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1. Introduction to Functional Differential Geometry 2. Computational Smooth Manifolds 3. Vector Fields and One-Form Fields 4. Basis Fields and Frame Operations 5. Integration and Differential Forms 6. Pullbacks and Integration Over a Map 7. Directional Derivatives and Connections 8. Curvature Tensors and Lie Brackets 9. Metric Tensors and Riemannian Geometry 10. Hodge Star and Electrodynamics 11. Mathematical Structures in Special Relativity
Functional Differential Geometry by Gerald Jay Sussman, Jack Wisdom, and Will Farr bridges the gap between abstract mathematical formalism and executable computer code. Accessing this gerald sussman functional differential geometry pdf enables computer scientists, mathematicians, and physicists to explore coordinate-free geometry using functional programming principles. The book systematically covers vector fields, Lie derivatives, directional derivatives, exterior calculus, and metric tensors through precise executable algorithms. Studying this unique functional differential geometry sussman book equips readers with unambiguous computational structures for classical mechanics and general relativity. Offered as an open academic reference functional differential geometry pdf download, this masterwork remains an indispensable guide for software engineers, topologists, and theoretical physicists seeking computational clarity in differential geometry.
Title: Functional Differential Geometry by Gerald Jay Sussman Publisher: The MIT Press Year: 2013 Pages: 249 Type: PDF Language: English ISBN-10 #: 0262019345 ISBN-13 #: 978-0262019347 License: CC BY-NC-SA 4.0 Amazon: Amazon
The author Gerald Jay Sussman is the Panasonic Professor of Electrical Engineering at the Massachusetts Institute of Technology (MIT) and co-creator of the Scheme programming language and the landmark textbook SICP (Structure and Interpretation of Computer Programs). Co-authored with Jack Wisdom, Professor of Planetary Sciences at MIT, their collaborative volume Functional Differential Geometry by Gerald Jay Sussman demonstrates how functional abstractions bring absolute mathematical precision to differential geometry.
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