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Tensor Algebra and Tensor Analysis for Engineers

2009-04-30 Technology & Engineering
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Release : 2009-04-30
Genre : Technology & Engineering
Kind : eBook
Book Rating : 075/5 ( reviews)

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Book Synopsis Tensor Algebra and Tensor Analysis for Engineers by : Mikhail Itskov

Download or read book Tensor Algebra and Tensor Analysis for Engineers written by Mikhail Itskov. This book was released on 2009-04-30. Available in PDF, EPUB and Kindle. Book excerpt: 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 Algebra and Tensor Analysis for Engineers

2012-08-13 Science
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Release : 2012-08-13
Genre : Science
Kind : eBook
Book Rating : 791/5 ( reviews)

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Book Synopsis Tensor Algebra and Tensor Analysis for Engineers by : Mikhail Itskov

Download or read book Tensor Algebra and Tensor Analysis for Engineers written by Mikhail Itskov. This book was released on 2012-08-13. Available in PDF, EPUB and Kindle. Book excerpt: 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 consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area. This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.

Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds

2017-04-18 Science
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Release : 2017-04-18
Genre : Science
Kind : eBook
Book Rating : 649/5 ( reviews)

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Book Synopsis Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds by : Uwe Mühlich

Download or read book Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds written by Uwe Mühlich. This book was released on 2017-04-18. Available in PDF, EPUB and Kindle. Book excerpt: 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 Algebra And Analysis For Engineers: With Applications To Differential Geometry Of Curves And Surfaces

2023-02-27 Mathematics
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Release : 2023-02-27
Genre : Mathematics
Kind : eBook
Book Rating : 821/5 ( reviews)

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Book Synopsis Tensor Algebra And Analysis For Engineers: With Applications To Differential Geometry Of Curves And Surfaces by : Paolo Vannucci

Download or read book Tensor Algebra And Analysis For Engineers: With Applications To Differential Geometry Of Curves And Surfaces written by Paolo Vannucci. This book was released on 2023-02-27. Available in PDF, EPUB and Kindle. Book excerpt: In modern theoretical and applied mechanics, tensors and differential geometry are two almost essential tools. Unfortunately, in university courses for engineering and mechanics students, these topics are often poorly treated or even completely ignored. At the same time, many existing, very complete texts on tensors or differential geometry are so advanced and written in abstract language that discourage young readers looking for an introduction to these topics specifically oriented to engineering applications.This textbook, mainly addressed to graduate students and young researchers in mechanics, is an attempt to fill the gap. Its aim is to introduce the reader to the modern mathematical tools and language of tensors, with special applications to the differential geometry of curves and surfaces in the Euclidean space. The exposition of the matter is sober, directly oriented to problems that are ordinarily found in mechanics and engineering. Also, the language and symbols are tailored to those usually employed in modern texts of continuum mechanics.Though not exhaustive, as any primer textbook, this volume constitutes a coherent, self-contained introduction to the mathematical tools and results necessary in modern continuum mechanics, concerning vectors, 2nd- and 4th-rank tensors, curves, fields, curvilinear coordinates, and surfaces in the Euclidean space. More than 100 exercises are proposed to the reader, many of them complete the theoretical part through additional results and proofs. To accompany the reader in learning, all the exercises are entirely developed and solved at the end of the book.

Vector and Tensor Analysis with Applications

2012-08-28 Mathematics
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Release : 2012-08-28
Genre : Mathematics
Kind : eBook
Book Rating : 904/5 ( reviews)

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Book Synopsis Vector and Tensor Analysis with Applications by : A. I. Borisenko

Download or read book Vector and Tensor Analysis with Applications written by A. I. Borisenko. This book was released on 2012-08-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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