[.ca] Introduction to Vector and Tensor Analysis (ISBN 048661879X)

Rigorous:
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!

Excellent Book:
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.

Einstein also needed a tensor analysis coach:
This non-descript chestnut from Dover books is actually a good amateur's 'alibaba' entry to Tensor Analysis, with a short exposition of General Relavity at the end. Don't be put off by Experts, one reviewer 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, but 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 most electro-mag texts. From there you can take a flying leap into this neverneverland where there were supposed to be only twelve people who understood the subject. Not actually that bad. The grand finale shows us the grand spacetime metric, which looks 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.

A good referesher book:
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.

A Real Gem:
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.