Vector fields, introduction | Multivariable calculus | Khan Academy
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- Опубликовано: 22 авг 2024
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Vector fields let you visualize a function with a two-dimensional input and a two-dimensional output. You end up with, well, a field of vectors sitting at various points in two-dimensional space.
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Woah, woah, woah -- hold on a minute. When did 3Blue1Brown start working at Khan Academy? It's great to see such great creators being brought together.
I am 99% sure they worked together before 3Blue1Brown started his own channel
Can confirm that
Is this him tho?
Khan academy has top notch talents. The guy who wrote jQuery also works there.
Had to say this... Seeing the animation, I thought it was 3blue1brown at first.... Surprised to see the writing software being used instead, still confusing!! 😄😄
I don't understand how could I thank khan academy for clearing my concept in a crystal clear way...
May Allah bless you for sharing your knowledge.
The audio volume is way too low.
Jesse Meyer use a headset
i am on max, pc volume max, youtube on max, and equalizer maxed. still quiet
The problem is more that it goes up and down after each video.
I was just about to go back to my music. Thank you for reminding me to lower my volume 😂
Started learning about vector fields after i watched an anime where an anti hero had the most OP ability because he could manipulate, control, transform and reflect and vector.
Im glad i found this vid!
What program are you using to visualize vector fields?
anvaka.github.io/fieldplay/?cx=0&cy=0&w=8.5398&h=8.5398&dt=0.01&fo=0.998&dp=0.009&cm=1
very comprehensive video, many thanks again. I'm getting closer to my goal everyday!
Have you reached your goal yet? :)
We need a status update 7 years later :0
its unfortunate that for many of these videos, youtube doesn't recommend the next ones in the series... so i got to go to your channel manually and search for the next video you mention in the end of one video..
Hey i know i'm a year late but you can go on their channel and click the "multivariable calculus" playlist and it'll do as you wish
very clear and concise, thanks!
This is Maxwell language. It is beautiful!
Nice, Thanks. Just try to differentiate between 2 and z.
Audio quality problem
Chiming in to mention that the audio is far too quiet, again. Great to see you on KA, 3blue!
I *finally* understand them 😁
Sounds like 3brown1blue
he is 3brown1blue
3Blue1Brown* xD
He is Grant...
Personally, I feel it would give a better sense of the length relationship of each vector to each other if they had the same colour but different degrees of darkness.
It makes sense to me
Knew I recognised the voice! what a legend!!
omg omg it is 3b1brown god!
3blue1brown i know you
I think the concept of a vector field where we think of vectors as little arrows is quite confusing and pointless unless you think about something like velocity.
Because you might just as well think of each vector as a position coordinate and of the function as a transformation of space. If you do that, then attaching the vector to the tip of the function argument is severly missleading, since the result is not at all where the argument ends up.
Thank you, sir!
It's just a brilliant video..
All those going vector fields pointing inward and outward remind of the g2g shear in a tornado. You calculate it by adding the inflow bound and the outflow bound. Tornadoes seem to be.very hard to understand because some of them are very wide and extremely intense while some may be rope like and extremely intense.
Every time I watch this video, yeah, I feel like I am pretty clear about the stuff. But after a while, when I start thinking and try to visualise the vector field as the way he does, It feels pretty absurd despite the fact that he says that visualising the graph precisely needs 4 dimensions.
What I mean is, In the video, he is clearly taking a function with inputs x and y. Yeah, it is easy and clear about the plotting of the input points in the x and y axes. But, what about the outputs?? Those are completely different quantities and clearly can't be plotted along x and y axes as they have their own distinct values. So, Is the way he visualises the vector field in the video precise?? I don't understand.
Tanks
It was very helpful .
Marvellous💯
Can you please explain gradient of a vector function.
Thanks. I still don't understand what the point of these are, but I can identify the correct one for my class!
Take a look a an animation of airflow around, say, a formula 1 car. Now that I understand what a vector field drawing actually is, it's fairly clear that F1 aerodynamicists and use them to visualize the airflow behaviour like direction, velocity and, in some cases, the pressure of the air as it flows around the various aerodynamic elements of the car.
I suspect that they use CFD and wind tunnel data to create and confirm the design is producing the desired effect before they go to manufacturing and then, use the wind tunnel and track to confirm results and see if there is good correlation between what they saw in CFD and what the see in real life.
