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12 of 12 people found the following review helpful
5.0 out of 5 stars A Student's Guide to Vectors and Tensors, 31 Jan. 2012
This review is from: A Student's Guide to Vectors and Tensors (Paperback)
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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13 of 14 people found the following review helpful
5.0 out of 5 stars Like having your own personal tutor, 18 Nov. 2011
This review is from: A Student's Guide to Vectors and Tensors (Paperback)
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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2 of 2 people found the following review helpful
5.0 out of 5 stars Impressive starting point to learn basics of Tensors, 27 Oct. 2014
By 
ab..c (england) - See all my reviews
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This review is from: A Student's Guide to Vectors and Tensors (Paperback)
* 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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2 of 2 people found the following review helpful
5.0 out of 5 stars This is the best book so far that I have found on this ..., 20 Sept. 2014
This is the best book so far that I have found on this difficult subject. And I have been searching for years. It explains dual basis vectors better than any other, and it shows graphically the geometric representations of tensors and vectors. This is really helpful since it makes clear what in other books is represented as complicated arrays of partial derivatives which give me - and others - a headache. Well done, Dan Fleisch!
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13 of 15 people found the following review helpful
5.0 out of 5 stars so outstanding, 17 Oct. 2011
By 
Ronjoe (Worthin, West Sussex, UK) - See all my reviews
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This review is from: A Student's Guide to Vectors and Tensors (Paperback)
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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5.0 out of 5 stars Eureka!, 2 Jan. 2015
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Dr. John Bromilow (Okehampton, Devon United Kingdom) - See all my reviews
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This review is from: A Student's Guide to Vectors and Tensors (Paperback)
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 and 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.
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.
But it's worth it: isn't this subject more worthwhile and relevant that playing chess or finishing cryptic crosswords?
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5.0 out of 5 stars Very thorough, very clear, and well supported., 14 April 2014
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D. Williams "dwilliams" (Scotland, UK) - See all my reviews
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This review is from: A Student's Guide to Vectors and Tensors (Paperback)
This is a great introduction for anyone who needs to understand tensors. The book first focuses on the basics of vectors, and uses vectors to build the general concepts on which tensors are built. The text is very clear and well written, with clear and appropriate diagrams.

The book itself assumes the student is familiar with basic calculus, but partial differentials are given a brief introduction before they are used.

Most importantly, there is substantial online support for this book - the solutions to the exercises are online interactive, so can be revealed one hint at a time to guide you towards the answer rather than just revealing the whole thing at once. There are also some background materials for students who have not studied some of the more basic maths - I didn't use these personally but am sure they will be useful to many students who need to revise some of the more basic stuff.

There are also some very well narrated podcasts which follow the book closely. These supplement the text really nicely and will be especially useful for students who prefer not to learn everything from reading alone.

Highly recommended for any student who wants a compact but thorough introduction to vectors and/or tensors.
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5 of 6 people found the following review helpful
5.0 out of 5 stars So Clear., 10 July 2012
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R. Small (London UK) - See all my reviews
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This review is from: A Student's Guide to Vectors and Tensors (Paperback)
Having done my physics degree so many years ago my tensor (and vector) knowledge was rusty in the extreme. After reading "A Students Guide to Vectors and Tensors" I realised I had never fully grasped the subject the first time round. I now have a much better grasp of the subject. It starts off with vectors and leads you by the hand into tensors. The problems are clear and while there could be a few more examples in the text they are of a suitable level of difficulty. Very good value for money.
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4.0 out of 5 stars A very good introduction, 2 July 2013
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This review is from: A Student's Guide to Vectors and Tensors (Paperback)
I bought this book to support my understanding of general relativity since the book I purchased on the subject was somewhat succinct in the basics. This is a very good book in what it covers. Personally I would have liked to have more material on tensors but in conjuction with Barry Spain's book on Tensor Calculus which I purchased at the same time I think I now have a sufficient understanding of the basics to continue my general relativity studies.
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4.0 out of 5 stars Overall review, 5 May 2014
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Great and clear introduction to the field esp. For students at the beginning of their course. I am not professional engineering student or physicist but a neurologist with interest in this field as a hobby. Very easy to follow.
However one point not thoroughly shown is the symmetry of the Christofoel symbols which is needed to show the relation of thee symbols with the components of the metric tensor. I managed to find this elsewhere but such important links should at least be cross referenced online.
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A Student's Guide to Vectors and Tensors
A Student's Guide to Vectors and Tensors by Daniel A. Fleisch (Paperback - 22 Sept. 2011)
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