Tensor calculus for physics : a concise guide /
"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...
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Baltimore :
Johns Hopkins University Press,
2026.
|
| Edition: | Second edition. |
| Subjects: |
| Summary: | "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. "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. |
|---|---|
| Physical Description: | xii, 235 pages : illustrations ; 23 cm |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781421454474 1421454475 9781421454481 1421454483 |