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Older versions of Numerical Recipes are now available for free online:
Click here for
PDFs of chapters of the older editions. It's a good idea to get a
copy of the book at some point, but for our purposes the older stuff
is "good enough" to get by.
Note that Handbook of
Mathematical Functions by Abramowitz and Stegun is also hosted on
the above link.
Two papers that I found useful while learning about symplectic
integrators: Symplectic
Integrators for Hamiltonian Systems: Basic Theory, and Recent Progress in
the Theory and Application of Symplectic Integrators, both by
Haruo Yoshida.
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