Tensor Calculus Made Simple

This book does a good job of what my title says. It begins with a quick review of vector analysis. It then goes through the definitions and rules. What it doesn't do is provide any intuitive feel for why the rules are what they are. As a result, the presentation and subject matter are pretty dry. Fortunately for me, I've been using vector analysis and various coordinate transformations for over 60 years, so I have a sense for a lot of the "whys." I also covered some tensor analysis, notably in general relativity, in grad school, but I NEVER used it again. Now that I'm retired, I'm going back and back-filling.I gave the book 5 stars because what it does, it does well, and the cost is very reasonable in this age of overpriced textbooks. I do not recommend the Kindle version. I have it as well as the hardcopy, and the hardcopy is much easier to read. The Kindle edition gets very sloppy with equation layout at times.The book includes some detailed exercises, that are worth the trouble to go through. I recommend buying the answer-book. I have that in Kindle form, which is good enough.

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.

Good approachable introduction to the topic that is less caught up in terminology. Easy to read. Recommend.

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.

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.

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.