Introduction to Vector and Tensor Analysis

by Robert C. Wrede

A broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.

Genres: Mathematics, Physics

418 pages, Paperback

First published January 1, 1972

Reviews

[Paul · Rating 2 out of 5]

So I picked up this book back in the 1990s to continue my self-training in mathematics, and between my active video game addiction and, as I now see, the book itself, I didn't get very far. As it turns out, reading Penrose's Road to Reality provided considerable motivation to tackle even the chunks that I did (chapter 1 and most of chapter 5 of this 5 chapter book; definitely a book's worth of effort!); I can't imagine my teenage self having any idea why we were talking about this covariant and contravariant gibberish, for instance.

In any case, this book has serious flaws. It's presented in the formal axiomatic style of Definition This and Theorem That, but it's seriously out of order. Important terms are introduced and left undefined, sometimes for chapters, possibly never at all (if the index is to be believed)...the idiosyncratic use of the term "arrow," for example. When definitions do occur, they are by no means always clear, nor are they used coherently in the ensuing discussion. The proofs are generally pretty hurried. Without having taken the time, or having the background, to evaluate them, I merely comment that I suspect a number of them are quite shaky.

I anticipate seeking out other books to attack this material.