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Rating: 
Summary: Concise
Review: As a survey of the applications of differential forms to various aspects of the physical sciences, this book works quite well. However, for the non-mathematician, there are more intuitive texts available, although it is unlikely that they will have the same scope. The exposition is extremely concise, far more so than, for example, Lovelock and Rund, and at times this makes the text somewhat heavy going. Having said that though, the reader with a reasonable level of mathematical maturity will find the book very rewarding. A reader who is mainly focussed on differential geometry though would probably be better off with Lovelock and Rund.
Rating:
Summary: Concise
Review: As a survey of the applications of differential forms to various aspects of the physical sciences, this book works quite well. However, for the non-mathematician, there are more intuitive texts available, although it is unlikely that they will have the same scope. The exposition is extremely concise, far more so than, for example, Lovelock and Rund, and at times this makes the text somewhat heavy going. Having said that though, the reader with a reasonable level of mathematical maturity will find the book very rewarding. A reader who is mainly focussed on differential geometry though would probably be better off with Lovelock and Rund.
Rating: 
Summary: Good But not the best
Review: I was searching for a good source discussing the differential forms "from the ground up",while passing a course on GR. My motivation in studying this book was Weinberg's mentioning af it as "An extremely readable book" on the topic,in his book on GR.I belive that this is a good book if you have enough time and motivation to study differential forms from basic and without much hurry to use them operationally , but (at least in my opinion) it lacks that degree of clarity that one requires from a book on mathematical physics.To truly understand some parts (even at the early definitions)you may need to spend much more time that you could imagine at the first sight.Some basic ideas are expressed too concise.If you want to learn about differential forms in physics, this book would be some good, but not(I think) during a semester on something else (like GR), beacuse the way of presenting the material is not so stright , nor is operational enough.You may find the books by Lovelock & Rund or by Goldberg & Bishop more useful.
Rating: 
Summary: Generalize vector calculus for general relativity
Review: This book covers the basic math behind the "geometric approach" to tensor calculus. The math required is not heavy, but it requires some considerable mathematical maturity. If talk of "the boundary of a boundary is zero" or "exterior derivative" confuses you, this is a good book. An intuitive approach, not a sea of indices. If you want really heavy stuff then Bishop & Goldberg is good.Most Dover math books are first rate. This one is.
Rating:
Summary: Generalize vector calculus for general relativity
Review: This book covers the basic math behind the "geometric approach" to tensor calculus. The math required is not heavy, but it requires some considerable mathematical maturity. If talk of "the boundary of a boundary is zero" or "exterior derivative" confuses you, this is a good book. An intuitive approach, not a sea of indices. If you want really heavy stuff then Bishop & Goldberg is good. Most Dover math books are first rate. This one is.
Rating:
Summary: Read on
Review: Why is it that any book that contains the word "physics" or "physical" in its title feels free to be sloppy? Flander's book is sloppy. There are no shortcuts to understanding - if you want to know differential geometry you have to learn it right, not from Flander's book. For example: he devotes 3 pages to antisymmetrical tensors. The way he manages to do this is by avoiding precise definitions, or giving elaborate proofs. He does not even mention the word tensor! This is unacceptable for anyone who seeks to truly understand differential geometry. After all, if you intend to invest effort and time learning a subject, shouldn't you do it the right way?
I'm not saying Flander's book is without merit - especially the low price - which might make it worthwhile purchasing it is an additional source of information, but as a primary source it is, in my opinion, a very bad one.
There are many alternatives to Flander's book I suggest you check out before trying your luck with this one. The standard reference is Bishop & Goldberg's "Tensor analysis on manifolds". Another good book is "differential forms and connections" by Darling. A comprehensive book about diff. geometry is "Geometry and Physics" by Frankel. I'm sure others will have their personal favorites, but these are a good place to start.
Rating:
Summary: Read on
Review: Why is it that any book that contains the word "physics" or "physical" in its title feels free to be sloppy? Flander's book is sloppy. There are no shortcuts to understanding - if you want to know differential geometry you have to learn it right, not from Flander's book. For example: he devotes 3 pages to antisymmetrical tensors. The way he manages to do this is by avoiding precise definitions, or giving elaborate proofs. He does not even mention the word tensor! This is unacceptable for anyone who seeks to truly understand differential geometry. After all, if you intend to invest effort and time learning a subject, shouldn't you do it the right way?
I'm not saying Flander's book is without merit - especially the low price - which might make it worthwhile purchasing it is an additional source of information, but as a primary source it is, in my opinion, a very bad one.
There are many alternatives to Flander's book I suggest you check out before trying your luck with this one. The standard reference is Bishop & Goldberg's "Tensor analysis on manifolds". Another good book is "differential forms and connections" by Darling. A comprehensive book about diff. geometry is "Geometry and Physics" by Frankel. I'm sure others will have their personal favorites, but these are a good place to start.
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