Rectangle and Trapezoid Formulas

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

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

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

Explores Legendre polynomials and their role in numerical integration techniques.

Covers numerical integration techniques, focusing on Lagrange interpolation and various quadrature methods for approximating integrals.

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

Explains Lagrange interpolation with M=2, covering base polynomials and linear independence.

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

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.