Numerical Integration: Legendre Polynomials

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Polynomials: Legendre and Gauss

Explores Legendre polynomials properties and their use in numerical integration.

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.

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.

Attack on RSA using LLL

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

Orthogonal/Orthonormal Bases and Polynomials

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

Numerical Integration: Composite Formulas

Explores numerical integration through composite formulas, accuracy estimation, and error evaluation in integration methods.

Quadrature Formulas: Newton-Cotes, Lagrange Polynomials, Simpson Rule

Covers quadrature formulas, Lagrange polynomials, and the Simpson rule for accurate integration.