Gradient of a scalar field | Multivariable Calculus | Khan Academy

[@thegimhae]

For 25 years, I haven't figured out what gradient means. Now I understand gradient. It feels amazing! Thanks a lot, Khan academy.

[@noblemagar]

How old are you now? I hope you are doing well sir 🙏

[@ob-won]

The computations are straightforward I'm here for the visualization

[@turcugeorge5874]

Sal, your videos rock! It was only after I watched some of these short videos you made that I really understood what the concepts were about rather than taking them as they are (like we're encouraged to do in school) and never intuitively understand anything..your work is of enormous value and I hope you won't stop here. In fact, I wanted to ask you if you could make new videos on these topics( grad, divergence, curl)..that'd be awesome. Sorry for my crashed English

[@keeganmaloney3440]

10 kelvin! holy handbags batman! thats cold!

[@Lucas747G]

heating up a room with an energy source of 10 Kelvin is gonna be hard. but always good to save electricity

[@igorbeleze5222]

Thought no one would talk about it ! Thank u!

[@ralphwalters906]

These are the best videos on KZbin. This man gives me a clear explanation and picture of mathematics that has always confused me. Not confused anymore. Thank you Khanacademy.

[@RohanSingh-py5cv]

For 2 years I couldn't understand what the hell a Gradient of a scalar field is intuitively. Understood it in 10 mins. You're a God to me.

[@rahimShah]

You flew me inside the vector filed... I love you...

[@SwatiRasoiVlog]

2 hours lft for my exam and a 24 year old video helped me

[@youspinmerightrounds]

It's where we assign a vector to each point in space. The vectors all point in the direction which the field is 'flowing'. Thus the collection of vectors (arrows) tells us the behaviour of the field as a whole. A weather map will often show arrows moving or a series of arrows in a row which indicates how the field (wind flow in that case) is behaving.

[@gobberpooper]

wait what? this is Calc 3? I thought it was the beginning or middle of Calc 2. I wouldn't know I'm not even in Calc 1!!! I just started taking notes and that voice, that soothing, cool voice dragged me into a hunger for knowledge.

[@RanjeetKumar-or3vh]

Show that the vector field A~ = yzˆi + zxˆj + xyˆk can be written both as the gradient of a scalar field and as the curl of a vector field. Find the scalar and vector potentials for this function

[@RanjeetKumar-or3vh]

Sir please send the solution I am not able to proof and I have to submit my assignment

[@MrStinkyhindu]

Could you please explain why "The gradient of a scalar function can be written as the sum of a constant vector and the gradient of a periodic function." I would appreciate it if you make a VDO of that!

[@devolskii]

Learning in 240p never felt this fun.

[@raboof2]

The multiplying by a unit vector is just a standard adopted to ensure that the calculated value of the gradient (the magnitude) is always consistent; at least, this is what I learned from my professor.

[@ladiesman21747]

yeh we have just been learning bout this in physics at first it makes you want to beat your head in with a calculator but after ten mins of reading the books you really get the the whole concept.

[@vaibhavbhalla8170]

thank you, the understanding of what gradient really means is important and that was skipped by my college teacher, she just told the formulas and you covered that so thank you

[@VinothKumar-qo7ry]

Fantastic institution u gave to us . Salute u sir!. U one f the best teacher, I seen. U making more students knowledgeable rather than taking formula as it is.

[@captaindisguise]

if there is a god, u are godsend....thanks a lot man, i just might pass my calc 3.

[@bakhodirjonkakhkharov344]

I don`t get tired saying that you are the best!!!

[@juaneshero]

Great explication!

[@kevaltosar9724]

Even after 15 years this vid is super helpful

[@Svenskivsk]

Right now I'm taking college algebra, but I got bored of it and decided to move on to calculus because of these vids, and a couple others, I can do partial derivatives and such, It'll take a few reviews of these gradient and curl vids to get it down but yep :] thanks man you are awesome!

[@TimesNuRoman]

awesome! this helps me visualize gradients soooo much . thanks!

[@adynizamani]

Thank you so much... Only 2 days are left in my exam, so it was a big help. Thanks again for making it a bit easier for me to tackle these monsters 8)

[@Bearkiller777]

great video I was confused about the gradient before I started and you explained EXACTLY what it was!!! you didn't go through some theory that I would have no comprehension of whatsoever you instead was down to earth and understandable! I will be watching more of your videos to help me through my calculus 3 class i am taking now, God Bless!!

[@trollfootballgeneration8645]

Let me make it easier for you guys,the gradient is actually any derivative of the partial differential above the first derivative.Just like the second,third and fourth derivative in simple calculus..

[@henrylee8366]

Still makes great help in 2019

[@kshitijbalonie4361]

i have read that gradient is always perpendicular to the surface. i just cant imagine why should we always go in perpendicular direction to get the maximum increase?

[@blzKrg]

Because the maximum increase in a scalar field occurs in its perpendicular direction.

[@jordanriver4505]

thank you for taking your time and explaining!! am a foreigner taking math courses in Japanese!

[@mmacademy139]

which software is used to plot the graphs used here?

[@gurukirans266]

Thank you so much your effort is appreciated 👏

[@guilhermedantas3200]

I enjoy these videos for the intuiton,visualization makes a hell of a difference, by the way, only think that having a higher definition would greatly improve these, thanks :)

[@kunalkolambe4414]

My doubt is solved in less than 10 mins. well done... But how you write these equations? using a mouse??? sounds Awesome

[@raboof2]

@AnaticulaeIratae14 My apologies, I confused the unit vectors i, j, and k with the unit vector used in calculating the directional derivative in my first comment. The actual purpose of the unit vectors i, j, and k is to simply give the vector direction in n dimensions.

