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Functional differential geometry

Author: Gerald Jay Sussman; Jack Wisdom; Will Farr
Publisher: Cambridge, MA : The MIT Press, [2013] ©2013
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
"Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Sussman, Gerald Jay.
Functional differential geometry.
Cambridge, MA : The MIT Press, [2013]
(DLC) 2012042107
(OCoLC)825398878
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Gerald Jay Sussman; Jack Wisdom; Will Farr
ISBN: 9780262315609 0262315602
OCLC Number: 854583698
Language Note: Text in English.
Notes: New math 17.
New phys 17.
Description: 1 online resource (xx, 228 pages)
Contents: 1. Introduction --
2. Manifolds --
3. Vector fields and one-form fields --
4. Basis fields --
5. Integration --
6. Over a map --
7. Directional derivatives --
8. Curvature --
9. Metrics --
10. Hodge star and electrodynamics --
11. Special relativity --
A. Scheme --
B. Our notation --
C. Tensors.
Responsibility: Gerald Jay Sussman and Jack Wisdom with Will Farr.

Abstract:

"Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level. The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding."

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