Lecture
This lecture covers the Gauss quadrature method for numerical integration, which optimizes the points where the function is evaluated and the corresponding weights. It explains the Gauss-Legendre formula, solving a nonlinear system of equations, and achieving exact solutions for polynomials up to cubic dependency. The lecture also discusses the advantages of Gaussian quadrature over Newton-Cotes integration, emphasizing the adjustment of weights and nodes based on orthogonal polynomials.