Lectures related to Development Limit: Order 1 and 2

Introduces Lagrange interpolation for approximating data points with polynomials, discussing challenges and techniques for accurate interpolation.

Explores polynomial operations, properties, and subspaces in vector spaces.

Explores Taylor polynomials, odd orders, simplification, residues, and special cases of zero polynomials.

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Explores the uniqueness of minimal polynomials and the division algorithm for polynomials.

Covers linear approximations up to order 2 and the Hessian matrix.

Covers examples of Taylor polynomials and discusses their convergence when approximating functions.

Explores Taylor polynomials for multivariable functions and their applications in function approximation.