rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Tensor calculus for physics
    sub title: a concise guide
  name:
    name part: Neuenschwander, Dwight E.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: mdu
    date issued: 2026
    copyright date: 2026
    edition: Second edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    form: regular print
    extent: xii, 235 pages : illustrations ; 23 cm
  abstract: "Most of physics involves relationships between observables. When those observables include spatial direction information, tensors are used. The jet stream rushing horizontally overhead stimulates the vertical convection that spawns thunderstorms. An unbalanced automobile wheel spinning about a horizontal axis produces a wobble in the vertical plane. When coordinates change in the translation from one system to another, tensors change according to the same rules. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are introduced to tensors in special-case applications. In Classical Mechanics they meet the "inertia tensor," in Electricity and Magnetism the "polarization tensor." This piecemeal approach can set the student up for misconceptions when they have to learn about tensors in more advanced studies in physics, mathematics, and related fields. This book provides a bottom-up approach by explaining the logic of tensors in the contexts that make the logic worth pursuing"-- Provided by publisher.
  abstract: "An essential guide to understanding tensors through physics.Understanding tensors is essential for physics students who encounter phenomena where direction matters. A jet stream rushing overhead can trigger vertical convection that leads to thunderstorms. An unbalanced car wheel spinning around a horizontal axis produces a wobble in the vertical plane. Astronauts orbiting Earth observe an electrostatic field as a magnetic one. In all these cases, tensors offer a language that captures directional relationships with precision. In the second edition of Tensor Calculus for Physics, Dwight E. Neuenschwander provides an accessible guide that shows how tensor logic arises naturally from physical problems.Tensors' true elegance lies in how they transform: when coordinates change from one system to another, tensors follow the same rules, allowing physical laws to retain their form across perspectives. Students are often introduced to tensors piecemeal through the inertia tensor in classical mechanics or the polarization tensor in electricity and magnetism. While useful, this fragmented approach does not prepare the student for tensor features such as affine connections, dual basis vectors, and covariant derivatives they will encounter in advanced studies such as general relativity, continuum mechanics, or non-Euclidean geometry. This concise guide builds from the ground up, providing a clear, step-by-step progression that embeds tensors in contexts where their power becomes self-evident.This extensively revised second edition incorporates more illustrative examples and carefully designed homework problems to strengthen understanding. Now accompanied by a solutions manual, this edition is an ideal resource for courses in general relativity, covariant electrodynamics, continuum mechanics, fluid dynamics, materials science, and any discipline where tensors illuminate the structure of physical reality"-- Provided by publisher.
  table of contents: Machine generated contents note: Contents -- Preface -- Acknowledgments -- 1. 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 -- 2. 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 -- 3. The Metric Tensor -- 3.1. The Distinction between Distance and Coordinate Displacement -- 3.2. Relative Motion -- 3.3. Upper and Lower Indices -- 3.4. Converting between Vectors and Duals -- 3.5. Contravariant, Covariant, and "Ordinary" Vectors -- 3.6. Tensor Algebra -- 3.7. Tensor Densities Revisited -- 3.8. Discussion Questions and Exercises -- 4. Derivatives of Tensors -- 4.1. Signs of Trouble -- 4.2. The Affine Connection -- 4.3. The Newtonian Limit -- 4.4. Transformation of the Affine Connection -- 4.5. The Covariant Derivative -- 4.6. Relation of the Affine Connection to the Metric Tensor -- 4.7. Divergence, Curl, and Laplacian with Covariant Derivatives -- 4.8. Discussion Questions and Exercises -- 5. Curvature -- 5.1. What Is Curvature? -- 5.2. The Riemann Tensor -- 5.3. Measuring Curvature -- 5.4. Linearity in the Second Derivative -- 5.5. Discussion Questions and Exercises -- 6. Covariance Applications -- 6.1. Covariant Elec…
  note: Dwight E. Neuenschwander.
  note: Includes bibliographical references and index.
  subject:
    topic: Calculus of tensors
  subject:
    topic: Physics
  subject:
    topic: Calcul tensoriel
  subject:
    topic: MATHEMATICS / General
  subject:
    topic: SCIENCE / Physics / General
  subject:
    topic: Linear and multilinear algebra; matrix theory -- Basic linear algebra -- Multilinear algebra, tensor products
  classification: QC20.7.C28 N48 2026
  classification: 515/.63
  classification: MAT000000
  classification: SCI055000
  classification: 15A69
  related item:
    title info:
      title: Tensor calculus for physics
    name:
      name part: Neuenschwander, Dwight E.
    origin info:
      publisher: Baltimore : Johns Hopkins University Press, 2026
      edition: Second edition
    identifier: (DLC) 2025054432
  identifier: 9781421454474
  identifier: 1421454475
  identifier: 9781421454481
  identifier: 1421454483
  identifier: 9781421454498
  identifier: 2025054431
  record info:
    record content source: DLC
    record creation date: 251231
    record change date: 20260611154436.5
    record identifier: in00005789234
    language of cataloging:
      language term: eng