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" A primer in tensor analysis and relativity / "
Ilya L. Shapiro.
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BL
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862755
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| Main Entry
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Shapiro, I. L., (Ilya Lvovitch)
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| Title & Author
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A primer in tensor analysis and relativity /\ Ilya L. Shapiro.
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| Publication Statement
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Cham :: Springer,, [2019]
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, ©2019
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| Series Statement
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Undergraduate lecture notes in physics,
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1 online resource :: illustrations
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| ISBN
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3030268942
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: 3030268950
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: 3030268969
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: 9783030268947
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: 9783030268954
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: 9783030268961
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9783030268947
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Includes bibliographical references and index.
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| Contents
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Intro; Preface; Reference; Acknowledgements; Preliminary Observations and Notations; Contents; Part I Tensor Algebra and Analysis; 1 Linear Spaces, Vectors, and Tensors; 1.1 Notion of Linear Space; 1.2 Vector Basis and Its Transformation; 1.3 Scalar, Vector, and Tensor Fields; 1.4 Orthonormal Basis and Cartesian Coordinates; 1.5 Covariant and Mixed Vectors and Tensors; 1.6 Orthogonal Transformations; References; 2 Operations over Tensors, Metric Tensor; 3 Symmetric, Skew(Anti) Symmetric Tensors, and Determinants; 3.1 Definitions and General Considerations; 3.2 Completely Antisymmetric Tensors
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10.4 Solutions to Exercises from 410.5 Solutions to Exercises from 5; 10.6 Solutions to Exercises from 6; 10.7 Solutions to Exercises from 7; 10.8 Solutions to Exercises from 8; Part II Elements of Electrodynamics and Special Relativity; 11 Maxwell Equations and Lorentz Transformations; 11.1 Maxwell Equations and Lorentz Force; 11.2 Universal Speed of Electromagnetic Wave; 11.3 Invariant Interval and Minkowski Space; 11.4 Lorentz Transformations; References; 12 Laws of Relativistic Mechanics; 12.1 Relativistic Kinematics; 12.2 Relativistic Dynamics of a Free Particle
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12.3 Charged Particle in an External Electromagnetic Field12.3.1 Gauge Invariance of the Particle Action; 12.3.2 Continuous Description and Electric Current; References; 13 Maxwell Equations in Relativistic Form; 13.1 Action and Relativistic Equations for Aµ; 13.1.1 Minimal Action Principle for Fields; 13.2 Maxwell Equations in Relativistic Form; 13.2.1 Invariant Action for the Electromagnetic Field; 13.2.2 Relativistic Form of Maxwell Equations; 13.2.3 Lorentz Transformation of Electromagnetic Field; 13.3 Energy-Momentum Tensor
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3.3 Determinants3.4 Applications to Vector Algebra; 3.5 Symmetric Tensor of Second Rank and Its Reduction to Principal Axes; References; 4 Curvilinear Coordinates, Local Coordinate Transformations; 4.1 Curvilinear Coordinates and Change of Basis; 4.2 Polar Coordinates on the Plane; 4.3 Cylindric and Spherical Coordinates; 5 Derivatives of Tensors, Covariant Derivatives; Reference; 6 Grad, div, rot, and Relations Between Them; 6.1 Basic Definitions and Relations; 6.2 On the Classification of Differentiable Vector Fields; References
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| Abstract
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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.
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Calculus of tensors.
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Relativity (Physics)
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Tensor algebra.
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Calculus of tensors.
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Relativity (Physics)
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Tensor algebra.
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| Dewey Classification
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515/.63
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| LC Classification
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QC20.7.C28S53 2019eb
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