Polynomials: Legendre and Gauss

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Gauss-Legendre Quadrature Formulas

Explores Gauss-Legendre quadrature formulas using Legendre polynomials for accurate function approximation.

Numerical Integration: Legendre Polynomials

Explores Legendre polynomials and their role in numerical integration techniques.

Numerical Integration: Gauss Quadrature

Explores Gauss quadrature for numerical integration, optimizing evaluation points and weights for accurate results.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Rectangle and Trapezoid Formulas

Covers numerical integration using rectangle and trapezoid formulas, with decreasing error as step size decreases.

Interpolatory Quadrature Formulas

Covers interpolatory quadrature formulas for approximating definite integrals using polynomials and discusses the uniqueness of solutions and practical applications in numerical integration.

Gauss Formulas

Explains the construction and benefits of Gauss formulas for numerical integration.

Attack on RSA using LLL

Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.

Numerical integration: continued

Covers numerical integration methods, focusing on trapezoidal rules, degree of exactness, and error analysis.

Orthogonal/Orthonormal Bases and Polynomials

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.