Ebook: Tensor Analysis and Continuum Mechanics

This book is designed for students in engineering, physics and mathematics. The material can be taught from the beginning of the third academic year. It could also be used for self­ study, given its pedagogical structure and the numerous solved problems which prepare for modem physics and technology. One of the original aspects of this work is the development together of the basic theory of tensors and the foundations of continuum mechanics. Why two books in one? Firstly, Tensor Analysis provides a thorough introduction of intrinsic mathematical entities, called tensors, which is essential for continuum mechanics. This way of proceeding greatly unifies the various subjects. Only some basic knowledge of linear algebra is necessary to start out on the topic of tensors. The essence of the mathematical foundations is introduced in a practical way. Tensor developments are often too abstract, since they are either aimed at algebraists only, or too quickly applied to physicists and engineers. Here a good balance has been found which allows these extremes to be brought closer together. Though the exposition of tensor theory forms a subject in itself, it is viewed not only as an autonomous mathematical discipline, but as a preparation for theories of physics and engineering. More specifically, because this part of the work deals with tensors in general coordinates and not solely in Cartesian coordinates, it will greatly help with many different disciplines such as differential geometry, analytical mechanics, continuum mechanics, special relativity, general relativity, cosmology, electromagnetism, quantum mechanics, etc ..

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This volume combines an illustration of the theory of tensors and the foundations of continuum mechanics.

This work lays the groundwork for more technical subjects as strength of materials, plasticity, viscoelasticity, and nonlinear continuum mechanics. The material is presented with great pedagogical care, a summary of formulae and a glossary of symbols are provided, as well as ninety-five solved problems. The book is suitable as a text for third year students of mathematics, physics and engineering, and for anyone wishing to acquire insight into the mathematics of mechanics, the mathematics of physics, the mathematics of engineering, continuum mechanics, elasticity and viscoelasticity, linear and multilinear algebra, or matrix theory.

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This volume combines an illustration of the theory of tensors and the foundations of continuum mechanics.

This work lays the groundwork for more technical subjects as strength of materials, plasticity, viscoelasticity, and nonlinear continuum mechanics. The material is presented with great pedagogical care, a summary of formulae and a glossary of symbols are provided, as well as ninety-five solved problems. The book is suitable as a text for third year students of mathematics, physics and engineering, and for anyone wishing to acquire insight into the mathematics of mechanics, the mathematics of physics, the mathematics of engineering, continuum mechanics, elasticity and viscoelasticity, linear and multilinear algebra, or matrix theory.

Content:
Front Matter....Pages i-xvi
Tensors....Pages 1-145
Lagrangian and Eulerian Descriptions....Pages 147-169
Deformations....Pages 171-261
Kinematics of Continua....Pages 263-313
Fundamental Laws; The Principle of Virtual Work....Pages 315-454
Linear Elasticity....Pages 455-540
Back Matter....Pages 541-591

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This volume combines an illustration of the theory of tensors and the foundations of continuum mechanics.

This work lays the groundwork for more technical subjects as strength of materials, plasticity, viscoelasticity, and nonlinear continuum mechanics. The material is presented with great pedagogical care, a summary of formulae and a glossary of symbols are provided, as well as ninety-five solved problems. The book is suitable as a text for third year students of mathematics, physics and engineering, and for anyone wishing to acquire insight into the mathematics of mechanics, the mathematics of physics, the mathematics of engineering, continuum mechanics, elasticity and viscoelasticity, linear and multilinear algebra, or matrix theory.

Content:
Front Matter....Pages i-xvi
Tensors....Pages 1-145
Lagrangian and Eulerian Descriptions....Pages 147-169
Deformations....Pages 171-261
Kinematics of Continua....Pages 263-313
Fundamental Laws; The Principle of Virtual Work....Pages 315-454
Linear Elasticity....Pages 455-540
Back Matter....Pages 541-591
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