Lectures related to Polynomials: Legendre and Gauss

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.

Numerical Integration: Gauss Quadrature

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

Differentiable Functions and Lagrange Multipliers

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

Rectangle and Trapezoid Formulas

Covers numerical integration using rectangle and trapezoid formulas, with decreasing error as step size decreases.

Interpolatory Quadrature Formulas

Covers interpolatory quadrature formulas for approximating definite integrals using polynomials and discusses the uniqueness of solutions and practical applications in numerical integration.

Gauss Formulas

Explains the construction and benefits of Gauss formulas for numerical integration.

Attack on RSA using LLL

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

Numerical integration: continued

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

Orthogonal/Orthonormal Bases and Polynomials

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

Numerical Integration: Composite Formulas

Explores numerical integration through composite formulas, accuracy estimation, and error evaluation in integration methods.

Numerical Integration: Basics

Covers digital integration, interpolation polynomials, and integration formulas with error analysis.

Nonlinear Geometric Transformation: Analysis and Approximations

Explores nonlinear geometric transformations in structural engineering, emphasizing accurate integration methods and practical applications.

Power Systems Dynamics: Transient Stability

Explores transient stability in power systems dynamics, covering algebraic equations, generator models, and numerical integration techniques.

Numerical Integration: Quadrature Formulas

Covers numerical integration using quadrature formulas for accurate results.

Quantum Chemistry: Lecture Series

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

Numerical Analysis: Introduction to Computational Methods

Covers the basics of numerical analysis and computational methods using Python, focusing on algorithms and practical applications in mathematics.

Nonlinear Analysis of Structures: Integration Methods

Covers integration methods and element stiffness matrices for nonlinear structural analysis.

Polynomial Approximation: Orthonormal Basis and Projection

Explores polynomial approximation with orthonormal bases and orthogonal projection methods.

Numerical Integration: Lagrange Interpolation, Simpson Rules

Explains Lagrange interpolation for numerical integration and introduces Simpson's rules.