A&S for the 21st century

Sweet, I just discovered that the old classic 1000-page mathematical reference Abramowitz and Stegun has been updated and distributed for the new millennium (well, and century too) in a more modern way.  It's all there free on its own NIST website (the National Institute of Standards and Technology were the ones who published A&S in the first place back in the 1960s).  Here it is right here:

http://dlmf.nist.gov

It was released just two years ago, with both a book version and this online version, which as far as I can tell is a superset of the book.  Here are the three coolest practical aspects of the website version:

1. next to each equation there's a permalink so you can reference a link straight back to the original section of the equation reference
2. and perhaps even better, also next to each equation there's a link to the TeX source for the equation, so you don't even have to rework it all up in TeX again yourself when using it.
3. and even better than that! - ALSO in each section is a list of links to modern software references for finding software libraries & codes to compute the quantities discussed in each section.  (typically in Fortran; note for each code the link puts you at a bibliography entry for a relevant journal paper, but at the right of that ref there's another link that'll get you to the code and other related documents)

NIST Digital Library of Mathematical Functions

(Note the Riemann zeta function used in their cover plot - for these 3D plots you can even interactively go zip around in them via VRML and X3D)

Tarantola's new physics book

This is kindof an interesting idea (just recently read the intro to this book):  You know how vectors are defined independently of any coordinate system -- they're specific points in space regardless of how you name those points, and e.g. their sum and so on is the same regardless of coord system.  For those who've done a little higher level physics you've seen this is true for tensors in general.  Well, so Albert Tarantola's point in his new textbook Elements for Physics (having only read the intro, mind you) is that our laws of physics are all derived or empirically found in a particular coordinate system, but the quantities they describe needn't be -- for example a scale of temperature could be quantified via the temperature value, the inverse temperature, log temperature, etc., but any given value of one of these quantities is still talking about a particular hotness/coldness.  And his thought is that rather than have one equation that relates temperature to say heat flux, another equation to relate the inverse temp, and another for log temp (even though these particular examples might be simply related), he would go derive the equivalent of those which instead relates the invariant quantities and try to learn something more fundamental about their relationship in the process.  At the end one can always take the invariant quantity and express it in a given coord system.  Ideally that would produce the original historical physics law, and in his examples generally did but at least once apparently didn't (heat flux vs temp, Fourier's Law), which is surprising, not sure came of that.  Anyway, as with his wonderful inverse theory textbook he offers this one in a PDF file free online, with the understanding that if you can afford it and use it then please buy it...