Numerical Methods

  1. Numerical Differentiation
    1. Finite Difference Formulas
      1. First Derivative Approximations
        1. Forward Difference
          1. Backward Difference
            1. Central Difference
              1. Error Analysis
              2. Higher-Order Derivatives
                1. Second Derivatives
                  1. Higher-Order Formulas
                    1. Multi-Point Formulas
                    2. Unequally Spaced Data
                      1. Lagrange Polynomial Approach
                        1. Finite Difference Tables
                      2. Richardson Extrapolation
                        1. Extrapolation Principle
                          1. Error Reduction
                            1. Implementation Algorithm
                            2. Error Analysis
                              1. Truncation Error
                                1. Round-off Error
                                  1. Total Error
                                    1. Optimal Step Size
                                      1. Step Size Selection

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                                    6. Curve Fitting and Least Squares

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                                    8. Numerical Integration