Curl 3 | Partial derivatives, gradient, divergence, curl | Multivariable Calculus | Khan Academy

[@DescartesRenegade]

I go to UC Berkeley, supposedly ranked one of the best Engineering Colleges in the world. I have never been so lost in my life... until I came here. I say CAL has NOTHING on SAL! You are a savior!

[@MayankGoel447]

Sal even after 12 years your videos are still relevant and interesting

[@effortless35]

"It's always fun to analyze a vector field to death" Vector Fields Hate Him

[@andresdiez9332]

in 10 minutes you did what my teacher was not able to do in 3 months

[@akuraoo]

It is actually 0i + 0j + 2k = 2k = 2 in the z direction, since the curl is a vector which is perpendicular to the cross product ot the del operator and the vector field .

[@victordonascimento6546]

Bravo! Thank you Khan, your material simply fantastic.

[@Ahfjo]

4:44 Because each point (x,y) has a vector [with a magnitude and direction associated with it]. For example, at the point (5,5) the equation: v=(-y)i+(x)j gives v=(-5)i+(5)j as the vector at point (5,5). Thus, the vector rises up 5 and runs -5.

[@bhaskarbanerjee1974]

the intuitions are mind blowing.......they are very nice to conceptualize the math and visualize it properly

[@Kurtlane]

This is all great, but the answer is really 2k, and the k is either into or out of the plane. What does this mean? Would a twig shoot up or down in the rotating V=-yi+xj? Would it stand up or down (I've seen actual twigs do that in water vortexes)? Please explain. Thanks.

[@muddwell]

thats pretty crazy, ta for another clear, precise and well explained vid.

[@vaidyt]

@khanacademy you are really good... people like me are really grateful to you...thank you so much..

[@AvinashRanganath]

Sal, when u calculated the divergence for this vector field field, it came up zero. But as we move outward from the center of the graph, doesn't the magnitude of the vector increase? So doesn't that mean that at any given point [circle], there are more number of particles moving out than coming in? Or have i got it wrong somewhere?

[@YTMadushan]

Thank you for the nice work, I have a problem, here the value you get for the curl is 2 K (magnitude of vector is 2 for the k direction). but you didn't consider it, please tell me how it will change graph when the answer is 2 i or 2 j, thanks

[@polmrll]

you should receive a Nobel Prize in philantrophy

[@TheMrNalsur]

Khan Academy to the rescue! :D Guys, does anyone know any channels or video series about electrical engineering? My circuits professor is not that great at delivering the material, and thus a series about the AC would be of great help. Thanks in advance.

[@fmartin59]

Try Eugene Physics Videos.

[@NayyabAkhtar]

​@@fmartin59 😢

[@keikavoosafghahi5753]

best lectures series on curl so far

[@hubenbu]

Curl and divergence are pretty hard to conceptualize, you made it easy!

[@paul1964uk]

Excellent explanation at 5:25 Mr Khan

[@swiftingstar]

saved my life!!

[@MrTacoSr]

Sal khan deserves my tuition money

[@vaidyt]

@Kurtlane yup you are right.. but It doesn't mean the particle would jump up or down.. it just means that the rotation is about the z axis (or the k direction) which is in tune with our intuition (for a particle in x-y plane)..

[@dhimanroy1671]

Many many thanks

[@NehadHirmiz]

Thank you for these wonderful tutorials :)

[@13Septem13]

@j0rdan2k You are right. From wikipedia - "At every point in the field, the curl is represented by a vector. The attributes of this vector (length and direction) characterize the rotation at that point." It would be more precise to write like you propose.

[@tacubaeulalio]

The photography used in the video reminds me of the the sky in Alaska

[@vivekchaugule121095]

exellent video ..makes my concept clear

[@aaronchow2366]

Great Explanation SAL!!

[@princegaurav5598]

good job khan acadamy......u r real great in ur work......thnx .....

[@kianushmaleki]

awesome, awesome, awesome. thank you , thank you, thank you. it is great , i did understand it. thanks

[@GuilherHast]

The second graph looks like a laminar flow of water being poured into a mirror. By this I thought the div would be zero ( which is not necessary true ). But as the div is zero you can think about the illustration above.

[@Arseniy_Arseniyy]

Excuse me for my english? it isn't realle good/ But i thought? thft the curl is a VECTOR quantiti and it can not be equal 2 ) In this example it might be that the answer is 2k

[@ArnoHenckes]

yes it's (0, 0, 2), but when taking curl of a 2 dimensional vectorfield your x- and y-components will always be 0 while the z component indicates the curl, the reason behind this he explained in the video.

