Introduction to Vector and Tensor Analysis

Rating:
Summary: A Real Gem
Review: I first 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 first would be be very 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 good as this one.

Rating:
Summary: A Real Gem
Review: I first 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 first would be be very 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 good as this one.

Rating:
Summary: A good referesher book
Review: I think this book is beyond a simple introduction. First half of the book is Vector Analysis and other half is mixture of transformations and Tensor analysis. It covers a lot and has examples for each concept. What I did not like was that the concepts were introduced from general to particular. So if you are not exposed to Vector or Tensor analysis, it is not easy to follow a new concept defined on n-dimensional space and see application on two dimensional space.So it was a good refresher with some applications to Physics but for new starter it is difficult especially for self lerner. Also definitions were very abstract, dry without any meaning attached to it. I can not considered this book as a course book by itself.

Rating:
Summary: Review of Introduction to vector and tensor analysis.
Review: In order to facilitate the judgement of my review I will introduce myself. I am a retired professor of physiology with a background in medical physics. Since I have always wanted to grasp the relativity theory of Einstein, but did not have the necessary background in vector and tensor analysis, I am now studying in this area to fulfill my dream. I have tried several books on this subject and found Robert C Wrede's book to be the best. I have found his explanations rigorous and clear. No confusing errors as a matter of fact no errors. The reason for looking up this title on the internet again is that I enjoyed this title so much that I would like to order an additional copy with hard cover. One of the positive aspect of this title are the well chosen examples and exercises with always correct answers of the odd numbered ones in the back. An additional plus is that the author provides short historical background throughout the text.

Rating:
Summary: Good not great
Review: 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'm going elsewhere to understand tensors.

I've perused several books on tensors to get a better understanding. Wrede's is the first I've read cover to cover.

My impressions. Good, 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, but could not do the problems without quite a bit of fiddling. Answers to odd-numbered questions are provided for most sections, but some sub-section questions don't have answers. Answers are end-product without HOW they were arrived at. Tough for me, because there aren't a lot of good 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 first 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, didn't 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. But 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, but 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, but for some reason, there isn't as much foundation in later sections.

At least I was able to finish this one and feel like I understood most 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 first 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 looks like another one that I will be able to complete.

Eventually, MTW!

Rating:
Summary: Excellent Book
Review: 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 most 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 chapters one and two.

Rating:
Summary: Excellent Book
Review: 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 most 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 chapters one and two.

Rating:
Summary: fussy, verbose, unclear.
Review: This book tries hard to be clear, exact, neat, unfortunately it fails badly.Tensors are ill-defined, theorems are ill-stated and their proofs are long, boring and tedious, if not simply wrong. For vector analysis one should stick to "Vector Calculus"(J. Marsden and A. Tromba); for tensor analysis, let's read "Tensor Analysis on Manifolds"(Bishop and Goldberg) or Spivak's "A Comprehensive Introduction to Differential Geometry", first volume.

Rating:
Summary: Rigorous
Review: 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:
Summary: Rigorous
Review: 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!