Approximation of Functions

This lecture covers the topic of approximating functions using polynomials through the method of interpolation. The instructor explains the process step by step, from defining the partition of an interval to demonstrating the regularity of the error term. Various concepts such as the theorem of Rolle and the phenomenon of Runge are discussed in the context of function approximation. The lecture emphasizes the importance of choosing optimal points for interpolation to minimize errors and explores the impact of different types of functions on the accuracy of the approximation.