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Customer reviews

4.8 out of 5 stars
4.8 out of 5 stars

1st edition 2012. I agree with the other good reviews. There is a lot of support from the authors new site which has a 9h audio site (needs diagrams visible), solutions listing, a matrix review.
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on 22 August 2017
Tensor part was very interesting and educating.
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on 31 August 2012
Book was received soon after purchase, and in excellent condition.
Informally and cheerfully written, with an author who clearly cares about his readers fully understanding (and appreciating) the powerful nature of tensors and their uses. More worked examples would have been appreciated, but you would be really hard-pressed to find a better introduction to this kind of subject elsewhere!
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on 17 October 2011
What an outstanding book, I just wish I'd had it 10 years ago. The book is very deceptive - it is slim and starts out at what seems like an elementary as well as slow pace but don't be fooled. It's all there and more some; and everything is explained so clearly - Daniel Fleisch deserves a medal
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on 2 January 2015
Books on mathematics are almost without exception written by mathematicians for mathematicians, so that the latter can move onto the next level of study; they are seldom, if ever, written for the general reader. Why should this be: do these writers consider their subject too difficult, tedious or irrelevant for the general reader? Perhaps they are quite incapable of writing clearly for those who want to explore mathematics as interested amateurs.
If you read the blurb of this book, you will conclude that this is yet another inaccessible maths book. However, if you then read Professor Fleisch's preface, where he states '... but if you are a lifelong learner who wants to know more about vectors and tensors...welcome aboard', you will soon realize this is certainly not the case.
Professor Fleisch is a teacher of the highest order as this is a superbly written book which develops the subject logically, beginning with and explaining simple scalars and vectors very clearly and progressively moving on to the subject to tensors - those fearsome looking entities with all those sub and superscripts. This is done with the aid of many very clear diagrams. The book has a website on which Professor Fleisch presents an audio-visual introduction to the book and then a series of helpful audio discussions of each chapter. On the site too are solutions on how to solve the end of chapter questions: these are shown stage by stage so that if you become stuck on just one stage, you can understand that stage and then move on.
This does not mean to say that this is an easy book to read: it is certainly hard going at times and some sections will require several readings. You also need some basic maths knowledge of algebra, calculus and geometry, although, for example, differentials are explained in one page where other books can take a dozen. This book and its accompanying web site is only just short of having a personal tutor; other writers take note!
But it's worth it: isn't this subject more worthwhile and relevant that playing chess or finishing cryptic crosswords?
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on 25 July 2015
Fleisch has done an excellent job clarifying the "mystery" usually associated with tensors.

This is the best introduction I have come across, enabling one to dive in differential geometry e.g. starting with M. Lipschutz, then E. Kreyszig.

Also, chapter 6 is a succinct but invaluable introduction to Mechanics, Electromagnetism and Relativity, in terms of tensors.
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VINE VOICEon 27 October 2014
* Physical

This paperback book is well bound, and has a useful size of font related to the size of the page. If your wear specs, you may find its well chosen size of fonts pleasing to the reader.

* Target Audience, A -level, H.N.D, Undergraduate, Post Grad?

From the back of this book its for '...undergraduate and beginning graduate students'. Its covering Mechanics, electromagnetics and general relativity topics. To be honest, i initially thought that this thin book, as I started reading, was going to be too basic. Its more designed as a concise reminder of Vectors rather than learning Vectors afresh. Going as it does through Mechanics using Grad, Div, Curl, three - dimensional dot and cross products from scratch. Partial derivatives are particularly well explained earlier on with series of diagrams, in particular Fig 2.11 (a), (b), page 45, and Fig 2.15, (a), (b) page 52. And also a great and deep help is the matrix 4.44 on page 122 of the summation superposition of the three dimensional gradients in a three-by-three matrix when related to pages 142-146. But its part of ingenious design to fill - in the assumed knowledge and build upon it. And this it does brilliantly well. As the book expands into more advanced material topics, the requirement to use stricter mathematical precision in its explaining is noticed. As an example, the study of electromagnetic fields and its requirement to need vector addition with three point changes, as explained in the trusty right - hand rule.

The topics then include using Basis Coordinate System Transformations using Cramers rule, that eventually slide into matrices and its related notation. This areas i found ingenious. In its development into handing 3X3 and 4X4 dimensional symbolic Matrices notation, using it as bedrock for using its development with Tensors. I learned just as much knowledge relating to matrices notation as learning to use Tensor notation, and what it means. This is further explored up to three, 4x4 symbolic Matrices multiplied together. In particular as i have some electrical background, that the section 6 Tensor Applications (page 159- end of the book), The later part being Electromagnetic field Tensor was particularly interesting and engagingly explained and terrifically put over into terms you can grasp. This to my mind goes quite deep for an book I have classed as a first choice book. So be aware of this deeper area!

* Summary

This book is really well explained, and the order its developed is also brilliantly done. Its a great book that is really made to help the motivated reader to start to understand the capabilities such as Tensors. Based on an incomplete reading of five books(!) on tensors, this is the one i would humbly recommend to the fresh reader to Tensors to start studies from.

Also if you are really stuck, i also found through a third - party to try using a well - known video sharing site and search for topics your finding difficult at the moment, such as 'tensors', and you may find very helpful resources available that fit 'hand - in - glove' with these topics.
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on 8 September 2015
I found this to be a truly excellent book. In my case, my college level maths was very rusty (my formal tuition was decades ago) and I wanted to get to grip with tensors in the hope of helping to understand General Relativity better. OK, so this is basically an introduction to vectors & tensors - and my GR ambitions are still work-in-progress - but the way that Dan Fleisch presents the material in this book is first class.
At the end of each chapter there are a dozen or so test questions and the solutions are available on Dan's website. Most importantly, for each question the website offers the choice of: Hint 1, Hint 2, Hint 3 etc... or a Full Solution. In this way, I found it the chapters both easy to read and the questions a pleasure to answer (knowing that - if stuck - a supply of hints were to hand!).
I'm pretty sure I've never read any maths book from cover to cover before, let alone tackling all the end of chapter questions - but I did with this one!
If you have studied maths to high school level (or preferably, first year university physics or engineering) and have gotten a little rusty, then this book will provide a brilliant refresher. Or perhaps a gap filler - if you didn't pay the attention to your studies you should have done first time round!
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on 18 November 2011
An excellent book that will take you on a steady journey from the world of vectors and their applications, through to non-cartesian coordinate systems, basis vectors and dual vectors, covariant and contravariant components and finally through to tensors themselves. Dr Fleish's skill is in drawing out and communicating at each stage all of the really important insights before moving gradually onto the next topic. There are end of chapter problems with online hints and full solutions. Overall a great text and especially helpful for the independant student.
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on 31 January 2012
Many otherwise excellent maths books suffer from a serious failing - they fail to provide solutions to the problems they contain and so render themselves of limited value for private study. Professor Fleisch's book is most decidedly not one of these: fully detailed solutions as well as the option to view stepwise hints are provided on the website referenced in the book.

In addition, the actual text develops one of the clearest, simplest and most thorough presentations of the essential material concerning vectors and their systematic extension to tensors that I have encountered. The text also covers applications of both vectors and tensors that will prove useful to physics and engineering students as well as those commencing a study of general relativity.
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