Tensors, Differential Forms, and Variational Principles and over one million other books are available for Amazon Kindle. Learn more

Sorry, this item is not available in
Image not available for
Image not available

To view this video download Flash Player


Sign in to turn on 1-Click ordering
More Buying Choices
Have one to sell? Sell yours here
Start reading Tensors, Differential Forms, and Variational Principles on your Kindle in under a minute.

Don't have a Kindle? Get your Kindle here, or download a FREE Kindle Reading App.

Tensors, Differential Forms, and Variational Principles (Dover Books on Mathematics) [Paperback]

David Lovelock , Hanno Rund , Mathematics
4.2 out of 5 stars  See all reviews (17 customer reviews)

List Price: $17.95
Price: $9.32 & FREE Shipping on orders over $35. Details
You Save: $8.63 (48%)
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
In Stock.
Ships from and sold by Amazon.com. Gift-wrap available.
Want it Monday, July 14? Choose One-Day Shipping at checkout. Details
Free Two-Day Shipping for College Students with Amazon Student


Amazon Price New from Used from
Kindle Edition $8.85  
Hardcover --  
Paperback $9.32  
Unknown Binding --  

Book Description

April 1, 1989 0486658406 978-0486658407 New edition
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments.

Frequently Bought Together

Tensors, Differential Forms, and Variational Principles (Dover Books on Mathematics) + Differential Geometry (Dover Books on Mathematics) + Tensor Analysis on Manifolds (Dover Books on Mathematics)
Price for all three: $29.55

Buy the selected items together

Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 400 pages
  • Publisher: Dover Publications; New edition edition (April 1, 1989)
  • Language: English
  • ISBN-10: 0486658406
  • ISBN-13: 978-0486658407
  • Product Dimensions: 8.5 x 5.4 x 0.7 inches
  • Shipping Weight: 12.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (17 customer reviews)
  • Amazon Best Sellers Rank: #178,269 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews
77 of 81 people found the following review helpful
5.0 out of 5 stars One of the best books ever April 29, 2002
I don't know how they did it but, this is the book you want to buy if you're trying to learn differential geometry, especially if you're learning general relativity. It takes you from the concepts you are already familiar with into differential geometry faster than any other book I've ever tried (and I've tried many!). Before you know it, you are comfortable with covariant derivatives and Lie derivatives and.. well the list could go on. Do not be turned off by the reputation of Dover books-- "cheap and not worth it!" This is a gem.
For those of you learning GR: Buy this book and Schutz's "Geometrical Methods of Mathematical Physics." Read Lovelock and Rund first and then dive into Schutz's book. This will provide you with the necessary mathematical background to handle Wald's "General Relativity" with (some amount of) ease. You might want to try Schutz's "A First Course in General Relativity" before Wald's more advanced book.
I've read many glowing reviews on Amazon about books that I "must have" and, quite frankly, they turned out to be poor choices. But in this case I have to say you "must have" this book! It is that good. And it's cheap, so if you do not agree with me, it's not much money out of your pocket.
Was this review helpful to you?
40 of 42 people found the following review helpful
5.0 out of 5 stars Rigorous, yet informal enough to be a lot of fun. August 8, 2003
Many years ago, this became the first book I had ever read about tensor calculus, differential geometry, or classical field theories, and I still have not found a much better treatment of any of these subjects anywhere else.

The notation is often very classical, in the sense that there are a lot of indices, usually referring to coordinate bases, and there is a lot of talk of "transformation laws." While this style can be distressing to more advanced students, those familiar with the beautiful methods of avoiding such structures, I think it is useful to younger students, especially physicists, who yearn for concrete examples. Also, for the one section in which a more formal approach is advantageous, such a treatment is included as an appendix.

The book is also wonderful for its breadth. It is not a "tensor calculus" book, or a "differential geometry" book. It is really best described as a "geometrical methods" book "with applications to theoretical physics." Yet unlike most examples of this now-cliched subject, the breadth of material is matched by a cohesion of style.
Comment | 
Was this review helpful to you?
64 of 72 people found the following review helpful
2.0 out of 5 stars All in the indices January 11, 2005
As mentioned below, this book concentrates for 330+ pages on a "classical" index-based approach to tensors. Coordinate-free treatment is restricted to a brief appendix. There are only 10 illustrations in this very long book (none in the appendix). That means that you will need to concentrate very hard on the manipulation of many tiny indices in some long and hairy equations.

My hat's off to people who can learn this way, but I am in the camp that expects pictures for geometrical subjects. In this respect, Schutz is a much better book, as well as being coordinate-free from the get-go. (Ditto for Misner Thorne Wheeler and Carroll on general relativity, as well as various works by V. Arnol'd or J. Marsden that deal with this material in classical physics contexts.) I bought this book as a reference -- it might be useful also for people who want to come up with computational approaches to the material.

