN: 1898563853 | PDF | 11 MB

Schaums Outline Of Tensor Calculus

6 April 2010

**Schaum's Outline of Tensor Calculus**

McGraw-Hill | English | 1988-04-01 | ISBN: 0070334846 | 224 pages | PDF | 16,3 MB

This lucid introduction for undergraduates and graduates proves fundamental for pactitioners of theoretical physics and certain areas of engineering, like aerodynamics and fluid mechanics, and exteremely valuable for mathematicians. This study guide teaches all the basics and efective problem-solving skills too.

6 April 2010

McGraw-Hill | English | 1988-04-01 | ISBN: 0070334846 | 224 pages | PDF | 16,3 MB

This lucid introduction for undergraduates and graduates proves fundamental for pactitioners of theoretical physics and certain areas of engineering, like aerodynamics and fluid mechanics, and exteremely valuable for mathematicians. This study guide teaches all the basics and efective problem-solving skills too.

Tensor Geometry: The Geometric Viewpoint and Its Uses (2nd edition)

13 April 2013

**Tensor Geometry: The Geometric Viewpoint and Its Uses (2nd edition)**

C. T. J. Dodson, Timothy Poston

Published: 1991-10 | ISBN: 038752018X, 354052018X | PDF | 432 pages | 19 MB

13 April 2013

C. T. J. Dodson, Timothy Poston

Published: 1991-10 | ISBN: 038752018X, 354052018X | PDF | 432 pages | 19 MB

Spin-Curvature and the Unification of Fields in a Twisted Space

24 September 2010

**Spin-Curvature and the Unification of Fields in a Twisted Space**

Swedish physics archive | 2008 | ISBN: 918591701X | 80 pages | PDF | 12 MB

The book draws theoretical findings for spin-curvature and the unification of fields in a twisted space. A space twist, represented through the appropriate formalism, is related to the anti-symmetric metric tensor. Kaluza's theory is extended and given an appropriate integrability condition. Both matter and the isotropic electromagnetic field are geometrized through common field equations: trace-free field equations giving the energy-momentum tensor for such an electromagnetic field solely via the (generalized) Ricci curvature tensor and scalar are obtained.

24 September 2010

Swedish physics archive | 2008 | ISBN: 918591701X | 80 pages | PDF | 12 MB

The book draws theoretical findings for spin-curvature and the unification of fields in a twisted space. A space twist, represented through the appropriate formalism, is related to the anti-symmetric metric tensor. Kaluza's theory is extended and given an appropriate integrability condition. Both matter and the isotropic electromagnetic field are geometrized through common field equations: trace-free field equations giving the energy-momentum tensor for such an electromagnetic field solely via the (generalized) Ricci curvature tensor and scalar are obtained.