Numerical Methods

  1. Numerical Integration
    1. Newton-Cotes Formulas
      1. Trapezoidal Rule
        1. Single Application
          1. Composite Rule
            1. Error Analysis
              1. Adaptive Implementation
              2. Simpson's Rules
                1. Simpson's 1/3 Rule
                  1. Simpson's 3/8 Rule
                    1. Composite Simpson's Rule
                      1. Error Analysis
                      2. Higher-Order Newton-Cotes
                        1. Boole's Rule
                          1. Weddle's Rule
                            1. Stability Issues
                          2. Romberg Integration
                            1. Richardson Extrapolation
                              1. Romberg Table
                                1. Implementation Algorithm
                                  1. Convergence Analysis
                                  2. Gaussian Quadrature
                                    1. Gauss-Legendre Quadrature
                                      1. Orthogonal Polynomials
                                        1. Nodes and Weights
                                          1. Error Analysis
                                          2. Other Gaussian Rules
                                            1. Gauss-Chebyshev
                                              1. Gauss-Laguerre
                                                1. Gauss-Hermite
                                              2. Adaptive Quadrature
                                                1. Error Estimation
                                                  1. Recursive Subdivision
                                                    1. Tolerance Control
                                                      1. Implementation Strategies
                                                      2. Improper Integrals
                                                        1. Infinite Intervals
                                                          1. Singular Integrands
                                                            1. Transformation Techniques
                                                              1. Special Methods
                                                              2. Multiple Integrals
                                                                1. Iterated Integration
                                                                  1. Product Rules
                                                                    1. Monte Carlo Methods
                                                                      1. Coordinate Transformations

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                                                                    7. Numerical Differentiation

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                                                                    9. Ordinary Differential Equations