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Product Description
Tensor calculus is a generalization of vector calculus, and comes near of being a universal language in physics. Physical laws must be independent of any particular coordinate system used in describing them. This requirement leads to tensor calculus. The only prerequisites for reading this book are a familiarity with calculus (including vector calculus) and linear algebra, and some knowledge of differential equations.
About the Author
Nils K. Oeijord is a science writer and a former assistant professor of mathematics at Tromsoe College, Norway. He is the author of many scientific works in English and Norwegian. Nils K. Oeijord is the discoverer of the genetic catastrophe (GC).
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Most Helpful Customer Reviews
15 of 15 people found the following review helpful
This book is actually for beginners of tensor calculus! I would have never thought so, even if the title says basics, because of the way it looks. Then I happily realised that as long as you can do partial differentiation and know what an absolute differential is you are safe for the first 20-30 chapters! That is where I am but it looks that the rest will be just as good. Very nice and clear explanations. If you can visualise what a differential of a position vector and its relationship to its variables or coordinates is, then that is fine, you can buy this and expect to learn without being put off after 2 pages! Maybe you need to know the physical and mathematical meaning of the gradient, etc. also but that is elementary calculus if you really want to start doing tensor calculus. So the book is truly an introduction to tensors if you know teh basics of multiple variable calculus.
***
I have now finished the book, two weeks later and I am very pleased. Everything is well expplained from the begining to the end. The best thing about the book is that is so well structured in the definitions and so easy to follow that you would think you're doing easy maths again! Nevertheless this is only theory. It doesnt come with exercises of tensors applied to the physical sciences or real applications. Also, it doenst interpret or explain from a physical point of view what tensors are and what their use is. In other words, if you want to use tensors after reading this book only, you wont be able to do so. I like books that explain why things are useful and where they cant be used but I still like this book because, mathematically, it is well organised and takes you from the basics of multiple variable calculus to tensor calculus.
By the way, I read to learn. So I cant advise as to how good this is for passing exams which I dont particularly care about.
***
I have now finished the book, two weeks later and I am very pleased. Everything is well expplained from the begining to the end. The best thing about the book is that is so well structured in the definitions and so easy to follow that you would think you're doing easy maths again! Nevertheless this is only theory. It doesnt come with exercises of tensors applied to the physical sciences or real applications. Also, it doenst interpret or explain from a physical point of view what tensors are and what their use is. In other words, if you want to use tensors after reading this book only, you wont be able to do so. I like books that explain why things are useful and where they cant be used but I still like this book because, mathematically, it is well organised and takes you from the basics of multiple variable calculus to tensor calculus.
By the way, I read to learn. So I cant advise as to how good this is for passing exams which I dont particularly care about.
7 of 7 people found the following review helpful
This book has no diagrams whatsoever so its very hard to learn from if you just begining to learn about tensors.
There are free pdf on several university sites that are better then this as an introduction to tensors.
The book I found much better and explained geometrically was :
Vector and Tensor Analysis with Applications.
Also Feynmans lectures Vol 2 chp 31 is a basic introductions - does not cover lie groups, lie derivatives etc but is much clearer if you're just starting off learning about tensors.
There are free pdf on several university sites that are better then this as an introduction to tensors.
The book I found much better and explained geometrically was :
Vector and Tensor Analysis with Applications.
Also Feynmans lectures Vol 2 chp 31 is a basic introductions - does not cover lie groups, lie derivatives etc but is much clearer if you're just starting off learning about tensors.
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
3 reviews
37 of 38 people found the following review helpful
Bare Bones
2 Dec 2005
Amazon Verified Purchase
This book is exactly what it says and nothing more. It is an extremely concise development of tensor math. It is only basic in the sense that it has no frills, for it covers several advanced topics. (Riemannian space, Lie derivative, and the Riemann-Christoffel tensor to name a few)
If you are trying to learn tensors for the first time I wouldn't recommend this as a first book. It will tell you the bare bones of how tensors work without examples or problems along the way to check your understanding.
This is not a bad thing if you already have some working knowledge of tensors and want a succinct review. For that purpose this is a great no-nonsense treatment of the subject.
If you are trying to learn tensors for the first time I wouldn't recommend this as a first book. It will tell you the bare bones of how tensors work without examples or problems along the way to check your understanding.
This is not a bad thing if you already have some working knowledge of tensors and want a succinct review. For that purpose this is a great no-nonsense treatment of the subject.
21 of 22 people found the following review helpful
Awful
4 Jan 2008
I can't imagine why it was given the title "The Very Basics of Tensors".
Could be great for people who already know a lot about tensors :>) however I was looking for a basic introduction to tensors (or even better, a VERY basic introduction to tensors).
In my opinion this book is neither of these. It is terse and formal and reads like a 130 page mathematics paper.
On the back of the book it says - "the only prerequisites for reading this book are a familiarity with calculus (including vector calculus) and linear algebra and some knowledge of differential equations." I have these prerequisites but it didn't help.
Could be great for people who already know a lot about tensors :>) however I was looking for a basic introduction to tensors (or even better, a VERY basic introduction to tensors).
In my opinion this book is neither of these. It is terse and formal and reads like a 130 page mathematics paper.
On the back of the book it says - "the only prerequisites for reading this book are a familiarity with calculus (including vector calculus) and linear algebra and some knowledge of differential equations." I have these prerequisites but it didn't help.
4 of 5 people found the following review helpful
Good Reference Book
24 Jun 2009
This is an excellent little reference book. It is divided into very short chapters with each chapter devoted to a single concept. At the end of each chapter there is usually a white space where you can jot additional notes. I first learned tensors from Schaum's "Tensor Calculus"; I covered them again in Schutz's "A First Course in General Relativity". Oeijord's book is a great summary of what I have learned and has a good index for quickly finding and reviewing a concept. Add to this my notes in his white spaces and I have a great piece of reference material on tensors. On the other hand, I would not try to learn tensors from this book; the explanations are lacking and there are virtually no examples or problems to work.
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