Introduction to Vector and Tensor Analysis (Dover Books on Mathematics)

This is, without a doubt, the best text I have ever studied on the subject of vector and tensor analysis (and believe me, there have been many). As the author describes, it is written for those who seek to work with the subject in a theoretical mindset, and yet it is not devoid of empirical applications. Wrede takes us so much further than our rudimentary understandings, which most of us acquired in our basic undergrad and grad studies. Proper definitions are given with a special attention to detail. However, the text is not overly rigorous. His notation is very user friendly and accommodating, and his exercises are perfect for mathematics, physics, or engineering majors. For example, if you're a math major, you can focus on the exercises associated with proofs and conjecture. Physics majors can work problems associated with the big picture concepts, where our quantities are of-course associated with mass, length, and time. The engineering major will be delighted to find particular problems associated with the rote calculations of quantities in the structural, electromagnetic, and fluid disciplines, amongst many others.Because his definitions are so precise, the sections should be read through slowly, or perhaps even two or three times to acquire a full and proper understanding. Yet, the benefits of doing so are enormous. For example, most of us who read this text are familiar with the "position vector", but how many of us actually know that it is not really a vector at all? As all vectors are tensors, and as tensors are invariant under coordinate transformations, the "position vector", or as I now prefer to call it, the radius arrow, could not possibly be a vector. That is due to the fact that the "position vector" is bound to the origin in the coordinate system in which it is described. Clearly, something as simple as a linear transformation in R2 will force it to vary, and thus, since the "position vector" is not invariant under coordinate transformations, we could not possibly consider it a vector.Wrede's text is full of useful information that will guide people in their studies of full analysis in vectors and tensors. Learning those analysis techniques, is absolutely essential in developing one's own theories for describing the wonderment of our universe. When you're ready to move beyond the basic problem solving skills associated with multi-variable calculus and physics, then you are ready for Wrede. Five Stars from me; incredible book!

book as described shipped promptly

An excellent book for anyone interested in vector and tensor analysis.

A very good book. The exercises are well thought out, and require a little critical thinking (unlike modern text books). I used this book as additional reference material for my matrix theory class. The best element of this book is that applications in physics are utilized in almost every chapter. Do not be thrown off by the notation used in the book. Yes, the author's notation can be confusing, but he uses it in order to get the student familiar with tensor notation. As an engineering student, it is beneficial to be familiar with different notations in mathematics, and this book will add to any student's mathematical syntax.

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.

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.

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 boring book with unclear and non-consistent notations, making the book hard to follow. It is neither a good book for beginners nor for anyone who want to do further readings on vector and tensor analysis. The nasty notation style really drove me crazy.