Gradient

[@atraps7882]

the moment i heard that deep, soothing voice, I knew I'm in good hands for multivariable calc.

[@youngkim5909]

3Blue1Brown fans detected! That man is a genius, not only mathematically, but also pedagogically

[@EliteCubingAlliance]

@@youngkim5909 True. He's inspirational.

[@swatantradhara4153]

Ahhh yes! 😌

[@alexandergrunbacher9357]

@@youngkim5909 is he actually a professor though?

[@xiaomenghu88311]

3B1B has such an iconic voice.

[@eduquest3169]

Tears roll down my face after listening this beautiful voice.

[@yashagrahari]

It has been 12 years of uploading videos still I found it best lecture series to understand vector calculus so far. Thank you Khan Academy. You beauty.

[@anonymoustraveller2254]

Khan academy videos are like happy start to my day , after all chaos around when i hear voice of the tutor , i fall in love with the subject , now its only the subject & me, nothing else in my mind , i think that black background also helps in escaping the chaos of this world , blissss.

[@lexuanbach1127]

Shut up

[@littletravel]

The way you are teaching is really making sense to me. I am watching all videos in sequence. And it really make a big change in my understanding. Previously I found all my teachers jump to the subject in such a way that the students already know everything. Specially, the lecturers during my Undergrade at BUET really failed to make any sense of this subject. Thank you for being so detailed. I am committed to finish this course here.

[@furqaanilahi8078]

The hardest thing is to watch these videos in a sequence, I mean how do u do that? It takes half an hour for me to just understand the sequence 😂

[@littletravel]

@@furqaanilahi8078 haha. I think sequence is there. Good luck to your study. This is really well done work.

[@Stopitgetsomehelp3012]

Are you from Bangladesh?

[@littletravel]

@@Stopitgetsomehelp3012 yes but live abroad. But why?

[@Stopitgetsomehelp3012]

@@littletravel you mentioned BUET, that's why.

[@ShirimeCid]

Keep em coming, I can't help be be proud of seeing you be a teacher in khan's free knowledge.

[@douglasespindola5185]

Grant, you're the best!

[@slickwillie3376]

I like it. Thinking of the gradient as the "full derivative" is an easy way to remember the whole thing. 😀

[@cubby091398]

This is much more straightforward. My Calculus III book looks and seems like total chaos. It skips way too many steps. However, the last chapter in the book which is first and second order Differential Equations makes more sense and is more straightforward, than the Multivariable Calculus in the other chapters. Thank you for your help sir. I will not only have a great professor this Fall but also you as a backup for extremely useful help.

[@God-sz4pf]

Hey can I ask what are you studying and what year are you?

[@EliteCubingAlliance]

Dude, I understand this and I'm a freshman in high school. I'm learning this for a science fair that I'm trying to win. I'm trying to get into the nationals competition for 9th grade, and I think this video will help. This man(3blue1brown) is a legend!

[@jrremix5878]

3blue1brown with sloppy animation. love it

[@That_One_Guy...]

He's mostly not using animation when teaching in khanacademy, but uses khan writing tools (but he still use that cool 3D graphing software)

[@AlexanderNghiem]

4:40 when he says "its like how many dimensions you got" i died laughing and then had to awkwardly explain to my parents that i was unironically laughing at a youtube math lecture about gradients

[@PandaKittenhybrid]

omg me too the way he said it was just so funny

[@aadityasingh8553]

Its weird...... Your voice is the reason i understand maths....

[@MeatMaster69420]

Literaly was my savior throughout my school life so far

[@ramankumar41]

Dear @khanacademy , you are the greatest gift for students !

[@MrLikon7]

3blue1brown? come to numberphile next pls xD

[@unrelentingawesomeness7501]

Numberphile sucks balls imo

[@realcirno1750]

your wishes have been answered

[@PranabMallick.]

Your wish was granted.

[@bartonpaullevenson3427]

Very simple and to the point! Thanks for posting!

[@lizzybach4254]

Wait, that sounds like 3b1b. Omgggg!

[@empty-m3m]

OMG ... He's voice is Soo OMG ... So Soothing 🥴

[@danieljaszczyszczykoeczews2616]

thank you very much for a video!!! :D I don't know what I would have done if I hadn't watched this video

[@강봉준-m4k]

나블라는 다양한 경우에 X y z에 대하여 적용되기에 '연산자' 지만 '벡터'와 같이 표기된다. / 나블라는 스칼라f(x,y)값을 벡터로 변환함을 주목한다

[@namik2b]

WOW, you did it so simple.

