The Curl of a Vector Field: Measuring Rotation

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This video introduces the curl operator from vector calculus, which takes a vector field (like the fluid flow of air in a room) and returns a vector field quantifying how much, and about what direction, the flow is locally rotating, or swirling, at every point. The curl is a fundamental building block in vector calculus, and is used to measure the vorticity in a fluid. A tornado is a region of high curl.

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This video was produced at the University of Washington

%%% CHAPTERS %%%
0:00 Introduction & Overview
5:22 Simple Example
9:07 Interpretation of the Curl
15:02 Intuition for Curl as Solid Body Rotation
24:29 Curl(Grad)=0 and Div(Curl)=0
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Be careful at 13:59 since the video is flipped, this is actually showing the "left hand" rule, not the right hand rule. I am actually left handed, so it is extra confusing...

Eigensteve
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BROO best playlist I've ever laid my eyes upon

jacques
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I have been recently watching your playlists. They are all great. One can see how much you are motivated to teach and your explainations seem to be very intuitive to understand.

theverner
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This man is what we need more in math teaching: Someone who thake the time to build the knowledge from the base just to be shure that everyone understand.❤❤❤❤

trylatdar
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I am actually arabic and we study math and physics in french and now am learning about gauss's divergence Theorm and mass con... All of this in english .. but i am still enjoying it

zahrounzouzou
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Love the "Ok, Good!" transitions. Keep up the great work prof!

erikgutierrez
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Fantastic video! Thank you for having it openly available

zaykoup
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Any SB fan who knows who is the SB of probabilities?
Thanks professor for respecting our minds and talking to us at the intuition level.

samirelzein
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Great lecture, professor! As always, you provide clean and concise explanations with examples that help the essence of the mathematical concepts to be understood. Are you intending to cover related topics in physics and engineering as well? In any case, thanks for these high quality videos!

murillonetoo
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This man advances my carrier. Thank you so much.

lula
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this is so on time, I have my Calc 3 final soon and your explanation is just perfect

ms.derenal
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Strongly suspected a fellow south-paw, and mirrored video. Partly the wedding ring but mainly that *no one* is that good at mirror writing! superb presentation. I did basic vector calculus at the Cavendish, but switched to other sciences before the course went on to tensors. It's all flooding back! Thanks. Chris

docrow
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Once again: brilliant video! Thank you for explaining this so clear and concise. Keep up the good work!

fredericoamigo
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By the time Steve said he’s left handed, I finally realised that the video was flipped all the time. That’s a big reveal to me.

Anyway, I always love your videos. Great work and amusing.

nickwisely
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Thank you for your effort and time. It would be great if you could create a playlist for your videos. Your videos are incredible but finding all the videos related to vector calculus is a bit difficult.

mostafaahmadi
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Great lecture! Actually the material isn't new for me. I'm radioelectronic engineer. I studied vector analysis and PDE in the university 10 years ago. And also I used all this maths stuff in electrodynamics applied to radar antenna arrays design. But your explanation is the best! I use your lectures to refresh my knowledge.

aliscander
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Never imagined soneone could create this awesome videos on calculus

amishijain
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At 12:59, curl of (-yi+xj) = 2 should come with basis vector k.

shuewingtam
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Steve, thanks again for what and and your team do! I started a machine learning course and for my birthday my friends presented me 2 books (they asked which I want): Deep Learning by Goodfellow, Bengio and Courville and guess what – your Data-Driven Science and Engineering! Both are published in color in Russia, which was a surprise. So far I like your book very much!

saitaro
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Professor, Thanks a lot for this lectures. They are really awesome.
Btw, no need to worry because u r a left hander and u need to use the right hand rules. You can verify the direction of the cross product or so without leaving your pen/ marker and use right hand to verify the direction and keep on with your calculations using left hand 😅.

saisaranvenkata