A Student's Guide to Vectors and Tensors (Student's Guides)

An EXCELLENT book! Let me put this up front so it doesn't get missed. You MUST download the errata sheet on the website given in the book. There are enough typos and errors to make a few sections hard to follow, but it does not detract from the quality. The errata sheet will however clear up some math issues. Did I mention it is an excellent book?! I've owned this since 2018...it is very dog eared now. Have read it multiple times, each time I get better insight into Tensors (including vectors!) and vector calculus. It is an excellent book for engineers, mathematicians, physicists, etc. If you have a fair to good foundation of algebra, vectors, vector calculus, calculus and differential equations, then you'll do fine (as I have the math background, but was very stale with it, I did some review and it helped). If not, the book will be good to get a conceptual level understanding of tensors, but the math will be hard to follow. Let me also recommend Professor Fleisch's companion book, ASG to Maxwell's equations. Written in the same easy to read style. If you want to read that book, I'd recommend buying this book too, as it goes into better background on the underlying math and that helped me a lot reading ASG to Maxwell's equations. Hope this helps. Happy reading!

I have the following reasons for loving this book:1. This book has one of the best explanations of the meaning of gradient, divergence, curl, and the Laplacian I've ever seen.2. The diagrams deriving the magnitude and direction of the centripetal acceleration vector are beautiful.3. I found the end of chapter problems "do-able" and there is a nice web-site to go along with the book showing complete answers and solutions if you get stuck.4. There is a gentle but rigorous introduction and explanation of covariant and contravariant vector components which is very nicely done.5. The book starts to get more abstract when it discusses tensors, tensor derivatives, and Christoffel symbols but the author does an excellent job explaining them along with giving examples of their use.6. The last chapter has 3 more very nice detailed examples of tensor use. Although I read the clear explanation of the first two (the inertia tensor and the electromagnetic field tensor), I omitted the end of chapter problems dealing with these examples since I wanted to concentrate my attention on the tensors involved with General Relativity. The author does a superb job explaining the foundations of General Relativity and the origin and use of the Riemann Curvature Tensor. Along with this he shows how the Ricci Tensor and Ricci Scalar come about. The author does a great job giving an example of how the Riemann Curvature Tensor is calculated for a 2-dimensional spherical surface.If I had anything I wish I could have seen it would be to have a little more explanation of the Ricci Tensor and the Ricci Scalar in the last chapter. Also, although they were briefly mentioned, I would like to have seen more dealing with the "Einstein Tensor" and the "Einstein Field Equation". But, that could have easily lead to another chapter which was probably beyond the goal of what this book was trying to teach.In summary, I don't think you could find a better introductory book for vectors and tensors than this one!

This book surpasses any other math/physics book I have ever read. I no longer write reviews, but for this one I will. This book actually describes the "geometric" difference between co and contra variant tensors. I have never seen this done before. I spent weeks years ago trying to figure the difference(geometrically). One is upper and the other lower incidences, so what. This book would have put me so far ahead, why did someone not do it earlier. The part on vectors is great, but the tensor part is the best I have ever seen. This book is like cheating!! Instead of banging you head on the wall one hundred times, it like some putting a pillow between you and the wall and saying just bang your head once. I am finishing string theory, having already completed general relativity and quantum field theory. I know what I am talking about. I know money is tight so I would never endorse a book that wasted money. This book puts you at the graduate level fast, again this book is like cheating.For the prices and time saved now and later, I would have payed three times the price years ago.NOTE: I did not do a chapter by chapter review because it was not needed. This book gives the geometric as well as the mathematical view.Look at all the reviews around me. I found some errors in the book, but guess what the author already has the errors posted. I cannot say enough about this book. Also the solutions are posted online, you do not have to look at them but you will know if you did the problem right. This man really wants to teach. He also has videos on youtube to show you visually what is going on. I am finishing up string theory and I picked up a few new things from this book. If you understand what is going on geometrically you can understand what is going on. Tell your friends the geometric different between co and contra variant tensors, some graduate students do not know the geometric difference, try it.