On many F1 weekends, during FP1, engineers will put Pitou Tubes matrices on the car to measure air speed as it is compressed, and therefore accelerated, as it moves around the car. Like this.
s.hswstatic.com/gif/co2-powered-dragsters-1.jpg
From these numbers they can then calculate things like local or overall drag and downforce
This analysis helps determine if the design is behaving as expected. If you watch F1 you might hear the term "correlation" used to describe how tightly the predicted performance, calculated from wind tunnel and/or cfd testing, aligns with empirically derived data and/or car performance.
Oh, I forgot, this stuff also applies to meteorology. Consider this map of wind speed and direction.
about.metservice.com/assets/static-content/learning/how_to_read_5.gif
I submit that if those little arrows line up in a certain way you can assume you are looking at a specific type of weather pattern. If the little lines form a circle and they are red RUN for the storm cellar.
Ok Rocky, Take a look at the little strips attached to the lift providing surfaces of this aircraft. They look a LOT like a vector field.
ruclips.net/video/bsQcfzNWJWc/видео.htmlm11s
Thank you!
Hey ... You said you will talk about toruses more!
is this teacher 3blu1brown? the guy's voice i mean?
Hi guys, use a microphone like Blue Yeti or Rode Broadcaster and turn up gains if you want proper volume.
Great video!!
Is there anyone here knows the software used to sketch the field and some tutorials?
Thanks!
Manim by grant Sanderson ( 3blue 1brown)
Wow....really appreciatable🙏
This reminds me of the grid I used to levitate objects
thank you!
Thanks!
mind blown
Cool! 😊
4:04 please, can you name some software that can help in drawing vector fields?
Eesa Manim
thanks man!
3Blue1Brown
“Warmer colours are supposed to indicate this is a veeery long vector *smiling pi creature*... somehow *pi creature scraping its head*”
What software are you using
3:00 that's what she said
hi sir, what can this method vector field using for civil engineering?
Isn't the 4th dimension just time? So can't we graph f(x, y, z) on a 3D graph, but just reference each point on the graph to its corresponding f(x,y,z) -- "time" -- value?
The 4th dimension can be anything. Actually, all of the dimensions may represent anything you wish to model or understand. You may have eighteen dimensions all representing different properties (physical or what not) of different objects.
Why on earth would you equate vectors of different sizes? What if theyre exponentially larger, would you still consider em equal? Its counterintuitive
Wouldn't it completely depend on how it's applied? Maybe you only care about the angle at that point.
What program is this?
It wld give really really messi messy
2:41 why does he say it doesn't matter where vectors start? I thought all vectors have to start at (0,0)?
Hi Eru, Good question. I think you are right. Vectors start at (0,0) in the output space. However, in this case as you know we are only viewing the input space, so to get a sense of what vectors result from those points in the input space, we attach the vector to the relevant point in the input space. Cheers, Laura.
Eru Ilúvatar Don't listen to Laura- you aren't correct. Vectors are identical after translation, so translating a vector from (0,0) to (1,2) keeps all aspects of the vector constant. It is conventional to start vectors from (0,0), but as that it a convention, we could just as well start vectors from (283, 192828) and we would mathematically have the same object.
But how would one know where we started from if it isn't assumed to be (0,0)?
Eru Ilúvata it would just be the location of the tail xD
Whoops sorry Eru! Thanks Maxim for clarifying!
Fix the audio vol
why are you so quiet
Low voice
Why it doesn't matter from where vector starts?
there are two vectors. One is point coordinate (starts from world center) and poit normal (starts from each point)
or world position (starts from center) vs local (starts from parent coordinate) a.k.a. absolute vs relative
I know this voice
3BLUE1BROWN??????
that is not symmetry that is asymmetry my guy
I guess I am confused as to why your graph has x value -10 and y value -8. Why wouldn't your y value be -10 considering arithmetically 2^3-18 is -10.
because it's [1,2] vector, not [2,2] and it seems x value calculated with y, and y with x thats why its [-10,-8], not [-8,-10]
what?!
he has a throat ache?? :P
technical problem !
i thought khan academy was in india but here american accent is being used.
Crazy Movie box
Lol yeah cause 'Khan' sounds like Indian. Idiot.
please do not change the calculus volume of audio :)
Marvellous💯