Lectures related to Legendre polynomials

Linear Algebra: Abstract Concepts

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

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.

Orthogonal/Orthonormal Bases and Polynomials

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

Quantum Chemistry: Lecture Series

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

Differentiable Functions and Lagrange Multipliers

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

Legendre Functions of 2nd Kind & Spherical Harmonics

Explores Legendre functions of the second kind and spherical harmonics properties and relationships.

Complex Numbers: Operations and Applications

Explores complex number properties, roots, and polynomial equations in the complex plane.

Linear Combinations and Vector Spaces

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

Complex Roots and Polynomials

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

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Constraints, Power, Work, and Kinetic Energy

Explores constraints, power, work, and kinetic energy, including oscillation periods, elliptic integrals, Legendre polynomials, and their applications.

Digital Derivation: Evaluation and Formulas

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

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.

Interlacing Polynomials

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

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Mathematics: Analysis and Algebra Overview

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Bezier Curves: Control Points and Regularity

Explores Bezier curves, emphasizing control points and curve regularity.