- #1
advphys
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Hi to all
∫∫∫∇ψdv = ∫∫ψ ds
over R over S
R is the region closed by a surface S
here dv and ψ are given as scalars and ds is given as a vector quantitiy.
and questions asks for establishing the gradient theorem by appliying the divergence theorem to each component
Divergence theorem
∫∫∫∇.Fdv=∫∫F.ds
i tried writing ψ as some components or some functions of F. i actually tried lots of thing like writing ds or ψ or F in open forms.
but probably i do not understand what it means by "to each component"
and i couldn't find the way that i should approach to the question.
this homework is due tomorrow, so i would really appreciate any help.
Thanks a lot.
Homework Statement
∫∫∫∇ψdv = ∫∫ψ ds
over R over S
R is the region closed by a surface S
here dv and ψ are given as scalars and ds is given as a vector quantitiy.
and questions asks for establishing the gradient theorem by appliying the divergence theorem to each component
Homework Equations
Divergence theorem
∫∫∫∇.Fdv=∫∫F.ds
The Attempt at a Solution
i tried writing ψ as some components or some functions of F. i actually tried lots of thing like writing ds or ψ or F in open forms.
but probably i do not understand what it means by "to each component"
and i couldn't find the way that i should approach to the question.
this homework is due tomorrow, so i would really appreciate any help.
Thanks a lot.