[@jhonma1]

Beautiful explanation thank you men

[@fahmidaafreen9855]

you're the best!

[@jamescalebpeters5827]

This one is Awesome

[@bhimbdrlama]

Thank you very much

[@zakaofficial9226]

Excellent job

[@Ensign_Cthulhu]

Nicely done. How does the final value for curl in that circulating vector field translate to how fast your twig is actually rotating (e.g. around its centre of mass)?

[@ECOMMUSK]

"its always fun to interpret a vector field til death" lmao

[@deeptotop]

thanks for sharing some good videos and thanks for sharing the knowledge

[@volintine]

yup his vid are awesome

[@deeshmamp9385]

Thank you

[@farizrahman4450]

Cross product of 2 vectors can not be a scalar. 2 is just the X component of the curl!

[@HT-rq5pi]

+Fariz Rahman Actually it is the z-component. Curl is sometimes defined as a scalar in the two dimensional case because it will always have zero x and y components, and the z-component being positive = counterclockwise and z-component being negative = clockwise. In other words, in the 2D case there is no need to specify about which axis the microscopic rotation is taking place since it is always about the z-axis.

[@bmcws]

Very nice lectures - I particularly like your enthusiasm for the topics - far better than the multitude of dry monotone lectures elsewhere on KZbin. I'm still confused about the meaning of div though. For example, in this video (Curl 3), div is akin to 'density' increase in a infinitely small circle. But also, density increase in the same direction of the vector field (in 'Curl 1' video). Not sure what this means at the origin since the field is zero (seems like the interpretation in the video is that it's isotropic, summing to zero, rather than just zero since the magnitude is zero). Away from the centre, I'm slightly confused by 'what's coming in in 1 direction is coming out in other directions' - but only w.r.t. 'direction' of the vector at that point?

[@HAWXLEADER]

twig twig twig twig... just funny how he says it... he has the perfect voice and attitude for educating!

[@KlaousP4c3]

I might be wrong but should in the curl, the j component be d/dz(-y) -d/dx(0) Instead of d/dx(0)-d/dz(-y) ????

[@ninosawbrzostowiecki1892]

what is Sal using to graph the vector fields? can I get the program somewhere for free?

[@MartinLarsson]

No, it doesn't. If you look at the graph at say (3, 3) you can se that even though particles are leaving faster along the line y=x, the circle is reinforced from the side. So to make up for the faster speed for the particles leaving the circle, particles are comming in from more angles into the circle. Makes sense? :)

[@CaptainKleptan]

Thanks!!

[@HarryWoo]

I can't open this page.

[@amandadube156]

Drag the video forward a second or two and it will play!

[@9772783]

Amanda Lee Dube ive been here for an hour... THANK YOU!!!!!

[@AhmedHesham]

Amanda Lee Dube Thanks! I`ve been here for too much too

[@volintine]

can anyone tell me which soft he is using to shows us that graph

[@ooker777]

@khanacademy, i still wonder about why there is a minus before j?

[@mailoisback]

yes it's 2k

[@baxtrom]

Hey, isn't that Frank Zappa doing vector analysis? Sounds like it!

[@therealjordiano]

greaat lecture imo :O

[@j0rdan2k]

shouldn't the curl be (0,0,2)?

[@lawrencemwangi8846]

Should be 2k...forgot the vector k..no cross product can produce only a scalar..2 cant be an answer to a cross product

[@fortoday04]

No

[@zander35e98]

2k also can mean [0, 0, 2]

[@ahmadsum1]

it's definitely a mistake on the author's part... "Note that the result of the curl is a vector field. We can say that the curl operation turns a vector field into another vector field." clas.sa.ucsb.edu/staff/alex/VCFAQ/GDC/GDC.htm

[@ninosawbrzostowiecki1892]

holy, this video is old

[@KishanRaval00]

Video no working

[@13Septem13]

@ooker777en Because of this method of finding determinant( called Cofactor expansion ) read more here ( dot ) wikipedia (dot ) org/wiki/Cofactor_expansion

[@nicholasbiester8870]

this video doesn't work for me...

[@ShayJorge]

His curl 2 video is amazing, does the job for me

[@shavuklia7731]

Curl 2 is just calculations tho. This really helps intuition.

[@MeroFuruya]

he just shows you how to push symbols in that one

[@sanjumon1991]

Thank you sir. The video was helpful. Thank you very much