When Integration is Hard

Numerical Analysis · Axiom Academy

INTRO When Integration is Hard Understanding why numerical methods are essential INTRO No Elementary Antiderivative Many common functions have no closed-form antiderivative in terms of elementary functions: Essential in statistics and physics Sometimes we only have discrete data points, not a formula: Tabulated values from simulations We need methods that work with sampled data directly. Multi-dimensional integrals become exponentially harder: With n points per dimension and d dimensions, we need n d evaluations. For n=100 and d=10, that's 10 20 evaluations - impossible! Monte Carlo methods help here.

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