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23 of 23 people found the following review helpful
5.0 out of 5 stars The best book on vector/tensor analysis out there
This excellent book,by Soviet mathematicians, is a book which all students wishing to gain a clear understanding of tensor notation should study.I have often thought that the undergraduate curriculum should feature a second course in vector analysis, particularly general (ie non-orthogonal) coordinate transformations,so that students should gain a clear understanding of...
Published on 20 Oct 2006 by Mr. B. I. Precious

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2 of 2 people found the following review helpful
3.0 out of 5 stars I found it Hard Going
Probably not the author's fault - I was probably being too ambitious. Maybe I need to try something a bit less advanced to begin with.
Published 15 months ago by Book Boy


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23 of 23 people found the following review helpful
5.0 out of 5 stars The best book on vector/tensor analysis out there, 20 Oct 2006
By 
Mr. B. I. Precious (London, Greater London United Kingdom) - See all my reviews
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This review is from: Vector and Tensor Analysis with Applications (Dover Books on Mathematics) (Paperback)
This excellent book,by Soviet mathematicians, is a book which all students wishing to gain a clear understanding of tensor notation should study.I have often thought that the undergraduate curriculum should feature a second course in vector analysis, particularly general (ie non-orthogonal) coordinate transformations,so that students should gain a clear understanding of the geometric distinction between covariant (downstairs) and contravariant (upstairs) indices,and the fact that a vector can be represented in either covariant or contravariant form according to which of the two local bases is used.These two local bases are dual to each other.

This then leads into the definition of a tensor of arbitrary rank,each of whose components is defined in a similar manner ie a tensor is a 'multivector'which can be thought of as a tensor product of vectors (first rank tensors) ,which tensor product has a magnitude -or NORM- which is invariant under a 'permissible' coordinate transformation.

All students of e.g. elasticity theory and of relativity should consider this book compulsory.It is without doubt the best book of it's kind I have seen.
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9 of 9 people found the following review helpful
5.0 out of 5 stars Best book Ive seen so far on tensors, 11 Feb 2011
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A. Patel - See all my reviews
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This review is from: Vector and Tensor Analysis with Applications (Dover Books on Mathematics) (Paperback)
Ive seen a lot of books on tensors and trying to understand them.
Im not a physics or mathematics major. This book is the best I've seen especially as it has
several diagrams and then explains them - not just pages and pages of equations without showing what they mean geometrically. Ok, you cant draw it out when it comes to many dimensions but atleast once you see what it looks like for a few then the equations make more sense.
So far, best book Ive come across and Ive tried five to six others which said "intrductory" books but no where as clear as this one. I dont see why lots of books waste pages when a few diagrams would drive home the point very easily.
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1 of 1 people found the following review helpful
5.0 out of 5 stars Good text for engineering students, 22 Oct 2013
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This review is from: Vector and Tensor Analysis with Applications (Dover Books on Mathematics) (Paperback)
The book give a relatively detailed discussion about why tensor and what for. Via checking each example carefully, one may gain a clearly view about tensor concept and application.

However, there are few errors in subscripts (if you check each step you can figure it), especially in the first two chapters. And one better make some marks about those important formulas (results) cause some derivations are not refer all the previous result, so you may got stuck if you don't know where it coming from. Most of example are derived clearly, and explain in detailed about its engineering application.

Finally, a good understanding about linear algebra (determinant, cofactor,linear transform are intensively used) can offer extra help.
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2 of 2 people found the following review helpful
3.0 out of 5 stars I found it Hard Going, 17 July 2013
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This review is from: Vector and Tensor Analysis with Applications (Dover Books on Mathematics) (Paperback)
Probably not the author's fault - I was probably being too ambitious. Maybe I need to try something a bit less advanced to begin with.
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Vector and Tensor Analysis with Applications (Dover Books on Mathematics)
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