Concept

Orthogonal polynomials

Related lectures (30)

Orthogonal/Orthonormal Bases and Polynomials

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

Linear Algebra: Abstract Concepts

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Orthogonality and Subspace Relations

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Differentiable Functions and Lagrange Multipliers

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

Norms and Orthogonality

Explores norms, orthogonality, and the Pythagorean theorem in vector spaces.

Linear Combinations and Vector Spaces

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

Orthogonal Families & Projections

Covers orthogonal families and projections in vector spaces, including the Gram-Schmidt process.

Interlacing Polynomials

Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.

Numerical Integration: Legendre Polynomials

Explores Legendre polynomials and their role in numerical integration techniques.

Error Analysis for Galerkin Scheme

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

Gauss-Legendre Quadrature Formulas

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

Digital Derivation: Evaluation and Formulas

Explores digital derivation, function evaluation, and polynomial approximations for accurate measurements and evaluations.

Quantum Chemistry: Lecture Series

Series covers spherical coordinates, harmonics, Legendre polynomials, and angular momentum.

Complex Plane and Polynomials

Covers the complex plane, operations, transformations, and complex polynomials.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Correlations of the Liouville function

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Orthogonality and Least Squares

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

Complex Roots and Polynomials

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

Orthogonal Vectors and Projections

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Design Optimisation and Orthogonality: Multilinear Regression

Explores multilinear regression for design optimization and orthogonality, covering teamwork, abstracts, linear and quadratic models, ANOVA, and alias structures.