TY  - BOOK
AU  - Sussman,Gerald Jay
AU  - Wisdom,Jack
AU  - Farr,Will
TI  - Functional differential geometry
SN  - 9780262019347 (hardcover : alk. paper)
U1  - 516.36 23
PY  - 2013///
CY  - Cambridge
PB  - MIT Press
KW  - Differential Geometry
KW  - Functional differential equations
KW  - Mathematical physics
N1  - Includes bibliographical references and index; 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--
References--
Index
N2  - 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
ER  -