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PY 502, Computational Physics, Fall 2021 Numerical Integration and Monte Carlo Integration

Here we will begin by deriving the basic trapezoidal and Simpson’s integration formulas for functions that can be evaluated at all points in the integration range, i.e, there are no singularities in this range. We will also show how the remaining discretization errors present in these low-order formulas can be systematically extrapolated away to arbitrarily high order; a method known as Romberg integration. Multi-dimensional integrals can be calculated ”dimension-by-dimension” using these one-dimensional methods.