The obvious answer is via Sage and SymPy, which will do differentiation and integration symbolically to some degree.
http://www.scipy-lectures.org/advanced/sympy.html#differentiation However even plain old core Python helps in that students get a sense of functions as top-level citizens. I'm not saying Python is alone in providing this. If the C language could be written: function func(function f1, function f2):{ } with type function both eaten and returned, then we could use C for this kind of thing also. http://mathforum.org/kb/message.jspa?messageID=10168568 (more on this general topic) The repl below (you may skip modal window) shows my latest slimmed down version of Compose, something I introduce to the O'Reilly course as well. https://repl.it/HxMo/2 Function type objects don't ordinarily multiply but what if we want to write h = f * g instead of h(x) = f(g(x)). For one thing, why mention x at this point (the argument object) as we're simply defining a function, not calling it with an input right? The Compose class is just the ticket, swallowing and wrapping a function with a __mul__ API. Now * is your compose operator. Or use __matmul__ for @ symbol. Note then, the use of Compose as a class decorator to the same end. Feel free to recycle this animal in your own lesson plans. MIT license or whatever. Kirby PS: one of the Pycon keynotes was about the affordability of nuke energy, with the claim / calculation that it's less risky to workers than coal. I didn't have time to go up to the podium after and listen in on the conversation. We should have started a BOF. Simulating / modeling risk is something I'm into through CERM Academy. We could start a thread on Facebook.
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