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Daniel A. Fleisch
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A Student's Guide to Vectors and Tensors (Student's Guides) 1st Edition

by Daniel A. Fleisch (Author)
4.7 4.7 out of 5 stars 366 ratings
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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.



Previous page
  1. ISBN-10
    0521171903
  2. ISBN-13
    978-0521171908
  3. Edition
    1st
  4. Publisher
    Cambridge University Press
  5. Publication date
    November 14, 2011
  6. Part of series
    Student's Guides
  7. Language
    English
  8. Dimensions
    5.98 x 0.47 x 8.98 inches
  9. Print length
    206 pages
  10. See all details
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Editorial Reviews

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

Book Description

This book explains vectors and tensors in plain language to give undergraduate and beginning graduate students a better understanding.

Product details

  • Publisher ‏ : ‎ Cambridge University Press; 1st edition (November 14, 2011)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 206 pages
  • ISBN-10 ‏ : ‎ 0521171903
  • ISBN-13 ‏ : ‎ 978-0521171908
  • Item Weight ‏ : ‎ 12 ounces
  • Dimensions ‏ : ‎ 5.98 x 0.47 x 8.98 inches
  • Customer Reviews:
    4.7 4.7 out of 5 stars 366 ratings

About the author

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Daniel A. Fleisch

Daniel A. Fleisch

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Dan Fleisch is a Professor Emeritus in the Department of Physics at Wittenberg University, where he specializes in electromagnetics and space physics. He is the author of six books in the Student's Guide Series published by Cambridge University Press: A Student's Guide to Maxwell's Equations, A Student's Guide to Vectors and Tensors, A Student's Guide to the Mathematics of Astronomy (co-authored by Dr. Julia Kregenow), A Student's Guide to Waves (co-authored with Prof. Laura Kinnaman), A Student's Guide to the Schrödinger Equation, and A Student's Guide to Laplace Transforms, published in 2022. He is also co-author with the late Prof. John Kraus of The Ohio State University of the McGraw-Hill textbook Electromagnetics with Applications. 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, and he will serve as the Grand Canyon Astronomer in Residence in the fall of 2022. 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

4.7 out of 5 stars
4.7 out of 5
366 global ratings

Top reviews from the United States

FrankAir1
5.0 out of 5 stars Excellent primer of Tensors.
Reviewed in the United States on January 2, 2024
Verified Purchase
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!
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Ed L.
5.0 out of 5 stars Excellent Why are Tensors invariant under coordinate transformations.
Reviewed in the United States on November 25, 2023
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The clarity of presentation and its completeness are very original. In particular his entire Chapter 4. Very clear explanations of contravariant and covariant tensor components. In particular I greatly appreciated the explanation using parallel and perpendicular to basis vectors projections. Additionally the explanation of original basis vectors and dual or reciprocal basis vectors. Filled with complete numerical examples. You will not find that kind of presentation in numerous other books, at basic, intermediate (or much less at advanced) levels. In a future edition I'd like to see "Contraction of Tensors" with examples.
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Just a Guy
5.0 out of 5 stars Clear, simple, and direct.
Reviewed in the United States on January 20, 2022
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I was already comfortable with vector analysis and (second rank) tensor algebra, at least as matrix repesentations, from mechanics and electrodynamics. So I thought I might not have much to learn from this book. Boy was I wrong! The second half in particular includes all the goodies on contravariant/covariant vs. vector/one-form business, the metric tensor, Christoffel symbols (of the second kind), the Riemann curvature, Ricci, and Einstein tensors - everything I needed to start reading about general relativity on my own. Bear in mind, it's mainly about differential (and not so much integral) calculus, and you won't find anything on variational principles or Lagrangians, but my goodness, let's learn to walk before we run! To get up to speed mathematically, particularly to study general relativity, this is the very best book I have seen on the subject.

As an aside: For physicists and engineers looking to learn mathematical techniques, I recommend looking at physicists' books first. I'm not anti-math, but unless you're some kind of genius, I always find the physicsts' explanations easier to follow the first time around. You can always fill in the rigor later if you really want.
2 people found this helpful
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Paulo Silva
4.0 out of 5 stars an easy to understand perspective, but could be even better.
Reviewed in the United States on November 23, 2013
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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 several forms of the nabla operator. In chapter 3 the author presents some example applications of vectors, such as in the calculation of Newtonian linear and angular forces, and also some applications related to electromagnetism. In chapter 4 the author introduces contra- and covariant basis and transformations, and tries to have the reader understand why vectors are more than just arrows in the usual Cartesian referential. In chapter 5 the author presents the operations on tensors, and introduces some other important forms such as the metric tensor, the Christoffel symbols and one-forms. Chapter 6 presents some examples of tensor applications, such as the inertia tensor, the electromagnetic field tensor, the Riemann tensor and its relation with general relativity.

