I Computing the Directional Derivative ...

Math Amateur

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I am reading Jon Pierre Fortney's book: A Visual Introduction to Differential Forms and Calculus on Manifolds ... and am currently focused on Chapter 2: An Introduction to Differential Forms ...

I need help with Question 2.4 (a) (i) concerned with computing a directional derivative ...

Question 2.4, including the preceding definition of a directional derivative, reads as follows:


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My question/problem is as follows:

In question 2.4 (a) (i) we are asked to find ##v_p[f]## where ##f## is given as ##f(x) = x## ... .... BUT ... ##v## and ##p## are given in ##\mathbb{R}^3## ... so doesn't ##f## need to be defined on ##\mathbb{R}^3## ... say something like ##f(x,y, z) = x## or similar ...

Help will be appreciated ...

Peter
 

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pasmith

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I agree; none of the examples given in 2.4(a) make sense as functions from [itex]\mathbb{R}^3[/itex] to [itex]\mathbb{R}[/itex].

Are there any hints or solutions in the text which shed light on what the author intended to say here?
 

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