Tensor Analysis on Manifolds (Dover Books on Mathematics)

Good

As a physics-math major, I have never come across such a perfect book to start differential geometry. I buy a lot of Dover publishing books because of their cheapness, but this one is probably my most valued geometry book. No other book has been this terse and this clear at the same time.This book provides a solid foundation for everything it does without assuming your understanding of anything before-hand.For example, physicist-geared introductions tend to hide a lot of the real topology and linear algebra behind the subject. Almost every other book I've read assumes knowledge of dual spaces for vector spaces, and just gives a quick definition. This book does not do any of that. It gives clear mathematical details and motivation to go with them.Don't let the book's low price make it appear to be low quality.

Great book to read with Wald and Weinberg. It has the mathematical background if one would like to seek in order to understand the role of tensors in space and what it has to do with GR. Great book well written and understandable.

This book is for mathematics students only. I guess it's considered the "go to" differential geometry starter for mathematicians so I don't want to give it a poor rating. But I'm taking off a star since the authors make the claim that the book is an attempt to broaden the "rather restricted outlook" of tensor analysis "at the stage where the student first encounters the subject," referring to all students of the physical sciences. No, it's an attempt once again by mathematicians to cram their pinheaded tripe down physicist's throats. No physics department I know of would ever use this as a textbook, as it's far too abstract and far too focused on rigorous proofs throughout (but of course that's what mathematicians need so fine for that).The "go to" differential geometry book for physicists is "Geometrical methods of mathematical physics" by Schutz, the top choice of physics departments for decades if pure differential geometry is taught as a "stand alone" course at all (it's usually just recommended reading). It uses the same "concrete" notation and quantities as used in MTW and Wald (and therefore Schutz's "A first course in general relativity"), but covers essentially the same material as Bishop & Goldberg without trying to rigorously prove each tiny step (most of the stuff is obviously true for physicists, but mathematicians are required to rigorously prove everything).

I have just started to read it, generally while waiting for doctors. Chapter "0" provedan excellent review of that which I had learned in '62 and chapter 1 is proving similar.My use of the book at 76 years is to keep the mind alive and it does provide thenecessary challenge!

Great reference for answers on introductory differential geometry. Clear, concise, theory with good examples.

This book leaves too many gaps which need to be filled by readers. For some parts, if the author was not intending to give proof, that is OK, could just give a clear conclusion, instead of offering some half hearted, confusing narration. Too many parts of this book look like English essay, not a rigorous math text book.

Not for someone without a strong background in topology, linear algebra, and analysis. But definitely THE go-to book for mathematicians interested in tensor analysis...

The bible of tensor!

El libro es excelente en cuanto a su contenido y la calidad es muy buena pero el detalle es que por lo general todos mis envios han llegado un poco maltratados por motivo del empaquetamiento, estaría dispuesto a pagar unos cuantos pesos mas por libro para que tuvieran una protección plástica y llegaran en mejor estado.

The text is suitable for anyone interested to learn the basics of differential geometry. The explanations are clear and concise. Among many other introductory differential geometry books, I found this one the best. The book is also suitable for the General Relativity students (like me) and can be treated as a companion to Wald and MTW.

En esta obra se presenta una introducción rigurosa y bien ordenada al Análisis Tensorial. Incluye un par de capitulos sobre Topología y Teoría de Conjuntos para facilitar el estudio tensores en variedades, aunque es necesario tener unos mínimos conocimentos de Cálculo. Además, explica en detalle sus aplicaciones en física (Mecánica de Lagrange y Hamilton).Un aspecto negativo del libro es que no viene con demasiados ejemplos. Sí los tiene, sobre todo en la parte de aplicaciones físicas, pero a veces se echan de menos para afianzar conceptos.Muy buen libro (y buena edición) a muy buen precio.

Very interesting book for those who have come across tensors via general relativity in "the usual way" - ie, with tensors defined in terms on their components. Whilst the concepts and arguments are clear enough, I found (coming from the applied mathematics side) the notation rather opaque at times.