Exercise 2: Deriving the 1st Order and 3rd Order Optics Formulas https://youtu.be/leZ0QK_n07k

In this video, I derive the first-order and third-order optics formulas by approximating the refraction formula for light using first and third-order Taylor polynomials, respectively.

Example 1: Approximating Cube Root Function by a 2nd Degree Taylor Polynomial https://youtu.be/0616gOyjbyQ

In this video I approximate the cube root function x^(1/3) by using a 2nd degree Taylor polynomial at a = 8. The first step is to obtain the first 2 derivatives of f at x = 8, and then the third derivative to be used for the error estimation.