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EmmaTassone
 one year ago
Help with multivariable calculus please.
EmmaTassone
 one year ago
Help with multivariable calculus please.

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EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.0Being F a vector field with continous partial derivatives, If rot(F)=0 and Div(F)=0 is F constant?

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.0I tried using Gauss and stokes theorem but i dont see anything

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.0yep, sry xD here in spanish we call it rot

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.0i think the solution should be find using those theorems

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if the curl(F)=0 => F is a conservative vector field

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.0yep, and if Div(F)=0 => F=curl(G) being G another vector field

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it's been a while since i've dealt with this stuff so i'm a bit rusty. sorry

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.31) curl F = 0 is not the definitive test for a conservative field: http://mathinsight.org/path_dependent_zero_curl 2) i've had a look about for examples and \((2x,2y,−4z)\) has zero curl and divergence

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0hint: if we apply this vector identity: \[\Large \nabla \times \left( {\nabla \times {\mathbf{F}}} \right) = \left( {\nabla \cdot {\mathbf{F}}} \right)\nabla  {\nabla ^2}{\mathbf{F}}\] using your condition, we have: \[\Large {\mathbf{0}} = {\nabla ^2}{\mathbf{F}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0curl is tendancy to rotate and divergence is compressibility. if they're both 0, doesn't that just mean that an incompressible fluid is flowing in a way that it tends not to rotate?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3@pgpilot326 +1 or its just not actually compressing

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3and does F is constant mean? like 1,2,3 ?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3well we have an example so that is not true

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.0yep thank you very much guys , i really appreciate the help

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3or think gravity! zero curl, zero divergence.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we can show, that, from the condition: \[\Large {\mathbf{0}} = {\nabla ^2}{\mathbf{F}}\] the general field \( \large {\mathbf{F}}\) depends linearly on the cartesian coordinates \( \large x, \; y, \; z \)

EmmaTassone
 one year ago
Best ResponseYou've already chosen the best response.0yes and it doesnt have to be necessarily constant, thanks! :)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3@Michele_Laino interesting why did you set the triple product to zero ? and what does \(\nabla \times ( \nabla \times\vec A)\) actually mean if we already know that \( \nabla \times\vec A = 0\)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3because that nails it :)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0since: \[\Large \nabla \times {\mathbf{F}} = {\mathbf{0}}\]

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3indeed. the curl is zero so can we use the bac cab rule for anything? like 2 x 0 = 3 x 0 2 = 3

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0yes! I think so, since the vector equation above, it is an identity

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0furthermore, also this condition: \[\Large \nabla \cdot {\mathbf{F}} = 0\] holds

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3aaahhh! i think i am getting you. so, ok, ....the gravitational field, inverse square but no curl no divergence.... i hate to think how you fit that into cartesian to get a linear.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I have developed, component by component the cndition: \[\Large {\mathbf{0}} = {\nabla ^2}{\mathbf{F}}\] using this other condition: \[\Large \nabla \times {\mathbf{F}} = {\mathbf{0}}\]

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3yep, i get that bit the triple product is zero because AxB is zero and ..... if div F is zero, the laplacian must also be zero so we have a linear in x,y,z i get the reasoning, sure. it's very good.

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.3you need a medal :)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0no worries! I'm happy so! thanks! @IrishBoy123
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