Tensor Calculus for Physics: A Concise Guide

by Dwight E. Neuenschwander

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 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.

Genres: Physics, Mathematics, Science, Textbooks

Kindle Edition

First published September 20, 2014

Reviews

[Andrew Rosen · Rating 5 out of 5]

Going into this book, I had little intuition (mathematical or otherwise) what a tensor was, and, now that I have finished I book, I must say it was a solid introduction into the subject. Certain parts, such as the derivation of the Einstein Field Equations, did feel a bit un-rigorous at times, but I am no expert in the field nor did I expect to become one from this book, rather I only sought to become acquainted with the subject. The last chapter on r-forms I must say I found confusing, but I am convinced that the issue lies in the difficultly of the subject at hand (i.e. the reader) and not the text. I must also add that the inclusion of practice problems at the end of each chapter is something I always appreciate :)

Overall, it was exactly as the title says - a concise introduction to tensor calculus.

Edit: The book didn't actually take a book for me to read (I took a gander into Griffith's Electrodynamics, which I would highly recommend); I read the first half in about a week and then the second in about the same amount of time.

[Rodney Bond · Rating 1 out of 5]

I enjoyed perusing this book. I give it only one star because extremely few people would have a non-trivial interest (probably only persons with PhDs in physics.) While it did answer the questions that I had, it took a lot of studying about other math-physics material to get the answer.

[Giorgos Vachtanidis · Rating 5 out of 5]

A very good book for physicists who are learning Tensor Calculus, but it's not a book for starting. It would be best for the potential reader to already have a first touch with tensors.