Sussman and Wisdom have written a fascinating book: Structure and
Interpretation of Classical Mechanics. It follows the earlier Sussman
and Abelson Structure and Interpretation of Computer Programs, one of
the true classics in teaching computer science. Both books use
Scheme, the more recent one includes utilities for mathematical
notation, which when integrated with scheme provide a really
interesting form of scripting for mathematics.
Here are some good links.
http://groups.csail.mit.edu/mac/users/gjs/6946/http://en.wikipedia.org/wiki/Structure_and_Interpretation_of_Classical_MechanicsFrank: note the supplement on Differential Geometry:
http://groups.csail.mit.edu/mac/users/gjs/6946/calculus.pdf -- Owen
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