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Numerical_Analysis - Home
  • 1. Preliminaries
    • 1.1. Mathematical Preliminaries
    • 1.2. Error Analysis
    • 1.3. Algorithms and Convergence
    • 1.4. Big O Notation
  • 2. Root-finding algorithms
    • 2.1. Bracketing Methods
    • 2.2. Fixed-point iteration
    • 2.3. Newton methods
    • 2.4. Error Analysis for Iterative Methods
    • 2.5. Acceleration of Convergence
    • 2.6. Zeros of Polynomials and Müller’s Method
  • 3. Interpolation and Polynomial Approximation
    • 3.1. Introduction
    • 3.2. Vandermonde Method
    • 3.3. Interpolation and Lagrange polynomial
    • 3.4. Newton Polynomial
    • 3.5. Linear Regression
  • 4. Numerical Differentiation
    • 4.1. Approximation of the First Derivative of a Function
    • 4.2. Approximation of the second derivative of a function
    • 4.3. Higher-order approximations
  • 5. Numerical Integration
    • 5.1. Introduction
    • 5.2. Trapezoidal rule
    • 5.3. Simpson’s rule
    • 5.4. Midpoint rule
    • 5.5. Gaussian quadrature
  • 6. Initial-Value Problems for Ordinary Differential Equations
    • 6.1. Introduction
    • 6.2. The elementary theory of initial-value problem
    • 6.3. First-order methods
    • 6.4. Higher-Order Taylor Methods
    • 6.5. Runge–Kutta methods
  • 7. Numerical Linear Algebra
    • 7.1. Gaussian elimination for Linear Systems of Equations
    • 7.2. Matrix Factorization
    • 7.3. Cholesky factorization
    • 7.4. LDL decomposition
    • 7.5. QR factorization
  • 8. Regularization Methods
    • 8.1. Savitzky-Golay Filter
  • 9. References

Numerical Integration

5. Numerical Integration#

  • 5.1. Introduction
  • 5.2. Trapezoidal rule
  • 5.3. Simpson’s rule
  • 5.4. Midpoint rule
  • 5.5. Gaussian quadrature

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4.3. Higher-order approximations

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5.1. Introduction

By Hatef Dastour

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