[@peanutbutter7639]

It’s Grant Sanderson 🤗🤗🤗

[@SerdceDikarya199]

I hate showing computation before giving a geometric interpretation😍😍

[@shane2286]

I couldn't be happier when I opened the video and heard Grant Sanderson

[@LoveLauwsPawuwls]

This has the "potential" to be very interesting!

[@SkanderTALEBHACINE]

Thanks for all the efforts, just one question(maybe far away from the context) , when trying to derive the expression for the gradient of a function , we compute the total differential of this function but why we suppose that this function is only coordonate s dependent but time free? i.e. df(x,y,z)=Dfx dx+Dfy dy+Dfz dz (but not Dft dt ) using df = Gradf . dr (dr desplacement vector) . thanks again

[@ycombinator765]

So, will the determinant of this nebula vector have some meaning when conbined with a function?

[@UntakenNick]

Does it make any difference, conceptual or practical, to place the derivatives in vertical order between square brackets or horizontally between parenthesis..?

[@redberries8039]

Why don't they provide a link to the related playlist?

[@kevinshao9148]

Hi, question please: does it have to be addition of all bases directions?

[@chamidumadumal7130]

is this the real grant?? is this just fantasy??

[@maddykim9348]

Caught up in the landslide, No escape from reality!

[@collardgreen]

Open your eyes, look up to the skies and seeeeeeeee

[@DylanFridman]

I'm pretty sure this was the best, funniest comment I've ever read on KZbin.

[@satyamprakash7030]

I am just a little boy, I need no sympathy

[@serotonin9218]

I’m just a poor boy, Nobody loves me.

[@ericsparkman1303]

Thank you for all your awesome videos

[@Festus2022]

Why is the magnitude of the gradient vector said to be the RATE of maximum ascent? When I see "rate", I think slope. Why isn't the rate of ascent simply the partial of y divided by the partial of x.? Isn't this the slope of the gradient....i.e. change in y over the change in x? What am I missing? thanks

[@mrhatman675]

It try to think of the nabla operator as a way of finding for example the 2d velocity vector when we have two axes of space and one of time

[@jvcmarc]

IT'S THE 3 BLUE 1 BROWN GUY!!!

[@phenomenalphysics3548]

Omg! The guy from 3blue1brown 💞💞💞

[@arachan5280]

thank you so much this is very helpful

[@ngm_4092]

3blue 1 brown... I love this guy

[@tripasect1271]

We lovve you Grant.

[@vanishnobin9159]

a bit hard to understand for beginner. I wanted to show my friend who is in high school how to understand gradient but i feel that this is closer to university level.

[@MyBilal19971]

Does this gradient means that it is the gradient of the tangent line at a point P on the surface?

[@Gunth0r]

if I'm getting this right, the first example with two variables x and y will give you the slope (also called gradient) (m) in a linear equation of form: f(x) = mx + y. In the second example, I'm assuming with spatial coordinates x, y, z; the gradient is a matrix whose components are spatial derivatives, which means that they represent the rate of change of a given scalar physical quantity with respect to the position coordinates. Note: Scalars are basically real values that can serve as a component of a vector, example: scalar x in vector v = [x,y] ). en.wikipedia.org/wiki/Gradient

[@scholar-mj3om]

Marvellous💯

[@afonsoczernin3615]

Thank you sooo much, amazing material

[@LeonieHanneChannel-c3v]

Thanks sir

[@JamesRobinson-pl1xx]

why am I doing this for my GCSE's, just crazy.

[@Real_Obi-Wan_Kenobi]

When did 3blue1brown start making Khan Academy videos?

[@fahnub]

That's Grant's voice!

[@ruidodevinilo]

That voice... 3blue1brown

[@arashchitgar7445]

What is the difference between this nabla (Gradient) and Jacobian?

[@ethanvirtudazo1657]

Thank you for the video! Could someone please explain what he means by "operators"?

[@luckygamer9197]

a function has an input and spits out an output, an operator takes a function and spits out another function

[@ankitaaarya]

I like grant but tbh i dont understand him, khan is better explainer for me.

[@Por-poI]

I love 3blue1brown men... so good

[@billbuyers8683]

derivative is the amount of change in a function

[@vkv392]

really good....

[@ΚωνσταντίνοςΛαζαρίδης-ξ9ι]

Thanks!

[@isaacfernandez2243]

What course is this video taken from?

[@kavourakos]

So how can I find which is the next video? ...

