Applied Differential Geometry 1st Edition by William L. Burke (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐very good

⭐pro: good introductory book to physicist. The words are far from rigorous in the mathematical sense, yet provide good intuition. Strongly recommend this book you are just curious about using differential geometry as a tool, without diving too much into the mathematics.con: Sometimes the the writes mentions with just one sentence an important property or intuition. But if you are not already familiar with the fact he is trying to say, you need quite an amount of effort to figure it out.

⭐”Although William Burke left this world – albeit prematurely – his book is still with us, today as a solid teacher of Differential Geometry. Few books have the depth and clarity required as an introduction.Burke was one of the few that both understood the value of twisted tensors and was deft at teaching Differential Geometry using forms with torsion.Few have been able to simplify Schouten forms for undergrads.Perhaps that was William Burke’s greatest academic achievement – bringing Differential Geometry mana from the heavens to students unaware of the benefits.Burke’s other tome ‘Spacetime, Geometry, Cosmology’ is also suitable as a reference for undergrads. ADG, here, is very flexible as a reference, and grad student primer.He was also a godfather to the Chaos Cabal and fostered the Eudaemons: […]

⭐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.

⭐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.

⭐The book does not make any sense to me. Explanation is fuzzy and the text is full of typos.

⭐Good quality book, quick service.

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