[Tutor] Python for Grade 12 Calculus

[Danny Yoo]

On Thu, Feb 11, 2016 at 2:56 PM, Nicholas Tomasic
<ntomasic.blyth at gmail.com> wrote:
> Hi,
>
> I'm a 12th grade Calculus teacher at a school in Toronto, Ontario, and I'm
> thinking about incorporating Python into an Independent Study Project for
> two of my students. Both are passionate about coding with Python and I'm
> thinking of asking them to produce something that can either a) calculate
> derivatives of simple functions or b) assign 1 student the product rule,
> one the quotient rule, and have them write a program that can tackle
> derivatives in those forms.
>
> The problem is: I know very little about Python.
>
> Unfortunately, I don't have a specific question but I'm looking for any
> valuable insights or suggestions.


This may be one of the places where they can see more clearly that the
type of the derivative operator is:

    derivative: (number->number) -> (number->number)

That is, that the derivative is a function that consumes functions as
first-class values, and produces first-class values.  Calculus is
supposed to be one of the first places where they see a function whose
domain and range are not plain, inert numbers, but functions.

A numerical approach leads naturally to:
http://aroberge.blogspot.com/2005/04/computing-derivatives-using-python.html


You might also want to look at:

    https://mitpress.mit.edu/sicp/full-text/sicp/book/node39.html

for some inspiration: it shows in another language (Scheme) how to
approach symbolic differentiation from first principles.