Vector Calculus curl's and divergence?Watch

#1
In the context of these questions what is r? Is it the sqrt(x^2+y^2+z^2)?
Also wherever you see an x it should be underlined/ highlighted because it's meant to be a vector.

. If f(r) is a differentiable function of r = ||x ||, show that
(a) grad f(r) = fâ€²(r) x /r,
(b) curl [f(r)x ]=0 .

15. Let x be the position vector in three dimensions, with r = ||x ||, and let a be a constant vector. Show that
0
4 years ago
#2
(Original post by CammieInfinity)
In the context of these questions what is r? Is it the sqrt(x^2+y^2+z^2)?
Also wherever you see an x it should be underlined/ highlighted because it's meant to be a vector.

. If f(r) is a differentiable function of r = ||x ||, show that
(a) grad f(r) = fâ€²(r) x /r,
(b) curl [f(r)x ]=0 .

15. Let x be the position vector in three dimensions, with r = ||x ||, and let a be a constant vector. Show that
please post a photo of the question
0
#3
Here it is
0
#4
I actually just can't do 14a
0
4 years ago
#5
(Original post by CammieInfinity)
I actually just can't do 14a
assuming x is not constant, i.e. x =(a1,a2,a3)

then write down |x| in terms of a1, a2 and a3

(maybe easier to do component by component.

It should be just a standard Chain rule with a tidy up at the end
0
4 years ago
#6
Well since you have had no other answer (well you didn't when I started typing this, TeeEm feel free to correct me.) I think you need a combination of the chain rule and partial differentiation. Taking the right hand side, the following should help short of doing the whole question and taking note that it is a very long time since I did vector calculus.

Example
Chain rule

The trick then is to write the differential of f using the chain rule for each of x, y and z and take out the common factor of

Which would leave

note that â€‹

Apols for my Latex however I can't say I am impressed by the typesetting in your book. Note to self, Shift-Cmd V for paste without nonsense.

0
4 years ago
#7
(Original post by nerak99)
Well since you have had no other answer (well you didn't when I started typing this, TeeEm feel free to correct me.) I think you need a combination of the chain rule and partial differentiation. Taking the right hand side, the following should help short of doing the whole question and taking note that it is a very long time since I did vector calculus.

Example
Chain rule

The trick then is to write the differential of f using the chain rule for each of x, y and z and take out the common factor of

Which would leave

note that â€‹

Apols for my Latex however I can't say I am impressed by the typesetting in your book. Note to self, Shift-Cmd V for paste without nonsense.

no correction/ I admire you latex skills.

Btw Chain rule whether in differentiation of one variable or several variables is still call it chain rule but then again I did this stuff a very long time ago so notation and vocabulary unfortunately is subject to fashion trends (even in Mathematics)
0
4 years ago
#8
(Original post by nerak99)

Apols for my Latex however I can't say I am impressed by the typesetting in your book. Note to self, Shift-Cmd V for paste without nonsense.

???
0
4 years ago
#9
??? ?
Assume you refer to my Note to self.
It took ages to realise that when copying and pasting a complex bit of latex, if I just did cmd V to paste, I got a whole host of html as well as the bit of latex. That when I stumbled on Shift-Cmd V to do a plain text copy.
0
4 years ago
#10
(Original post by nerak99)
??? ?
Assume you refer to my Note to self.
It took ages to realise that when copying and pasting a complex bit of latex, if I just did cmd V to paste, I got a whole host of html as well as the bit of latex. That when I stumbled on Shift-Cmd V to do a plain text copy.
I see ...
0
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