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

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

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

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Review

"This book is an excellent resource for science and engineering students who can use it as a quick reference while studying topics such as physics, statics, dynamics, electromagnetism, and fluid mechanics. The author is commended for his effective and elucidating style, with graphical explanations and without mathematical long-windedness. Reading specific sections in this book a priori not only serves as a just-in-time preparation, but also empowers students to tackle subjects that require a good grasp of vector algebra, vector differential operators, vector transformation, and tensors. Highly recommended." R.N. Laoulache, University of Massachusetts, Dartmouth for Choice Magazine"This book is a short, concise teaching aid devoted to vector analysis and tensors. Each chapter ends with a set of problems whose interactive solutions can be found on a website. This is both helpful and innovative. One of the author's goals for this book is to provide in-depth coverage of covariant and contravariant tensors. This is timely, since some undergraduate physics textbooks are now using both types of tensors. Fleisch's book is an excellent and challenging resource for students in this subject area." Albert C. Claus, physics department at Loyola University, Chicago for Optics and Photonics News"This highly readable introductory book will be of great assistance to those taking undergraduate or graduate courses and meeting tensors for the first time" George Matthews, AMIMA, IMA Book Reviews

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Book Description

Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language to give undergraduate and beginning graduate students a better understanding of how to use vectors and tensors to solve problems in physics and engineering.

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Product details

Series: Student's Guides

Paperback: 208 pages

Publisher: Cambridge University Press; 1 edition (November 14, 2011)

Language: English

ISBN-10: 0521171903

ISBN-13: 978-0521171908

Product Dimensions:

6 x 0.5 x 9 inches

Shipping Weight: 13.1 ounces (View shipping rates and policies)

Average Customer Review:

4.5 out of 5 stars

91 customer reviews

Amazon Best Sellers Rank:

#113,479 in Books (See Top 100 in Books)

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.

I have read many books that introduce such objects and concepts as coordinate transformations, contra/co-variance, covariant differentiation, parallel transport, Christoffel symbols and a host of important tensors, A clear understanding of these will allow a person to advance their understanding of physics dramatically. I read these books not just to deepen my understanding but I am always looking for the best way to teach such concepts to my students. If you are a person trying to find the best book to help you understand these concepts I suggest strongly that you get this text. It is easily the best introduction that I have encountered. I will be recommending it to my students. As always, if you are new to this material please do the exercises before moving to the next chapter. I know I know... life is hard. "We do these things not because they are easy ... but because they are hard" (paraphrase of JFK)And I would like to thank Professor Fleisch.

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