Applied Differential Geometry [Paperback]

William L. Burke (Author)

Book Description

ISBN-10: 0521269296 | ISBN-13: 978-0521269292 | Publication Date: May 31, 1985

This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

Product Details

• Paperback: 436 pages
• Publisher: Cambridge University Press (May 31, 1985)
• Language: English
• ISBN-10: 0521269296
• ISBN-13: 978-0521269292
• Product Dimensions: 8.9 x 6 x 1.2 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,439,645 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

18 of 19 people found the following review helpful:

4.0 out of 5 stars The man was a complete loon, but in a good way., August 14, 2000

By 

Brad Holden (Bay Area, CA USA) - See all my reviews

This review is from: Applied Differential Geometry (Paperback)

The previous review is amazingly perceptive into Bill Burke's personality and thinking. He was not the most discplined writer or lecturer, (I had no less than 4 courses from him) but his insight and intuition could be amazing. I would recommend this book as a companion to something more traditional. If you are interested in General Relativity, which is what the book was suppose to be a precursor for, get Schutz or Misner, Thorne and Wheeler, or Wald.

Also, if you do want this book, get the errata from Burke's webpage,...is quite helpful.

I would also hearitly recommend Burke's best book: Geometry, Spacetime and Cosmology which is out of print. It is much physical and the examples are clearer. He taught english majors and theater students general relativity with that book.

16 of 17 people found the following review helpful:

5.0 out of 5 stars Thinking geometrically..., August 15, 2004

By 

Felipe M. Pait (São Paulo, Brazil, and Brookline, Massachusetts) - See all my reviews
(REAL NAME)   

This review is from: Applied Differential Geometry (Paperback)

A unique book. Changes the way one thinks about geometry. The concepts and tools become second nature. I strongly recommend it for engineers who need differential geometry in their research (they do, whether they know it or not).

To give an example from page 134: "Vector fields that do not commute are called anholonomic. If two transformations commute, then the system would never leave a 2-surface. This obvious results is called the Frobenius Theorem."

Now after reading about the Frobenius Theorem elsewhere, few people would call in "obvious." Nonetheless, when you read Burke, you will agree. (Granted, it will not happen at first reading unless you are already familiar with the material. So you will read the book several times, which only adds to the pleasure.) Afterwards, you will be happy to consult the proof elsewhere.

Caveat: this book is not the place to go for a formal presentation. It may cause conniptions in the more ideological bourbakistes. Nothing should prevent one from also reading some of the excellent texts that present the material in a precise way, for instance those by Manfredo Perdigão do Carmo, Spivak, or Lang. Nonetheless, Burke is the one to go for the intuition.

12 of 23 people found the following review helpful:

3.0 out of 5 stars It's a lot of work but I like it., October 26, 1997

By A Customer

This review is from: Applied Differential Geometry (Paperback)

I'm not a physicist or mathematician but I play one on TV. So I am more qualified to review a book on differntial geometry than either of the above professionals. This book is a very good introduction to all the hairy squibbles that theoretical physicists are writing down these days. In particular if you are perplexed by the grand unification gang then this book will help you understand the jargon. However, having only had physics when advanced vector calculus was enough to get by, it is a bit hard going due to the frequent errors and glosses the author makes. Burke gives a very hip and entertaining introduction to some of the most beautiful ideas in physics. It is enjoyable to read if you like sinking your teeth into something more rewarding than Ann Rice. I gave it a six rating because the errors and glosses are so annoying. I suspect Burke's puckishness is responsible; the book has no actual problem sets but he does work out problems that don't always work out. So the reader really has to work at understanding by correcting the possibly(?) intentional errors. Very sly of him. I am on my second reading and suspect that several readings down the line I will probably get the message. The book deserves loving attention.