Approximating Functions with Polynomials

This lecture covers the process of approximating functions with polynomials of degree 2 in the context of inner product spaces. The instructor demonstrates the construction of an orthonormal basis for the space, providing a detailed explanation of the calculations involved. Various methods for polynomial approximation are discussed, including the projection onto the space of polynomials. The lecture also explores the application of these concepts to cosine functions, showcasing the construction of bases and the calculation of inner products. Key topics include polynomial approximation, orthonormal bases, inner product spaces, and cosine functions.