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!

I'm working my way through "A Very Incomprehensible Thing", an introduction to General Relativity. Although I found it pretty much complete in covering the required math, I wanted to get another book to provide another perspective on tensors to help me along. I have a BS in physics from many years ago, so not too bad on calculus and vectors, but never studied tensors.This Student Guide is the best book on math and the associated physics I have ever read. It is a gem. Professor Fleish's explanations are crystal clear. His very brief summary of Maxwell's equations are a joy to read. And on top of this, he has provided online solutions to the problems (using hints, or the complete solution if you prefer). But wait - there's more - there are online podcasts of the author, going over the book chapter by chapter. It's like sitting in his class. I was stumped at a certain point in the text - just couldn't figure out an equation - until listening to the the podcast. In a few words, he eliminated the confusion. Professor Fleish is a superb teacher, and he went the extra mile to make sure the material is accessible.If you want to learn about vectors, tensors, and their physics applications, this book will make everything much easier.