Question

What is a real-world optimization problem solvable using Taylor Series?

I need to write a math paper, and I am interested in optimization using Taylor series approximations. I am looking for a good scenario or real-world problem to apply this to.

Answer 1

SHM - Simple Harmonic Motion of a Pendulum.

The full DE for the motion of a pendulum of length `l` swung through an angle `theta` is:

`(d^2 theta)/(d t^2) + g/l sin theta = 0`

This cannot be solved analytically but if we use a TS to estimate `theta`, on the assumption that `theta` is small the equation becomes the more familiar:

`(d^2 theta)/(d t ^2) + g/l theta = 0`

which is trivial to solve.