I've mostly been writing about a new kind of math class at the high school level that distinguishes itself from the precalculus  calculus track. This has partly to do with politics, as I think it's easier to develop something new and set that alongside already existing options (traditional courses) than it is to introduce reforms in already "programmed" offerings. However, Python has some capabilities when it comes to calculus, in scipy and Sage for example. Plus it's of course easy to take anything one might do with a calculator in support of learning calculus concepts, and do that same thing in Python instead. This was somewhat my approach in writings I did on the catenary some years ago (the catenary is a curve similar to a parabola but different). http://www.4dsolutions.net/ocn/catenary.html At this point though, it's maybe a moot point whether we try to embrace more calculus with Python or not. The premise was doing something more exciting with technology than scientific calculators, introducing a real programming language, and yet having this considered a math class as much as a computer class. This was against the backdrop of the "math pipeline" being broken according to many criteria, i.e. in need of some upgrades. Some progress has been made in small niches, but in many respects the current mood is to freeze features i.e. the response to rapid change is to codify and pickle that which once was. So I'm back to thinking only brand new courses will have a chance. They have to be seen as new, and the expectation must be that new material will be covered. Perhaps for this reason I find myself venturing into Wolfram territory as he's always talking about his "new kind of science". Those little cellular automata studies are actually pretty easy to implement in Python (we've done it here on edusig, with John Zelle's graphics.py, PIL and native Tkinter). http://www.4dsolutions.net/presentations/holdenweb/mini_nks.py I'm going to say more about these calculus exercises at some point, not sure how soon. This relates to the thread about generating tables. That was pretty fruitful thread, glad so many jumped in. We need to see that in some ways having computers put out to text files is a way to get back to the good old days, when we could explore reams of data. What's better nowadays is we don't really need all that paper (lets not waste it). We have hard drives and LCDs instead. Kirby PS: found this old exhange with Matthias of DrScheme fame. He just got some prestigious award, per an announcement on maththinkingl. ============= from scipy.integrate import quad, dblquad, Inf from numpy import arange from math import exp, log, pi, sin, cos def test0(): """ Integration example http://www.scipy.org/doc/api_docs/SciPy.integrate.quadpack.html """ def thefunc(x): return cos(x) for a in arange(0, 2*pi, 0.1): output = quad(thefunc, 0, a)[0] fmtstring = "Integral of cos(x) from 1 to {0} = {1}: sin({0}) = {2}" print fmtstring.format(a, output, sin(a)) def test1(): """ Integration example http://www.scipy.org/doc/api_docs/SciPy.integrate.quadpack.html """ def thefunc(x): return 1./x for a in range(1,21,2): output = quad(thefunc, 1, a)[0] fmtstring = "Integral of 1/x from 1 to {0} = {1}: ln({0}) = {2}" print fmtstring.format(a, output, log(a)) def test2(): """ Double integration example http://www.scipy.org/doc/api_docs/SciPy.integrate.quadpack.html """ def I(n): return dblquad(lambda t, x: exp(x*t)/t**n, 0, Inf, lambda x: 1, lambda x: Inf) print I(4) print I(3) print I(2) def test3(): """ Double integration example same as above but without using lambda http://www.scipy.org/doc/api_docs/SciPy.integrate.quadpack.html """ def mkfunc(n): def thefunc(t, x): return exp(x*t)/t**n return thefunc def xfrom(x): return 1 def xto(x): return Inf def I(n): thefunc = mkfunc(n) return dblquad(thefunc, 0, Inf, xfrom, xto) print I(4) print I(3) print I(2) def doall(): test0() #test1() #test2() #test3() if __name__ == '__main__': doall()
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kirby urner