[@LiamLind]

Thanks Sal you always clarify my clouded engineering maths lectures. Many thanks

[@revanthvarma2000]

Best academic channel, loved it

[@mirmuntasirhossain227]

Extremely grateful to you for the video.

[@sv9024]

What is the direction of maximum increase of scalar field at a specific point. Is it equal to gradient of the scalar field or it is equal to “ grad function / | gradient functions | “

[@printfhello747]

this is the a great explanation thanks so much for making this easier

[@C0mpanion]

This was so cool. Thnx :)

[@gyanarihant7113]

Love you Khan Academy :')

[@ECOMMUSK]

Amazing video. Excellent for engineering review.

[@MuhammadAli-nh5nz]

sir chaa gy o !!!

[@s_v2238]

Can u pls upload a video on theory behind all these?

[@s_v2238]

Sir can u upload a video on differentiability of scalar field...I mean I don't understand where that linear transformation comes in definition of differentiability of scalar field..

[@aseelso5794]

Thank you very much 😄

[@arvv92]

hey sal What graphing software do u use to graph the gradients? You're videos are amazing BTW!! Thanks for evreything!!

[@Ensign_Cthulhu]

HI - at 6:27, when you take the derivative of the outside function, why don't you pick up an extra minus sign? I understand that the -2x is the partial derivative of the inside function, but the outside function is still e raised to the minus something - which should give you MINUS e to the minus something. OR is the minus sign somehow wrapped up in the function and "hidden" so that doesn't happen?

[@amitt111]

what softwere does he use to show us the fields, and the functions ??

[@jejo63660]

I have a question..does anyone have a way to write in vector equations into a program and get the visual vector field? Or perhaps for any calculus term? Im trying to improve my visualization of different concepts and the one he gave on the gradient to the scalar field helps a lot I think.

[@Jjunior130]

WOW this is really interesting

[@saadsd7920]

thank you very much

[@zyrohnmng]

10K = 10 degrees above absolute zero...that is like...nothing will survive...colder than space...

[@bachirdh]

click on the CC button you have, it will open the subtitle menu of the video

[@yasithgamage]

Very well explained! Thanks

[@unotrenpentados]

Gracias.

[@bernhardriemann3821]

I LOVE YOU SENSEI

[@ibee244]

Wish you did something simpler, like f(x,y)=3x2 +3xy. Im over confused

[@durjoysarkar1729]

What application do you use for drawing?

[@morog666]

it's alike gravity

[@joek1121]

that looks like Maple, which was developed at MIT (?). Sal might know.

[@ayushprasad6159]

please increase the video quality. it is difficult to watch in laptop.

[@zeustheboerboel3794]

it is a video uploaded in 2008. The quality of videos were like this only back then. His current videos are of great resolution.

[@gireeshkumarkancharla4176]

I just want to know....which app u are using to draw the graphs ?...Any one please explain it

[@Curiouscucumber738]

this video is bloody brilliant :D

[@anabianoor131]

In chain rule nx^n-1 right?? So why you don’t subtract 1from power??? 🤔🤔

[@jamshid_ochilov]

That was an exponential function, not x^n

[@douhanezar4912]

Plz, I need to give us a nother matters in this lesson in the end of the video

[@youtubishification]

what program are you using for your plotting? i have matlab but i'm thinking that's maple or something

[@User-jr7vf]

what software he used to create the field?

[@joebhomenye]

What graphing program are you using?

[@HAWXLEADER]

so abroad this is calc 3? here in israel you start 3d in calculus 2.... (or as we call it: differential and integral mathematics/calculating)

[@Bear7747]

well taught!

[@minuchandran]

Nice

[@saadhaider9576]

What exactly is a vector field?

[@shreedevianantha983]

great

[@gyaneshwaragrahari7398]

which software is used to produce these images?

[@michelebianchi7861]

anyone know what software he was using?

[@cheneycheung]

what is the graphic software to generate vector field?

[@astralchan]

How would you type the vector into a calculator to graph it, what would be the equation?

[@vebben666]

+Zack Walker (JapaneseLearning101) This will depend on which calculator you are using. I don't think many calculators can make a 3D graph. But if you have a computer avialable there are many diffrent programs you can use.

[@shr28]

awesome

[@shoma63]

cryogenic heat source wow!

[@NitishChauhan1]

where is the next video?

[@Sarika428]

10 Kelvin??????? That's like -263 Celsius, it is a coldness source , not a heat one

[@Svenskivsk]

does anybody know the name of the graphing tool?

[@vector8310]

"This isn't relevant to learning gradients but..." Another instance where Kahn needlessly complicates things. Don't get me wrong, I like his videos and learn from them, but sometimes his examples can veer off

[@emlmm88]

I love it!

[@lunafoxfire]

A 10K *heat* source? That's a pretty cold room if that counts as heat...

[@therealjordiano]

dat was great :O

[@racsrk]

u r awesome !!hope i can pay back to you !!!!

[@LAnonHubbard]

Salman Khan is Chuck Norris' teacher.

[@everythingfun7069]

d.j.griffith

[@jbriane76]

its calc 1d or calc 4 ! omg

[@saadhaider9576]

Wait so is the gradient of a sc

[@hasinazaman8072]

Isn't temperature a scaler quantity? 🙄

[@775shahrukh]

y u murmuring in betwen ..ceating loads of tension and confusion

[@Ryan-eu4mr]

240p we meet again

[@nashanash]

@captaindisguise; da khor kuass dy

[@saprakr]

You talk slow and repeat, and repeat when you are writ8ng, I loose track.

[@devolskii]

That's how normal people talk

[@Ensign_Cthulhu]

@motleyfoolmania *slaps forehead* Stupid me.

[@reid300]

10 kelvin. jesus christ. You sir are dead anywhere in that room.

[@nagendertammali8775]

gshm