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  "body": "\n## Summary\n\nA finite difference of a function is the change of its value between two points at a fixed distance, such as $f(x + h) - f(x)$.\nDivided by the step $h$, it becomes a [[difference quotient|AZBDB5F4M4]], which approximates the derivative when $h$ is small.\nFinite differences are the basic operation of difference equations, of interpolation and of numerical methods for differential equations.\n\n## Explanations\n\n### L1 human\n\nA derivative measures change over an infinitely small step; a finite difference measures change over a step of fixed size.\nThink of reading a thermometer once every hour: the hourly changes are finite differences of the temperature.\nFor $f(x) = x^2$ and step $1$, the difference is $(x + 1)^2 - x^2 = 2x + 1$.\nThe three usual kinds look forward, backward, or symmetrically around the point.\n",
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