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Lecture
Weight of Quadrature Formula
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Quadrature Formulas: Newton-Cotes, Lagrange Polynomials, Simpson Rule
Covers quadrature formulas, Lagrange polynomials, and the Simpson rule for accurate integration.
Simpson's Rule
Covers Simpson's rule for numerical integration and its accuracy for polynomial functions.
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.
Numerical Integration: Basics
Covers digital integration, interpolation polynomials, and integration formulas with error analysis.
Numerical Integration: Quadrature Formulas
Covers numerical integration using quadrature formulas for accurate results.
Numerical Integration: Error Estimation
Covers error estimation in numerical integration methods using composite quadrature formulas and Lagrange interpolation.
Composite Quadrature Formula
Explores the composite quadrature formula, digital integration, and numerical integration techniques using interpolating polynomials.
Trigonometric Interpolation: Approximation of Periodic Functions and Signals
Explores trigonometric interpolation for approximating periodic functions and signals using equally spaced nodes.
Numerical Integration: Lagrange Interpolation, Simpson Rules
Explains Lagrange interpolation for numerical integration and introduces Simpson's rules.
Lagrange Interpolation
Introduces Lagrange interpolation for approximating data points with polynomials, discussing challenges and techniques for accurate interpolation.