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Tensor Calculus Paperback – July 1, 1978
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Top Customer Reviews
This is like blaming the author of a book on the grammar of a language, because you think the grammar is too complicated. Sorry, but the author of the book can only explain as well as he/she can the grammar that exists, it's not within his scope to improve upon it!
This book is a relatively easy-to-read and carefully motivated text on tensor calculus, a subject that does tend to lead to that eye-glazing-over effect because of the numerous indices. It does a very good job of keeping the focus on the concepts, without getting too bogged down in the equations - most of the time.
Does it need to be said that this subject is still useful, despite its comparative inelegance, because so many classic texts and articles on general relativity use this language? Will those who scorn to deal with indices demand that all these papers be properly translated into differential forms before they deign to read them?
Now, not being familiar with a modern differential geometry approach, I won't criticize the book as being dated. But I will criticize it as being a little obscure. Tensor calculus is inherently a sort of messy topic, and not the clearest thing ever, so there's all the more reason to provide text and explanations that don't do a lot more than sketch out the ideas and leave the rest as the proverbial "exercise for the reader."
The book is thorough and complete. Everything of importance to the classical approach is covered, and more. But if you haven't seen any of this before and you're attempting self-study, I think it's going to be a lot of work. Not that work is bad, but some of it is unnecessary. I'd rather concentrate on applications than on filling in the sketchy explanations provided in this book.
I'd have to say, pass this one up and get something, if not newer, then at least more detailed in its exposition.
If that's so, this is a very violent book. While it's true that physicists, particularly those working in General Relativity, were slow to abandon the coordinate approach, there can be little doubt that the sea of indicies form of Tensor Calculus runs counter to the modern approach to Differential Geometry, with its emphasis on abstract spaces, manifolds, bundles, exterior algebra, differential forms, diffeomorphisms, Lie groups, etc.
Physicists trained prior to the trend towards employing modern mathematics will likely be right at home with this book, which presents the tensor calculus in the form developed by Levi-Civita and Ricci in the late 19th/early 20th Century. On the other hand, classically trained Physicists tend to be hopelessly confused when confronted by modern Differential Geometry, which relies on so much more of the modern machinery from areas such as Topology, Global Analysis, and Group Theory/Representation Theory.
Students would be better served to pursue the subject framed in a more modern context. That means learning about manifolds and analysis on manifolds. The best introduction is probably Spivak's "Calculus on Manifolds", followed by Munkres "Analysis on Manifolds". Darling's "Differential Forms and Connections" and Sternberg's "Lectures on Differential Geometry" are well regarded, as is do Carmo's "Differential Geometry of Curves and Surfaces". A working knowledge of multivariable calculus, linear algebra, and elementary analysis are required for making heads or tails out of these books, even though they are introductory in nature.Read more ›
Most Recent Customer Reviews
Absolutely a great book. I have read it twice and have learned a great deal from it. It has answered some questions that have been bugging me for years. Read morePublished 24 months ago by Amazon Customer
This book greatly enhanced my understanding of general relativity and special relativity, this book for the subject was written at an most advanced level I would believe.Published on May 2, 2014 by Jesse ren
This is my first review on Amazon.com. I read bad reviews for this excellent book, so I react.
This is my first book on Tensor calculus, I have reach more than half on it, and... Read more
My copy was missing the introduction to tensors. It goes from the review of matrices straight to the calculus section. Read morePublished on January 9, 2010 by W. Sturgis
My background is being an electrical engineer with casual interest in physics. I was trying to start understanding more about relativity. Read morePublished on September 21, 2006 by Felipe Blin
this book dosen't take things from basics but goes to do high level calculus.Published on January 23, 2002 by amit