I occasionally fantasize about an “ideal math curriculum” for Physics graduate students, based on my experience, in school and out. Which topics make sense, which don’t, what should count as reasonably expected knowledge, what is actually useful?
There are also some textbooks, several of which having been published after I left school, that I would like to use (actually: like to have used) in the appropriate classes.
Besides the Normal Distribution Function, I occasionally need the Airy Function Ai(x): it arises in perturbation theory and some other contexts. This function is most definitely not part of most standard numerics libraries! While high-quality implementations of it are part of most “serious” numerics libraries (such as SciPy or GSL), these libraries are not always available or convenient.
Here is a really simple numerical approximation: it is numerically “good enough” for casual work, and simple enough to be implemented on the fly as needed.
I recently got interested in singular perturbation theory , and to get help with the algebra, I turned to SymPy. I had tried to use Mathematica in graduate school in the early 90s, but the experience had been sufficiently frustrating that I had steered clear of computer algebra systems since.
SymPy presents itself as a “friendly”, less intimidating alternative, with a more familiar and conventional language and operating model.
Formal perturbation theory, and in particular singular perturbation theory, are standard topics in applied mathematics, but seem to be largely unknown outside that specific community. Which is a shame, because they are both useful, and intellectually fascinating.
Perturbation expansions, in particular for higher orders, have a reputation for being “cumbersome”, as the say: the algebra quickly becomes both tedious and error-prone. Which is true, but it turns out that the SymPy computer-algebra system can be put to good use in this context.
It turns out, Caltech has made the Feynman Lectures available online on their website.
Occasionally, I like to drink hot chocolate — that is, real hot chocolate, from pure cocoa powder and whole milk; not some (sugared, flavored) drink mix.
So, I was somewhat devastated when I learned that the venerable, time-honored Droste (those of the Droste Effect) seems to have gone tragically out of business.
Some replacement was required: at least as good as the original, and satisfying my various purist predilections.