Legendre Functions of 2nd Kind & Spherical Harmonics

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Sturm-Liouville Problem: Legendre Equation

Explores the Sturm-Liouville problem linked to the Legendre equation and its significance in physics.

Spherical Harmonics

Explores spherical harmonics, discussing their mathematical properties and significance in quantum mechanics.

Linear Algebra: Abstract Concepts

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

Differentiable Functions and Lagrange Multipliers

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

Local Fields and Correlations in Ising Models

Covers local fields and correlations in Ising models and conformal field theory.

Error Analysis for Galerkin Scheme

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

Polynomials: Definitions and Operations

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

Angular Schrödinger Equation: Spherical Harmonics and Legendre Functions

Explores the angular Schrödinger equation, spherical harmonics, Legendre functions, and quantum numbers in defining electron states.

Complex Functions: Linear and Anti-linear

Covers complex functions, linear and anti-linear functions, harmonic polynomials, rational functions, and exponential functions.

Complex Numbers: Operations and Applications

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