Your problem statement says to "evaluate the surface integral of F," but then you evaluate the surface integral of the CURL of F in order to make use of Stoke's theorem. Since F is not equal to the curl of F, it seems there is something missing here. If there's a logical leap, it seems you neglected to explain it.
Could you please tell me if I'm right in thinking that surface integrals are always equal to the line integral along the 2D curve that the vector field goes round counter clock wise? if I'm right, then if the angle is not 0, then I have more than one 2D plane curves. they both can't have the same line integrals, if the angle is not 45. unless by counter clock wise, you mean perfectly so. please explain. Thank you.
just a heads up, around 1:34 you say that the net rotation along the surface of is going to be equal to the net rotation along the intersection curve. This is not true. The net rotation around the surface (double integral of curl(F)ndS ) is equal to the'work' done by the field along the curve of intersection ( integral of F dot dR ).
I know that we must use Stokes theorem to solve this problem but I tried another way with Divergence theorem by z=0 (xy plane), I used that to close and limit the area. In xy plane we have circle with area 4pi and the div(F) =0 and I got the flux -4pi. Why is my solution wrong ? I mean Integral (F dS) + Area of bottom = Integral(Div(F)). When Div(F) = 0 then I thought Integral(F dS) = - Area of bottom which is -4pi, but why ?!
First of all, thank you so much for all your videos! Insanely appreciated. Secondly, I would like to know how you choose which way you solve it (via surface integral OR line integral as you did this time). I watched part 1 and when I came to this I wanted to try the example out myself before watching you solve it and immediately started to evaluate the curl and ended up with the wrong answer. Thanks again for all the great vids!
Thanks for the video but I don't get how you were evaluating with stokes rheorem yet not finding the curl
Your problem statement says to "evaluate the surface integral of F," but then you evaluate the surface integral of the CURL of F in order to make use of Stoke's theorem. Since F is not equal to the curl of F, it seems there is something missing here. If there's a logical leap, it seems you neglected to explain it.
Thank you very much, your videos have helped my in my calculus and differential equation classes!
Graphing Calculator 3.2 by Pacific Tech
thanks a lot!, especially for your ending quotes, always:))
Could you please tell me if I'm right in thinking that surface integrals are always equal to the line integral along the 2D curve that the vector field goes round counter clock wise? if I'm right, then if the angle is not 0, then I have more than one 2D plane curves. they both can't have the same line integrals, if the angle is not 45. unless by counter clock wise, you mean perfectly so. please explain. Thank you.
just a heads up, around 1:34 you say that the net rotation along the surface of is going to be equal to the net rotation along the intersection curve. This is not true. The net rotation around the surface (double integral of curl(F)ndS ) is equal to the'work' done by the field along the curve of intersection ( integral of F dot dR ).
so what stokes theorem tells us that the total curl on a surface is the same as the boundary?(c)
Thank you sir, you help me pass final cause i was loss before
dear Friend, thanks for posting. what software do you use to plot 3D vectors?
Alright this wasn't Stoke's as Stoke's *must* require a curl computation. This was done using the Fundamental Theorem of Line Integrals. :(
I know that we must use Stokes theorem to solve this problem but I tried another way with Divergence theorem by z=0 (xy plane), I used that to close and limit the area. In xy plane we have circle with area 4pi and the div(F) =0 and I got the flux -4pi. Why is my solution wrong ? I mean Integral (F dS) + Area of bottom = Integral(Div(F)). When Div(F) = 0 then I thought Integral(F dS) = - Area of bottom which is -4pi, but why ?!
Can anyone answer me that isn't having volume by taking z=0 plane??
First of all, thank you so much for all your videos! Insanely appreciated. Secondly, I would like to know how you choose which way you solve it (via surface integral OR line integral as you did this time).
I watched part 1 and when I came to this I wanted to try the example out myself before watching you solve it and immediately started to evaluate the curl and ended up with the wrong answer. Thanks again for all the great vids!
where can i get that graphing software?
Amazing work
Awesome!
Thank you