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Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics
31 May 2013

Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics
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
Ricci and Levi-Civita's Tensor Analysis Paper
12 June 2011

Ricci and Levi-Civita's Tensor Analysis Paper

Ricci and Levi-Civita's Tensor Analysis Paper

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

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.
Tensor Calculus: A Concise Course
6 June 2011

Tensor Calculus: A Concise Course
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
Schaums Outline Of Tensor Calculus
6 April 2010

Schaum's Outline of Tensor Calculus


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.
Manifolds, Tensor Analysis and Applications
23 July 2010

Manifolds, Tensor Analysis and Applications
Manifolds, Tensor Analysis and Applications
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. ...
Applied Elasticity: Matrix and Tensor Analysis of Elastic Continua
13 May 2013


Applied Elasticity: Matrix and Tensor Analysis of Elastic Continua

Applied Elasticity: Matrix and Tensor Analysis of Elastic Continua
John D. Renton,
2003 | 203 Pages | ISBN: 1898563853 | PDF | 11 MB
Tensor Geometry: The Geometric Viewpoint and Its Uses (2nd edition)
13 April 2013


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

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
Ralph Abraham, Jerrold E. Marsden, Manifolds, Tensor Analysis, and Applications
6 May 2013


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

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

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

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.