Orthogonal Polynomials

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Explores Legendre polynomials and their role in numerical integration techniques.

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

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Explores Bezier curves, emphasizing control points and curve regularity.

Covers the error analysis for the Galerkin scheme and the importance of Galerkin orthogonality.

Introduces the problem of interpolation and demonstrates challenges with adding more points.

Explores polynomial approximation with orthonormal bases and orthogonal projection methods.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

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

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.