Tensor Analysis on Manifolds (Dover Books on Mathematics)
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Please try again later. The text is suitable for anyone interested to learn the basics of differential geometry. The explanations are clear and concise. Among many other introductory differential geometry books, I found this one the best. The book is also suitable for the General Relativity students like me and can be treated as a companion to Wald and MTW.
I could not find anything interesting in this book.
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- Tensor Analysis on Manifolds?
- Best Books on Tensor analysis to Enrich Your Mathematics Knowledge | Online Books Review.
Most helpful customer reviews on Amazon. However, after completing the page first chapter, and scanning chapters two through five, it appeared that the authors were only headed towards more formalizations for formalizations sake, which to pure mathematicians is a value and an end in itself. However, for someone in search of how and why one might need to use tensor analysis, this was not helpful at all.
And then how these abstract functional entities could be used in even more generalizable ways with even more complex structures and entities, as well as how they might be applied to higher dimensions. That said, however, it is not clear why those who use this tool or what falls out of its formalizations , must be required to wade through and understand the formalizations that justify its existence?
I get that we must understand how we get at least up to manifolds.
It seemed that here this nested process of formalization embedded within more generalizability, became an end in itself. And while that indeed might be a value for a pure mathematician, for one in search of how to use Tensor analysis in more practical ways, not giving us a road map to how and where these formalizations might be headed, and thus where they might be useful, is very unhelpful.
That is why I was happy to discover in chapter five, that it all did once again touch the ground of geometric reality, as here bilinear forms can clearly be seen to relate to vector lengths, to curves, to surfaces, and angles, all the way down to metrics, geodesics, and curvature. Bilinear forms even seem to be a distant cousin to linear transformations and linear independence from Linear Algebra.
901,57 RUB
While I was happy that the first two chapters dispensed with the more detailed proofs, I could not decide whether this was a virtue or a sin? It seemed to me too that proofs were required at every step of the way mostly to ensure that no sacred mathematical principles and conditions were ever violated — except, that is, in such circumstances where such exceptions were specifically allowed. I note here only in passing that in engineering mechanics, where they do use manifolds, they could care less about proofs, so why not have them, even here, as an addendum or an appendix? One reviewer suggested reading the book on Differential geometry by these same authors, I may do that before reading this book again, and then see what falls out the second time around, at which time I hope to be able to upgrade my rating.
This book is for mathematics students only. I guess it's considered the "go to" differential geometry starter for mathematicians so I don't want to give it a poor rating. But I'm taking off a star since the authors make the claim that the book is an attempt to broaden the "rather restricted outlook" of tensor analysis "at the stage where the student first encounters the subject," referring to all students of the physical sciences.
No, it's an attempt once again by mathematicians to cram their pinheaded tripe down physicist's throats.
Dover Books on Mathematics: Tensor Analysis on Manifolds by Samuel I | eBay
No physics department I know of would ever use this as a textbook, as it's far too abstract and far too focused on rigorous proofs throughout but of course that's what mathematicians need so fine for that. The "go to" differential geometry book for physicists is "Geometrical methods of mathematical physics" by Schutz, the top choice of physics departments for decades if pure differential geometry is taught as a "stand alone" course at all it's usually just recommended reading.
Great book to read with Wald and Weinberg. It has the mathematical background if one would like to seek in order to understand the role of tensors in space and what it has to do with GR. Great book well written and understandable. As a physics-math major, I have never come across such a perfect book to start differential geometry. I buy a lot of Dover publishing books because of their cheapness, but this one is probably my most valued geometry book. No other book has been this terse and this clear at the same time. The material proceeds from the general to the special.
Tensor Analysis on Manifolds
An introductory chapter establishes notation and explains various topics in set theory and topology. Chapters 1 and 2 develop tensor analysis in its function-theoretical and algebraic aspects, respectively. The next two chapters take up vector analysis on manifolds and integration theory. In the last two chapters 5 and 6 several important special structures are studied, those in Chapter 6 illustrating how the previous material can be adapted to clarify the ideas of classical mechanics. The text as a whole offers numerous examples and problems.
Best Books on Tensor analysis to Enrich Your Mathematics Knowledge
A student with a background of advanced calculus and elementary differential equation could readily undertake the study of this book. The more mature the reader is in terms of other mathematical knowledge and experience, the more he will learn from this presentation. Topics include function-theoretical and algebraic aspects, manifolds and integration theory, several important structures, and adaptation to classical mechanics.
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