Approximation: Polynomial

This lecture introduces the concept of orders of magnitude in physics, historically divided into classical physics, general relativity, and quantum mechanics. It explains how physicists use the notion of orders of magnitude to differentiate between scales of problems and introduces the concept of polynomial approximation through Taylor series expansions, illustrating how complex functions can be simplified by polynomials for analytical or numerical solutions. The lecture also demonstrates how small parameter domains can be approximated by higher-order polynomials, using examples like sine, cosine, and exponential functions to show the validity and usefulness of such approximations.