This book is very easy to read. It offers a clear explanation on just about every statement made. Nothing is left unsaid, and actually that's what I like about it.
However, there is some content that I find unnecessary, and which I believe distracts from the "important" material. I'm talking about the first and half of the second chapters, which cover topics that are probably too basic for anyone interested in learning about tensors. But truth be said, the title of the book does include vectors and not just tensors. I also find chapter 3 to be a bit out of place, and again, its presence is only justifiable because the title of the book conveniently includes the word vectors.

For those interested in learning about tensors, i can say that the interesting discussion starts in section 2.5 all the way to the end of the chapter and then from chapter 4 to the end of the book. That being said, one can conclude that this is very short. Exercises are also few, and only at the end of the chapter.
One thing I find unfortunate is the omission of, in my opinion, very important tensors such as the 2nd order strain and stress tensors, and the 4th order elasticity tensor.

The author also seems a bit biased in his preference for the electromagnetic topics, but that can be excused since it seems to be his speciality. He does strive to make it digestible even for those not necessarily interested in the topic.

Another thing is the usage of (what I find to be) unusual notation, such as the use of capital letters to represent vectors. If you're used to see Ax=b, you probably expect x and b to be vectors and A to be a matrix. In the book the author will use A and B to represent vectors, although he does use arrows this feels awkward in my opinion.

This review is on the kindle version, which I have to say has many issues. There are a lot of problems with the typesetting. Many symbols seem to be just images and not actual characters. This does seem to be a recurring issue with kindle books though. I don't understand if its an issue or limitation of the kindle software, of if it is a problem originating from the lack of skills or willingness by the editors and authors. Either way its very distracting when you have for example a φ replaced with an Á. You have to remind yourself constantly of what it means, as if the material was not hard enough by itself.

Nevertheless, I do recommend this book to anyone looking for an introduction to tensors. I've been using it with "Vectors, Tensors and the Basic Equations of Fluid Mechanics" by Rutherford Aris, and I can say that in the common part both perspectives do help me gain a better understanding of what I believe to be a very difficult subject.

It gets 4.5 stars, as it falls a bit short of what it could be.
9 people found this helpful
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Top reviews from other countries

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Durgesh Singh
5.0 out of 5 stars Excellent book of Vector
Reviewed in India on September 26, 2023
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Best for B. Sc.
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Ignacio A.
5.0 out of 5 stars explica tensores de una manea muy clara
Reviewed in Spain on July 23, 2022
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Es el mejor libro por ahora que razona el fundamento y la utilidad de los tensores de la manera mas clara que por ahora he leido. Lo recomiendo sin duda alguan
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A.H.
5.0 out of 5 stars Sehr gelungen
Reviewed in Germany on May 23, 2022
Verified Purchase
Wunderbare, sehr verständlich geschriebene Einführung in das Gebiet der Vektoren und Tensoren.
Wer wie ich Informationen lieber akustisch aufnimmt, wird die zu diesem Buch erhältlichen Podcasts schätzen (erhältlich auf Dan's Website).
Ich empfand es als völlig ausreichend, die Podcasts anzuhören und gleichzeitig die Formeln und Grafiken im Buch anzusehen.
Man merkt, dass sich Dan sehr viel Mühe gab, verständlich zu sprechen.
Am Ende eines jeden Kapitels gibt es noch Übungen, um das Gelernte zu vertiefen.
Ich habe übrigens die Kindle Version, welche m.E. am Tablet mit der Kindle App sehr gut lesbar ist, auch die Formeln und Grafiken.
Alles in allem sehr gelungen.
Schade, dass es von Dan Fleisch nicht auch ähnliche Bücher über Partielle DGLs oder Funktionentheorie gibt.
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Braulio
5.0 out of 5 stars Claro, conciso y fácil de digerir.
Reviewed in Mexico on November 5, 2019
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Una interesante introducción a los vectores y una guía muy clara con vectores. Bastante recomendado para estudiantes que estén pensando en tomar clases de cálculo tensorial o álgebra multilineal.
One person found this helpful
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diskxk
5.0 out of 5 stars Good book
Reviewed in Australia on February 6, 2024
Verified Purchase
I read the book and was able to understand nearly everything, although a summary page on each chapter with a formula page would have been very helpful.

Besides the General Relativity section, this book was understandable.
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