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Differential of a function vs differential forms

  1. Dec 29, 2012 #1
    I understand the concept of the differential of a (differentiable) function at a point as a linear transformation that "best" approximates the increment of the function there. So for example the differential of a function [itex]f : D \subseteq \mathbb{R}^2 \to \mathbb{R}[/itex] could maybe be [itex] df = 8 dx + 9 dy [/itex] at a given point, say [itex] (2,3)[/itex]

    But I wanted to know how this concept of differential is related to the integral concept of differential form, so for example [itex] 8dx + 9dy[/itex] can be thoght as a differential form and be integrated over a curve. But the differential form usually varies from point to point so it could be more like [itex] (3x+y^2)dx + (3xy) dy[/itex], so I'm not sure if it also is been thought as a linear map, or should I think of these both concepts as completly different and unrelated things?

  2. jcsd
  3. Dec 29, 2012 #2


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    I don't know if this is what you're looking for, but the differential of a differentiable function is a differentiable form, i.e., if f is a differentiable function, then df is a 1-form.
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