[@Mari-Bathwater]

On the website

[@poppyflorist]

3b1b pls provide a practical example of why we use this

[@tom_bhai675]

then what is the main purpose of the gradient it is simple the derivatives of the function

[@shararan23]

It’s grant!

[@kasimshobak3281]

Thank you!

[@suvamkumar3370]

gradient of a vector field exist or not?

[@SandeepSingh-hc3no]

Hail Grant Sanderson!

[@lszclement]

@3:50 why did you square it? Or it is some other symbol?

[@awsm1680]

its just a question mark (?)

[@kotsariniskonstantinos7440]

why does the gradient of a single variable function does not give the normal vector but gives the tangent one?

[@That_One_Guy...]

We uses vector in 3D instead of line, since it give you direction. But you may also use vector as tangent vector of 2D function/single variable function that would describe how the tip of the vector parameterizing/writing a curve should moves as parameter t changes

[@jizhang2407]

Thanks for sharing. Shouldn't the derivative of a "scalar valued function" w.r.t. a vector input (x, y), be a "row vector" instead of a "column vector", according to the book "Mathematics for Machine Learning"?

[@None_me_]

Row vector and column vector are the same if you consider the dimensions in them. As vector is just a "one dimensional array of elements". So row vector is just single row of "n" elements and column vector is a single column of "n" elements but they both refer the same thing. :)... The important part is the inputs and their change in direction from that input and it's not about the type of vector..

[@nevenazMadwrld]

i know that voice anywhere

[@sanjeevsaroy6019]

Grant Sanderson 3b1b

[@BlueOrange1]

Awesome! thumb up!

[@hje9021]

Thank you ...TT

[@curtpiazza1688]

Great! 😊

[@jamesmiller2521]

so basically bunch ("vector") of derivatives

[@samvhora9076]

3blue1brown 🔥🔥🔥🔥

[@samratpodder160]

What is the difference between slope and gradient??? Plzz tell me.

[@1eV]

slope is not a vector

[@niikurasu2855]

@@1eV Slope is pretty much just an one-dimensional vector

[@maxwellsequation4887]

Grant is grand

[@krishanlallaxiib4589]

🎉🎉❤️❤️ HEY GUYS HAVE YOU DIFFERENTIATED YOUR MOUSE POINTER ALSO???🎉🎉😂😂

[@Elzelgator]

I didnt understand why you said n dimensional would have a matrix of length of n? Isnt the example you gave 3 dimensional but the gradient matrix has length of 2?

[@EpicosityGuy]

Prisoner Of Paradise for an n-dimensional scalar field, the corresponding vector field would be the same dimension. Any scalar field is actually just a function that can be represented as a dimension higher than its scalar field.

[@jifathossain7637]

I came here randomly but when I heard that voice I was ......

[@1ts7ust7osh]

3b1b??

[@hyunwoopark9241]

Is this Gront Sonderson?

[@theoleblanc9761]

Grant Sanderson *

[@fificovfefe6247]

What is the speaker's name so I can find the rest of his stuff? Very understandable!

[@douglasespindola5185]

His name is Grant! The best math teacher I've ever seen besides Sal Khan!

[@juliocardenas4485]

3 blue 1 brown !!! I’m safe

[@abhishekgaur8800]

please name this software....

[@meena6032]

i’m learning this in year 8 i-

[@zes7215]

ts not fx or unfx or interx or uninteresx

[@TheHumanHades]

3b1b is my favourite youtuber. Are you really the same.

[@siddharthvijay8617]

is this the guy from 3Blue1Brown????

[@MaarceloHenrique]

3B1B????

[@mohtasimtamjeed]

yes Grant Sanderson, same person

[@maahir3871]

3b1b is that u sir ?

[@rosette_renah]

Nice 👍 👍 👍

[@rosette_renah]

@Bob Smith hi

[@avapwhl]

omg stan 3b1b

[@damejelyas]

i dont see khan Academy I see 3 blue 1 brown

[@tcatking9761]

is that 3blue1brown's voice?

[@Mohamed_Shokry]

is he the same person in 3blue1brown?

[@accumall3027]

exactly the same... no doubt

[@Kapilsharma-uc1fs]

is that grant

[@harshal.rathore]

I know this voice 😌

[@mayanksoni7635]

3b1b?

[@mayanksoni7635]

@Bob Smith hello?

[@PasanJayaweeraYashoda]

hi 3Blue1Brown

[@DylanWoods-kw6km]

THREEBLUEONEBROWN!

[@matheusyuri6004]

I love you 3 blue 1 brown

[@somerandomuserfromootooob]

Grant!!?..