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This is the fifth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. In accordance with the contemporary way of scientific publication, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. As such, this new edition also discusses such modern topics of solid mechanics as electro- and magnetoelasticity. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this textbook addresses graduate students as well as scientists working in this field and in particular dealing with multi-physical problems. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

Mechanics. --- Mechanics, Applied. --- Global differential geometry. --- Matrix theory. --- Solid Mechanics. --- Differential Geometry. --- Linear and Multilinear Algebras, Matrix Theory. --- Classical Mechanics. --- Geometry, Differential --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Tensor algebra. --- Algebra, Tensor --- Algebras, Linear --- Tensor products --- Differential geometry. --- Algebra. --- Mathematics --- Mathematical analysis --- Differential geometry

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This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course. The book is divided into three main parts, all based on lecture notes that have been refined for classroom teaching over the past two decades. Part I provides students with a comprehensive overview of tensors. Part II links the very introductory first part and the relatively advanced third part, demonstrating the important intermediate-level applications of tensor analysis. Part III contains an extended discussion of general relativity, and includes material useful for students interested primarily in quantum field theory and quantum gravity. Tailored to the undergraduate, this textbook offers explanations of technical material not easily found or detailed elsewhere, including an understandable description of Riemann normal coordinates and conformal transformations. Future theoretical and experimental physicists, as well as mathematicians, will thus find it a wonderful first read on the subject.

Mathematical physics. --- Mathematical Methods in Physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Classical Electrodynamics. --- Mathematical Physics. --- Numerical and Computational Physics, Simulation. --- Quantum Field Theories, String Theory. --- Physical mathematics --- Physics --- Mathematics --- Tensor algebra. --- Algebra, Tensor --- Algebras, Linear --- Tensor products --- Physics. --- Gravitation. --- Optics. --- Electrodynamics. --- Quantum field theory. --- String theory. --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Dynamics --- Light --- Matter --- Antigravity --- Centrifugal force --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Properties