Here are some links and resources for the fifth week of the course.
There is some interesting calculus going on. Linearization for example is extremely
important when doing computations fast. A recent movie
Shakuntala (2019)
demonstrates how fast humans can compute cube roots of very large numbers. Also interesting
is the foundations on how to define the exponential function. One can relate it to the
compound interest formula f(x)=(1+h)x/h where n=x/h is the number of steps (years)
and h is a small number (interest rate). This function f(x) satisfies [f(x+h)-f(x)]/h = f(x)
exactly and in the limit we get (ex)' = ex.
The compound interest formula appears in the movie
the bank (2001).
Linearization appears in the movie
Infinity (1996).
Here is a 400 second presentation of mine in 2013, where I do all 1a and 1b and part of 21a calculus
with proofs! Defining the exponential function in an intelligent way is key to this quantum calculus:
