Back to Numerical Methods
Session 10
Numerical Methods
Gaussian Quadrature and Special Integration Methods
3.5 hours
Duration
8
Materials
6
Objectives
Session Overview
Advanced integration techniques including Gauss-Legendre, Gauss-Laguerre, and Gauss-Hermite quadrature. Orthogonal polynomials, weight functions, and applications to improper integrals.
Learning Objectives
By the end of this session, you should be able to:
- Understand orthogonal polynomial theory and Gaussian quadrature principles
- Implement Gauss-Legendre quadrature for standard intervals
- Apply Gauss-Laguerre quadrature for semi-infinite intervals
- Master Gauss-Hermite quadrature for infinite intervals with exponential weights
- Transform integrals to utilize appropriate Gaussian quadrature methods
- Compare Gaussian quadrature efficiency with Newton-Cotes methods
Course Materials
Download materials for offline study and reference
Orthogonal Polynomial Theory (40 pages)
Available material
Gaussian Quadrature Node and Weight Tables
Available material
Gauss-Legendre Implementation Guide
Available material
Special Weight Function Applications
Available material
Integral Transformation Techniques
Available material
High-Precision Integration Examples
Available material
Programming Project: Gaussian Quadrature Suite
Available material
Comparison with Monte Carlo Methods
Available material