Interpolatory Quadrature Formulas

This lecture introduces the concept of interpolatory quadrature formulas, which are used to approximate definite integrals by evaluating the area under a curve corresponding to a polynomial. The instructor explains the construction of Lagrange polynomials, the properties of quadrature nodes and weights, and the degree of accuracy of these formulas. The lecture covers the process of finding the 'best' partition for accurate approximation, the uniqueness of solutions, and the basis of Lagrange polynomials. Practical applications in numerical integration and the representation of scalar and vector fields are also discussed.