![]() ![]() Two-Index Tensors 2.1 The Electric Susceptibility Tensor 2.2 The Inertia Tensor 2.3 The Electric Quadrupole Tensor 2.4 The Electromagnetic Stress Tensor 2.5 Transformations of Two-Index Tensors 2.6 Finding Eigenvectors and Eigenvalues 2.7 Two-Index Tensor Components as Products of Vector Components 2.8 More Than Two Indices 2.9 Integration Measures and Tensor Densities 2.10 Discussion Questions and Exercises Chapter 3. Tensors Need Context 1.1 Why Aren’t Tensors Defined by What They Are? 1.2 Euclidean Vectors, without Coordinates 1.3 Derivatives of Euclidean Vectors with Respect to a Scalar 1.4 The Euclidean Gradient 1.5 Euclidean Vectors, with Coordinates 1.6 Euclidean Vector Operations with and without Coordinates 1.7 Transformation Coefficients as Partial Derivatives 1.8 What Is a Theory of Relativity? 1.9 Vectors Represented as Matrices 1.10 Discussion Questions and Exercises Chapter 2. “Nonsense,” said Heisenberg, “space is blue and birds fly through it.” –Felix Bloch Contents Preface Acknowledgments Chapter 1. I had just read Weyl’s book Space, Time, and Matter, and under its influence was proud to declare that space was simply the field of linear operations. To my parents, Dwight and Evonne with gratitude We were on a walk and somehow began to talk about space. Johns Hopkins University Press uses environmentally friendly book materials, including recycled text paper that is composed of at least 30 percent post-consumer waste, whenever possible. ![]() For more information, please contact Special Sales at 41 or. Special discounts are available for bulk purchases of this book. ![]() Neuenschwander © 2015 Johns Hopkins University Press All rights reserved. Tensor Calculus for Physics Tensor Calculus for Physics A Concise Guide Dwight E. 8.5 An Application to Physics: Maxwell’s Equations. 8.3 Exterior Products and Differential Forms. 7.4 Derivatives of Basis Vectors and the Affine Connection. 7.2 Metrics on Manifolds and Their Tangent Spaces. 7.1 Tangent Spaces, Charts, and Manifolds. 4.7 Divergence, Curl, and Laplacian with Covariant Derivatives. 4.6 Relation of the Affine Connection to the Metric Tensor. 4.4 Transformation of the Affine Connection. 3.5 Contravariant, Covariant, and “Ordinary” Vectors. 3.4 Converting between Vectors and Duals. 3.1 The Distinction between Distance and Coordinate Displacement. 2.9 Integration Measures and Tensor Densities. 2.6 Finding Eigenvectors and Eigenvalues. 2.5 Transformations of Two-Index Tensors. 1.7 Transformation Coefficients as Partial Derivatives. 1.6 Euclidean Vector Operations with and without Coordinates. 1.3 Derivatives of Euclidean Vectors with Respect to a Scalar. 1.2 Euclidean Vectors, without Coordinates. ![]() 1.1 Why Aren’t Tensors Defined by What They Are?. Physical quantities are (mostly) calculated and observed within a coordinate system, and depend on it.Table of contents : Title Page. ![]()
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