Manifolds, Tensor Analysis and Applications (Applied Mathematical Sciences) [Hardcover]

Ralph Abraham (Author), Jerrold E. Marsden (Author), Tudor Ratiu (Author)

Book Description

Series: Applied Mathematical Sciences | Publication Date: December 31, 1988

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma dynamics and control theory are given using both invariant and index notation. The prerequisites required are solid undergraduate courses in linear algebra and advanced calculus.

--This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 654 pages
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K; 2nd edition edition (December 31, 1988)
• Language: German
• ISBN-10: 3540967907
• ISBN-13: 978-3540967903
• Product Dimensions: 9.3 x 6.4 x 1.6 inches
• Shipping Weight: 2.5 pounds
• Average Customer Review: 3.2 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #7,341,548 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

13 of 14 people found the following review helpful:

5.0 out of 5 stars A Unique Reference, October 9, 2000

By A Customer

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This review is from: Manifolds, Tensor Analysis, and Applications (Applied Mathematical Sciences) (v. 75) (Hardcover)

Students of mathematical physics in general, and general relativity in particular, face a formidable challenge in attempting to find coherent, readable references on manifold theory and tensor analysis. I think it fair to say that for every well-written work on the subject, there are ten that do more damage than good. Very few texts can claim to (1) be clear enough to assist the person who is studying alone, (2) offer valuable PHYSICAL insight into the subject, and (3) pass the standards of rigor that mathematicians would impose. Abraham, Marsden, and Ratiu manage to accomplish all three of these goals in this profoundly useful text. I studied from the first edition and I have taught from the second. The two chapters on differential forms, Hodge star duality, integration on manifolds, and the generalized Stokes' Theorem alone are worth the price of the entire book. I am unaware of any other reference which which treats differential forms with the same combination of clarity, physical motivation, and mathematical rigor. The concluding chapter on applications offers one of the clearest introductions to the relativistic form of Maxwell's equations to be found in any text. For students of physics who want to see the mathematics "done right," one would be hard pressed to do better than Abraham, Marsden, and Ratiu.

22 of 27 people found the following review helpful:

1.0 out of 5 stars Poorly writen, filled with errors, very long, poorly indexed, September 21, 1999

By A Customer

This review is from: Manifolds, Tensor Analysis, and Applications (Applied Mathematical Sciences) (v. 75) (Hardcover)

We used this book in a graduate course at UCLA. The professor had to hand out a list of all the errors we encountered, and it was about ten pages typewritten. The professor, Geoff Mess, wrote at the top of this list that many of the students had complained about this book, and that it was a disappointment to him as well. I often found myself scanning hundreds of pages in search of what should have been contained in their sparse index. The book is unnecessarily long and wordy for the matter covered. In the introduction, the authors mention that they invite comments from the readers. It seems that they depend on their readers to correct their copious errors and their poor writing.

13 of 15 people found the following review helpful:

5.0 out of 5 stars A complete book by very erudite authors, April 6, 2002

By A Customer

This review is from: Manifolds, Tensor Analysis, and Applications (Applied Mathematical Sciences) (v. 75) (Hardcover)

I actually read this entire book--it is quite long and dense. Actually I took the course from the author Jerry Marsden at Caltech and Tutor (Jerry's friend and co-author) gave a guest lecture while visiting. We flew through the entire thing and ch 9 on lie groups of his mechanics and symmetry text in a short 10 weeks! My background in math was relatively weak when taking the course so it was a little hard to keep up; i.e. I came from an engineering background. Anyway, it is probably the most complete/diverse text I've come across on the subject. Of course, it's actually more of a monograph than a text. Since I've read the whole thing, I have to admit there are "several" typos. But as it is that most people can't even write a damn email without a typo or two, the book really does a good job considering it is 800 pages of mostly dense mathematical rigor. I imagine that if I wrote 800 pages of mathematical symbols in latex, that I might forget a tilde or put something as subscript that should have been superscript here or there! None of these errors really matter too much-they should not hinder one's understanding. All and all I think that this book is a great ref, although I've never seen the index, if one exists. For the beginner, also check out Boothby's book, which covers a lot of the same material but tones it down a bit.