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The episode illustrates the use of linear approximation and thedifferentialofafunction.
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A closely related notion is thedifferentialofafunction.
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Importantly, the core of their insight was the formalization of the inverse properties between the integral and thedifferentialofafunction.
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This leads directly to the notion that thedifferentialofafunctionat a point is a linear functional of an increment "x".
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More precisely, an inexact differential is a differential form that can not be expressed as thedifferentialofafunction.
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