I might have given the book 3 stars but for the facts that (i) no solutions to exercises (only some of which are in the "show that this stuff = X" format) and (ii) text is filled with "clearly"s, "obviously"s and other superfluities.
Was this review helpful to you?
19 of 19 people found the following review helpful
I have to side with reviewers who say this book is near perfect. The original hardcover edition was a favorite of mine when I was an undergrad and its paperback reissue by Dover is a blessing. Readers who complain about the notation may be too easily blinded. Indices are certainly used abundantly, especially in the derivation of tensor theory on affine connections, but this practice actually fits well with the authors' objectives. By retaining traditional notation through most of the book, L&R provide the student with familiar handles to grasp, and the typesetting is the best I've seen for this kind of notation.

A huge value of this book is how it clarifies mathematical details that many other books make confusing. The material is well-organized and guides the reader clearly through most of the derivations. L&R carefully develop (as the notes say, by successive abstraction) the theory of tensor calculus on vector spaces to that of differential forms on Riemannian manifolds. They compare the deployment of affine connections in the former and metric tensors in the latter, enabling the reader to see how curvature can be defined in either context with minimum confusion.

Once differential forms are introduced, the notation becomes more modern and compact, though the use of boldface type common to "geometric" notation is nowhere in the book. Useful integral theorems of Stokes and the invariance properties of Lagrangian systems are derived in the language of differential forms. An appendix summarizing the theory of exterior calculus on differentiable manifolds closes the book.

In conclusion, this book is excellent complementary reading for anyone attempting to master the mathematics essential for General Relativity theory, and in good company with other Dover reprints by Bishop & Goldberg, Flanders and Pauli. Even if you have the dough for Misner Thorne & Wheeler and the spine to lug it around, you might want these other books in your library too.
Comment | 
Was this review helpful to you?
Most Recent Customer Reviews
5.0 out of 5 stars Strong on motivation. Heavy on the coordinates.
The authors make a very strong, and successful, attempt to motivate the key tensor calculus concepts, in particular Christoffel symbols, the Riemann curvature tensor and scalar... Read more
Published 12 months ago by Alan U. Kennington
I am quite mathematically oriented and have found 'Tensor Theory' as difficult as anything I have worked at. Read more
Published 15 months ago by Richard L. Pendleton
5.0 out of 5 stars Lovelock and Rund, Tensors, Differential Forms and Variational...
The book was shipped in a cardboard box which protects the corners of the book. The book is as described by the seller: tight binding, like new except for foxing on top edge, no... Read more
Published on May 24, 2012 by David C Hom
5.0 out of 5 stars Best book about tensors out there
Excellent for self study. If you work out ALL the problems, you will learn about tensors and their application to field theories more than in any other book. Read more
Published on September 1, 2009 by M. Nahmany
5.0 out of 5 stars One of the best books I've studied on invariant variational...
I bought this book six years ago for the exercises on tensor analysis and differential forms and it has become one of my favorite texts on invariant variational principles. Read more
Published on July 28, 2007 by A. Van Dyk
2.0 out of 5 stars Cryptic
I think I have a decent handle on the prerequisites for this subject, and I frankly found this to be cryptic. Read more
Published on February 22, 2007 by Peidyen
5.0 out of 5 stars Helpful for the advanced student
This is a helpful book for the advanced undergraduate/graduate student. It contains difficult mathematics, so it is a good overview of the matter, but not for the enthusiastic... Read more
Published on January 30, 2007 by Erik Bijkerk
2.0 out of 5 stars Not for self study
I bought this book togheter with Kay - Tensor analysis - when I began to study tensors. Kay could be not a masterpiece, but you can use it to learn the subject with some efforts... Read more
Published on April 21, 2006 by giancarlo bernacchi
5.0 out of 5 stars A MUST, if one wants to learn the subject
The two authors must be experts in this field. Without wasting words, they always well motivate, why something is done. Read more
Published on September 11, 2005 by PST
5.0 out of 5 stars Amazing, it's only eleven dollars but worth HUNDREDS
This is a book from which you can learn about tensors and really KNOW WHAT'S GOING ON!!! Sure, so you can complain about it's slight lack of rigor--big deal!!!!! Read more
Published on July 3, 2004
Search Customer Reviews
Search these reviews only

What Other Items Do Customers Buy After Viewing This Item?


There are no discussions about this product yet.
Be the first to discuss this product with the community.
Start a new discussion
First post:
Prompts for sign-in

Look for Similar Items by Category