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A Student's Guide to Vectors and Tensors [Paperback]

Daniel Fleisch
4.5 out of 5 stars  See all reviews (41 customer reviews)

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Book Description

November 14, 2011 0521171903 978-0521171908 1
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.

Frequently Bought Together

A Student's Guide to Vectors and Tensors + A Student's Guide to Maxwell's Equations + Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Fourth Edition)
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Editorial Reviews


"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

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.

Product Details

  • Paperback: 206 pages
  • Publisher: Cambridge University Press; 1 edition (November 14, 2011)
  • Language: English
  • ISBN-10: 0521171903
  • ISBN-13: 978-0521171908
  • Product Dimensions: 8.9 x 5.9 x 0.6 inches
  • Shipping Weight: 12 ounces (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (41 customer reviews)
  • Amazon Best Sellers Rank: #60,585 in Books (See Top 100 in Books)

More About the Author

Dan Fleisch is a 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 published by Cambridge University Press in 2008, and is co-author with the late Prof. John Kraus of The Ohio State University of the McGraw-Hill textbook Electromagnetics with Applications. His most recent book, A Student's Guide to Vectors and Tensors, was published by Cambridge University Press in 2011. Prof. Fleisch has published articles in the IEEE Transactions, the Journal of Atmospheric and Terrestrial Physics, and Microwave Journal. He has presented more than a dozen professional papers on topics related to high-speed microwave instrumentation and radar cross-section measurement. He has been a regular contributor of science commentary to PBS station WYSO of Yellow Springs and appears in the public-television documentary The Dayton Codebreakers. Prof. Fleisch was named Outstanding Faculty Member at the Wittenberg Greek scholarship awards in 2000, and in 2002 he won the Omicron Delta Kappa award for Excellence in Teaching. In 2003 and 2005 he was recognized for Faculty Excellence and Innovation by the Southwestern Ohio Council for Higher Education (SOCHE), and in 2004 he received Wittenberg's Distinguished Teaching Award, the university's highest faculty award. In November 2010, Fleisch was named the Ohio Professor of the Year by the Council for the Advancement and Support of Education and the Carnegie Foundation. Fleisch received his B.S. in Physics from Georgetown University and his M.S. and Ph.D. in Space Physics and Astronomy from Rice University.

Customer Reviews

Most Helpful Customer Reviews
42 of 43 people found the following review helpful
5.0 out of 5 stars Best ever June 10, 2012
Format:Paperback|Verified Purchase
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.
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21 of 24 people found the following review helpful
1.0 out of 5 stars Kindle version too hard to read December 29, 2012
Format:Kindle Edition|Verified Purchase
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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24 of 29 people found the following review helpful
5.0 out of 5 stars Best book ever for learning tensors December 18, 2011
Format:Paperback|Verified Purchase
This is the best book (or college course) I have ever run into over the past 20 years on learning tensors. The companion website is excellent too. I can't say enough good things about the book or the thanks I have for Dr. Fleisch.
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9 of 10 people found the following review helpful
5.0 out of 5 stars Just what the doctor ordered June 20, 2012
Format:Paperback|Verified Purchase
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!
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13 of 16 people found the following review helpful
5.0 out of 5 stars Excellent Mini-Course April 24, 2012
The book is doing a fine job of buffing and polishing what I already know about vectors, restoring what I'd forgotten about them and the various mathematics used to manipulate them, and laying the foundation for teaching this old dog some new tricks about tensors. Not exactly light bedtime reading but focused and clear. I recommend Fleisch's "Guide to Maxwell's Equations", as well.
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13 of 16 people found the following review helpful
5.0 out of 5 stars outstanding book. for every engineering student February 19, 2012
Format:Paperback|Verified Purchase
There is not a single page of this book wasted, and his technique of instruction is brilliant.
The website for this book includes interative solutions, podcasts which walk you through the book, and supplemental material.

This takes the reader from the basics of vectors from notation to which forms are used for what purpose. He takes you through the basics of math operations and basic applications.

Then it really gets interesting, his diagrams and examples really drive the points home. The chapters on coordinate transformations is gold.

He lost me at tensors, but that is my lacking not his, and the physics applications he employs are great.

His conversational manner leaves the proofs at the minimum as not to distract. Eventually I will get past the Laplacian material, but until then this book got me very far.
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10 of 12 people found the following review helpful
5.0 out of 5 stars very pedagogical book. May 6, 2012
By Morsi
Format:Paperback|Verified Purchase
I have many books on vectors and tensors, but this book is the best.
Many Many thanks to the author, and to Cambridge for publishing that Gem.
one thing that i have learned from this book in crystal clear way, is the covariant and the contravariant components, i have struggled badly to grasp this concept from other books and always it was vague.
i have found also here the best treatment for the Laplacian operator, explained in incredible ease, realy fantastic.
here, the author writes as if talking to you, and increment the ideas slowly till get you to the point.
one other thing i liked about the writing style, is how the author introduces the next chapter at the end of every current chapter.
i'm in the middle of the book now, but so far so excellent.
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Most Recent Customer Reviews
5.0 out of 5 stars A great guide to the evil that is vectors
I'll start by saying that vectors and tensors are the bane of my existence. But as an undergrad physics major, I'll never get away from them. Read more
Published 13 days ago by Immanuel Kant
5.0 out of 5 stars Best book I own
I'm really upset that I didn't find this book when I was taking high school physics. I spent SOOO much time working through the math to teach myself some of the content of this... Read more
Published 1 month ago by Nate
5.0 out of 5 stars An good introduction to tensors?!?
I'm a physics student, and while I was well schooled in vectors, no one really explained tensors to me. Read more
Published 2 months ago by Leon Maurer
5.0 out of 5 stars These Student's Guides are very useful to manage with complicate...
In a clear a simple way this book explains vectors and tensors , using examples and ways to understand the theory and practice of mathematical instruments that helps to understand... Read more
Published 3 months ago by Josi Antonio Padilla
5.0 out of 5 stars Good
A very good book. I recommend it to any student interested in vectors and tensors as an first time introduction
Published 4 months ago by Daniel Olson
3.0 out of 5 stars Fairly good - expected more
The book is excellent in introducing vectors, vector fields (with operations like div, grad), transformations (covariant/contravariant), and also in introducing tensors with some... Read more
Published 4 months ago by Remus
4.0 out of 5 stars A Good Book
The book is well written, particularly targeting students' needs on the subject. The part of tensors could be more developed such as the Einstein's tensor in the general theory of... Read more
Published 4 months ago by Amazon Customer
5.0 out of 5 stars Best I've Read for Vectors and Tensors
Great book! Best I've read regarding vectors and tensors. (I read a library, printed copy). I don't understand the comments written by people who gave it a one star: were they... Read more
Published 6 months ago by David W. Wood
5.0 out of 5 stars Best book ever on tensor analysis
This book explains tensors better then any previous books on tensor analysis I have ever read, and I have read several books. Read more
Published 7 months ago by Luther Howard
4.0 out of 5 stars an easy to understand perspective, but could be even better.
Chapter 1 introduces vectors and the related formalities. In chapter 2 the author explains basic vector operations, such as dot and cross products, and then operators such as the... Read more
Published 7 months ago by Paulo Silva
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