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A Student's Guide to Vectors and Tensors, by Daniel A. Fleisch
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Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. 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. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author.
- Sales Rank: #92319 in Books
- Published on: 2011-11-14
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .39" w x 5.98" l, .75 pounds
- Binding: Paperback
- 206 pages
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
About the Author
Daniel Fleisch is an Associate Professor in the Department of Physics at Wittenberg University, where he specializes in electromagnetics and space physics. He is the author of A Student's Guide to Maxwell's Equations (Cambridge University Press, 2008).
Most helpful customer reviews
72 of 74 people found the following review helpful.
Best ever
By Russell J. Barry
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.
17 of 18 people found the following review helpful.
Just what the doctor ordered
By RR
I have a bachelor's degree in Aerospace Engineering but felt lacking in Vectors and Tensors as applied to more advanced subjects. This book has helped fill in the gaps and really made a difference. It really helped strengthen my foundation in a crucial subject and now I feel much more comfortable around advanced subjects using tensors. The accompanying website is also a gem with hints to homework questions and pod-casts following the chapters. I thoroughly enjoyed this book and am now going to read the author's other on Maxwell's Equations for fun!
39 of 46 people found the following review helpful.
Kindle version too hard to read
By J. T. G.
Looks better, but still bad on iPad. Very tiring on kindle paper white. Math symbols not crisp, sometimes faint or misplaced (false superscripting), type face not consistent for unit vectors, etc.
Check errata. Many errors in Sec. 2.4.,and not in errata, but in general Ax(BxB) or (AxB)xB should have the second B as C. No mention that (AxB)xC = - Cx(AxB), only Ax(BxC) is explained.
I would add a few stars if the formatting was not so poor.
I understand the material; I got it to read for fun. The formatting makes it not fun.
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