Tensor Calculus Made Simple

First, this book is misleadingly titled. It is not about tensor calculus. It is about tensor algebra. It does include renderings of a few differentiation and integration formulas in Einstein summation notation but these are valid only for Cartesian coordinates and are a far cry from tensor calculus. Secondly, this book is not an introduction to tensor algebra. It is a collection of selected facts and calculation techniques organized by category. You can memorize these facts and techniques but you won't gain any understanding thereby. The pedagogical approach used in this book is basically the grammar school method of teaching mathematics as a set of calculations to be memorized. This approach hides the true beauty and power of tensors. Tensors extend the reach of geometry and hence calculus to non-Euclidean spaces. That's why Einstein needed tensor calculus for general relativity. If you want to understand why and how this is so, take any or several of the excellent introductions to tensor calculus available on YouTube.

I love this book. I am an electrical engineer (like the author). I have a good background in vector calculus, but other books I have, had poor explanations of the important concepts. Many other books spend too much time covering the fundamentals of vectors and matrices in painful detail, then have a poor introduction to tensors. Also, some books lose the reader by requiring them to learn relativity (or some other application of tensors) at the same time as being introduced to this subject. This book is about TENSORS. It is focused. It has great explanations, while maintaining mathematical rigor.I used this book for self study. I skimmed through Chapter 1, and focused on Chapters 2 through 7. When I went looking for a book on this subject, I was looking for a "programmed text" format. I find that format is a great way to be introduced to mathematically concepts. This is how I learned Laplace Transforms. This book is not a programmed text, but it does introduce concepts in a logical, step by step, way.The only negative is that I wish the author would provide solutions to the exercises (either in a separate book or online). For us people who self study, it would provide reenforcement.

The book is quite terse and is often not that simple. There are too few examples. Definitions are given but seldom well motivated. There are exercises but you need a different book to verify your answers. Footnotes are held to a final chapter outside of their context. I frequently found myself needing to consult outside material. The focus was too much on the notation rather than on meaning or utility. I like brevity, but not at the expense of clarity and understanding. (For reference, I took linear algebra, vector analysis, differential equations, and other classes in university several years ago, but not any courses covering tensors.)The book looked nice on my kindle. It was very legible. I liked the explanations of the coordinate systems and their diagrams. I learned new things about, for example, the permutation tensors and other topics. But, the book could have been more helpful.Topics that could be explained or motivated better include covariance, contravariance, Chrostoffel symbols, the metric tensor, and more.

Amended review: This book can provide the interested reader with a quick overview of vectors, tensors, inner products, tensor multiplication, and coordinate systems. It does require previous study of simple trigonometry and partial differential equations. It overlaps with subjects covered in the second year of calculus and linear algebra. Advanced high school students and college students interested in engineering and physics may find it is a useful supplement and review book for their standard texts. There are many exercises that range from easy to difficult. The author has now posted the solutions on the web. This now makes the book a wonderful resource for self learners. I would like to thank the author for taking the time in providing this solution set.

A total loss. The book just throws facts at you with very little explanation. If you have a thirst for understanding, this isn’t the book you’ll want. Just a ton of seemingly unrelated information regarding tensors that never really comes together.

I was asked if I recommend this book to undergraduates trying to cope with the maze of indices common in tensor algebra and calculus. The book is suitable to get started; however, it offers no illustrative examples within the text, and in general lays out the material as a collection of facts and theorems. While the approach is practical and gets a new student acquainted with the tensor notation and related theory, it does hide the powerful abstraction that lies beneath. Lastly, this book deals primarily with tensor algebra and elements of calculus are thinly discussed. Overall, a good supplement to many other standard texts, especially for the practicing scientist and engineer not keenly interested in complete mathematical rigor.

I'm sure that he really does "make it simple" for a well-versed mathematician. But, I do not know group theory or several other precursors, so I just gave up on it. Not for the casual reader.

A great start to the introduction to tensors. I bought both this book and the principles by the same author. This book does a great job explaining both the mathematical and physical significance. Sochi goes the extra mile to give a crash course in prerequisite material in the subject before hitting the new stuff. The format is expressive and not so dry like an ordinary textbook. To top it off the problem sets for each chapter usually start off with conceptual and historical questions before getting to the nitty gritty math problems. That gets the reader to go back and take closer looks for each chapter. I highly recommend it.

A self-published book without proper proof-reading. Does not explain what a tensor is anywhere in the book. Does not define what a tensor is. Just give a list of rules on how to label tensors. No numerical example in the entire book. Stresses how useful tensor maths is in physics and engineering, yet does not have a single example of such use. Diagrams that are described as in colour are in b&w. I will not be buying any books by this author again. Much better to buy a used copy of work/textbook by an established professor of maths or engineering instead of from a self-publicist.

If you want a simple introduction to the concept, practical use and manipulation of tensors, avoid this book. It is largely a set of definitions. There is little connection to the physical world, and no examples at all of the use of tensors in actual engineering.

Good coverage of the basic theory. Too few practical examples of using tensors in calculations. Very 'dry'.

Good student text. Well laid out with clear and detailed explanations of notation.

Expone los conceptos de forma muy detallada lo que facilita su comprensión y manejo. Muy claro y útil. Recomendable.