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Product Reviews:
Introduction to Vector and Tensor Analysis |
Rating: 3 (out of 5)
Summary: great not great
Comments: My purpose in studying vector and tensor analysis are two-fold. I hope the math will be helpful in my budding research efforts in kinematics. Also, I would love to be able to follow gravitation physics/relativity mathematically.
To that second end, I started with Misner et. al.'s GRAVITATION. They claim to teach you the math as you go along. Whoa!! Sort of. Not really. So I am going elsewhere to understand tensors.
I have perused several books on tensors to get a better understanding. Wrede's is the 1st I have read cover to cover.
My impressions. great, not great. The early parts of this book are clear and flow well. Wrede explains things from the beginnings, and works you through things. I could follow the proofs quite easily, however could not do the problems without quite a bit of fiddling. Answers to odd-numbered questions are supplied for almost all sections, however some sub-section questions do not have answers. Answers are end-product without HOW they were arrived at. Tough for me, because there aren't a lot of great examples outside of the proofs for these problems. Also, a lot of proofs are "left to the reader."
Wrede does a nice job of breaking down n-dimensions into simpler 2- or 3- dimensional examples to demonstrate concepts, particularly in the 1st third to half of the book.
However, as things progressed, even into the more technical aspects of vector analysis, Wrede got somewhat vague. He let his proofs explain everthing, did not really conceptually discuss the utility/significance of even basic tools, or the importance of their implementation in the process of various analytical applications.
Later, as things became more complex-- specifically tensor analysis, especially as symbology became progressively more convoluted and layered-- the text became difficult to follow, and Wrede's style seemed to falter. Even for such basic concepts as gradient, curl, and divergence, he never even comes out and says what they MEAN, or what they are FOR. Fortunately, I could figure these out on my own. however more complicated concepts seemed more like mathematical abstractions when I was done with the book, rather than solid tools available for my use. Perhaps I am too much an engineer.
For example, he never even defines what a tensor IS. This is problematic for a number of mathematical terms. After finishing, I could tell you what a tensor DOES, however it would take me longer than this review to do it.
Sections on special and general relativity are limited (perhaps appropriately) to the mathematical signficance of selected elements, rather than a summation of the physics themselves.
Much of tensor analysis is understanding notation, then realizing that much of calculus is applicable to a tensor, with tweaks here and there. Early notation is well defined in this book, however for some reason, there isn't as much foundation in later sections.
At least I was able to finish this1and feel like I understood almost all of it. Others, which I will try and go back to, I couldn't even finish.
I am reading another book on tensor applications-- so far the 1st chapter has clarified/summarized things quite well and enabled me to feel more concrete about more advanced tensor concepts. I will review that when I am finished with it-- it appears like another1that I will be able to complete.
Eventually, MTW!! |
Rating: 4 (out of 5)
Summary: Rigorous
Comments: This is quite a nice book for learning vector algebra, and vector calculus via indicial notation and the Levi-Civita tensor etc. There are not many books that I have found that go to this detail and breadth. Therefore I found chapters 1 and 2, as well as the rest of the book, quite important!! |
Rating: 5 (out of 5)
Summary: A Real Gem
Comments: I 1st encountered this book when I was 14 and trying to learn vectors and tensors to study relativity. That was, I am sorry to say, nearly 30 years ago... I liked the book then as a thoroughly grounded compilation of definitions and theorems that told the story. This is how I learned to use vectors and tensors. I also own Spivak (all 5 volumes) and I can tell you that approaching those 1st would be be confusing without the nuts-and-bolts component methods from Wrede. No matter how elegant you get with differential forms or manifold notation; when it comes time to use a tensor you have to break it down into components; and no other book is as great as this one. |
Rating: 4 (out of 5)
Summary: Excellent Book
Comments: This book is great. The author skillfully introduces
material as needed providing abundant examples and
exercies. You need some backround in linear algebra and calculus
to get started. What I like the almost all is the presentation and the way the theory is tied to physical applications.
My only concern is that the book covers some unneccesary
material, mainly in chapters1and two. |
Rating: 5 (out of 5)
Summary: Einstein also needed a tensor analysis coach
Comments: This non-descript chestnut from Dover books is actually a great amateur's 'alibaba' entry to Tensor Analysis, with a short exposition of General Relavity at the end. do not be put off by Experts,1reviewer suggests Spivak on Differential Manifolds. Please!! sneak into the subject armed with a sharp pencil, a sheaf of paper, and write out the tensors sans the summation convention. Tensors look humungous, and Christoffel tensors _are_ humungous, however the subject will yield to a few weeks of concentrated scratchpad figuring. The book actually requires the basics of vector analysis, a la the stuff in almost all electro-mag texts. From there you can take a flying leap into this neverneverland where there were supposed to be only12 people who understood the subject. Not actually that bad. The grand finale shows us the grand spacetime metric, which appears a bit like ye olde Pythagorean Theorem all over again, this time in grand style. Fun book to rummage through. Save Spivak and differential geometry for dessert. |
