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  "body": "\n## Summary\n\nTime-scale calculus develops derivatives and integrals for functions defined on a time scale, that is, on any nonempty closed subset of $\\R$.\nOn $\\R$ its delta derivative is the ordinary [[derivative|0V1EJCT8G6]], and on $\\Z$ it is the forward difference.\nSo it unifies differential equations and difference equations, and it covers mixed cases such as unions of intervals.\n\n## Explanations\n\n### L1 human\n\nSome processes run in continuous time, some in steps, and some in both, like an insect population that grows in summer and is counted once each winter.\nA time scale is the set of moments at which the process is observed.\nAt a moment followed by a gap, the derivative becomes a difference quotient across the gap; at a moment with no gap, it is the usual limit.\nFor example, on the time scale $\\Z$ the derivative of $t^2$ is $(t + 1)^2 - t^2 = 2t + 1$, not $2t$.\n",
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