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Hardcover | $35.00 Text | £24.95 | ISBN: 9780262019347 | 256 pp. | 6 x 9 in | 8 b&w illus.| July 2013
 

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Instructor Resources

Functional Differential Geometry

Overview

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.

About the Authors

Gerald Jay Sussman is the Matsushita Professor of Electrical Engineering in the Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology. He is also the coauthor of Structure and Interpretation of Computer Programs (MIT Press, second edition, 1996).

Jack Wisdom is Breene M. Kerr Professor of Planetary Science in the Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology.

Endorsements

"Another gem in the tradition of Structure and Interpretation of Computer Programs and Structure and Interpretation of Classical Mechanics, providing for applied mathematics what the previous two books did for computer science and physics."
Piet Hut, Institute for Advanced Study, Princeton, New Jersey