Gradient of a scalar field

[myterribletube]

can you just go and write a book pleas!! i have never seen anyone explaining things so good as you do,...

[unotrenpentados]

Gracias.

[ATERIFA]

"Let me make it bigger so we can explore it a little bit"

THATS WHAT SHEE SAID!! LOL!!

[reid300]

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

[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)

[TheTranceWhale]

This video is hot! ;)

[Killer9117]

Sal, have my children please.

[zyrohnmng]

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

[a4b3c2d1e0f]

Khan, keep on the great work! You are saving our lives here! Thanks :D

[MrTanookiMario]

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

[jbriane76]

its calc 1d or calc 4 ! omg

[rahimShah]

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

[jsm666]

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?

[motleyfoolmania]

@jsm666

d( e^f(x))/dx = df/dx * e^f

[jsm666]

@motleyfoolmania *slaps forehead* Stupid me.

[morog666]

it's alike gravity

[shr28]

awesome

[LAnonHubbard]

Salman Khan is Chuck Norris' teacher.

[moufpuncha]

You need to be hired by Texas Christian University

[1001014]

A rather unrelated question:

It is intuitive that the rate of increase of temperature increases as you get closer to the source but I somehow just can't get my head round the proof of this. I did y=10^(-x) where x=r^2 and plotted dy/dx, but when x decreases to zero , dy/dx DECREASES, can someone explain this to me!!!!!!F***ing irritating...

[TimesNuRoman]

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

[racsrk]

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

[dalcde]

I guess if you get further and further away from a 10 kelvin "heat" source you get hotter and hotter

[najafnajafali]

@dalcde LOL, its still gonna be a 10 K heat source and going away from it will be like going in a space with even lesser temp say 8, 7, 5 and so on. The equation is still valid.

[dalcde]

@najafnajafali The temperature of space is about 2 to 3 kelviin.

[arvv92]

hey sal

What graphing software do u use to graph the gradients?

You're videos are amazing BTW!!

Thanks for evreything!!

[GlowStringTheory]

@arvv92 in one of his later videos he drags the app far enough into the window that i could see the programs name. its called javaview. google magic! :D

[AnaticulaeIratae14]

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.

[AnaticulaeIratae14]

@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.

[fprecoiil]

just out of curiosity, what is the point of multplying by the unit vector? isn't it just one?

[apoca1ypse1]

@fprecoiil the unit vector has a length of one in a spacific direction, for example i is 1 in x and 0 in y and z. When you multiply the unit vectors at a given point it will increase the values a i, j and k. With gradients you are looking for a set of vectors within the vector space. The resulting vectors have directional components and intensity of these vectors which is defined by how long the vectors are.

[Svenskivsk]

does anybody know the name of the graphing tool?

[hsktoadftw]

you are truely amazing

[hsktoadftw]

oh my god! i have such a hunger for knowledge because of you sal!

[youtubishification]

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

[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!

[captaindisguise]

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

[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.

[Leonardus18]

@gobberpooper yeah thats cal 3

[nashanash]

@captaindisguise; da khor kuass dy

[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!!

[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.

[Vendresse]

This is great, I keep watching video after video and I just can't stop, it is all said and explained in such a way that it gets kind of addictive. Probably many more people would like maths if they learned it that way!

[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!

[zapata2004]

it was really great , thanks alot , and god bless you

[joek1121]

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

[Fubrub]

i believe Maple as developed in waterloo, ontario in canada

[ih8gamer]

Thank you.

[FHomeBrew]

Awesome software. What do you use?

[ArtemRomanov]

Sal uses JavaView for graph and MS Paint as a blackboard.

[FHomeBrew]

k thnx :) I'm also guessing he's using a pen as a mouse, a tablet.

[C0mpanion]

This was so cool. Thnx :)