Vector Integral Calculus - Gradient Vector Field p1

[ghkdfhr123]

You guys are no better than faggots

[XadaTen]

keep makin vids!!

[24Gucho]

I hate it when flute players practice during lecture...

[GilGame123]

calculas sounds like cockroach

[alquiora]

@GilGame123 more like cockulus LOL

[kchan05]

Hey... this guy is awesome at what he knows. Don't be arse in picking on his English.

[arsmith85]

this helped but its pronounced "FEE" not "fie"

[yusufer5000]

I like that he put up this video, but what is all that noise going on in the backgrounds. sounds like he is flying in some kind of steampunk dirigible.

[fancygremlin]

wow, jackie chan knows calculus

[redback3]

it's intresting on how you portrayed it...

[ssbahaggag]

thnx aloot man really helofull really appriciate it

[bcipods]

thanks man nice vid

[IdleWild999]

could there be any more background noise -- terrible.

[juliandeathgod]

where did 5 come from?

[coolsulemanboy99]

i would give u a piece of advice i love da way of ur teaching but i would recommend that if u give one example with every topic that would help people understand it well! that my opinion. but still i understand that topic becz i have already read it but it will be bit confusing for some people who havnt read it. so example will make ur lecture perfect!

[coolsulemanboy99]

that a nice effort 5/5 i like the way of ur teaching oh mannnnn y dnt u replace our teacher in university :D

[seamyb88]

you should be a lecturer at a top university.... im at a very well established uni (manchester uni) and you would be very well suited there

thanx again man

seamus (ireland)

[soccerrocks15]

that looks so confusing..

[tuncdogukan]

what's that noise coming from the background,like some flute or something,but in an obscure note between G# and A ?

Btw,the lesson helped me. Thanks for teaching.

[xiaoyuanz]

u're right. it's what we singaporeans call "garang guni". they buy "junk" from people.

[myshyviolet27]

Nevermind the calculus, I think donylee is hott. But really it was helpful.

[SunnyJimmizle]

@myshy

LMAO random..

[tangyx127]

OHH i didn't know Harold teaches calculus on youtube, wasn't Kumar the one that's good at math?

[fulti34]

this is useful but sometimes is complicated.

[JLack84]

What is that annoying noise in the background?

[lightsaber4]

lol i kno fucking kid with ADD

[drillsargentadog]

Ahhhh. It is good to know there are other Grad Students like myself who teach courses in calculus ect. to undergrads. I personally think it's the best part of being a grad student, but many of my peers DETEST it!

[beejusbeejus]

The gradient of a scalar function evaluated at a point P is just the direction that maximizes the rate of change, and the magnitude of said rate of change.

If you want to prove this, just consider what happens if you take the directional derivative at P along any vector that is NOT parallel to the gradient.

[seniorgomez666]

i think college should be like this, you log in your school account and each lesson is a video. or maybe i'm just lazy great vid!!

[tnichols321]

it will be when gas gets expensive enough.

[gavnila]

gradient is an operator that makes scalar functions into vector ones....

[wanfuad86]

there should be more such divergence and curl..

[Merrikat]

Awesome video! Thanks for the intro to GVFs.

[ayyytac]

LAPTÜ

[smartjoe2490]

Lol way over my head im just finishing calc bc. what level math is this

[sboyer03]

Calc III

[ThermalTeeth]

thanks Donylee!!!

[torth76]

Did someone really invent calculus as you said? Or did they discover it?

[snylekkie]

We created it. There is no maths apart from humans.

[ManuelHung]

Ever heard of Sir Issac Newton? (Props to Alfred Leibnitz, who came up with it at around the same time)

[beejusbeejus]

Isaac Newton was probably the smartest man who ever lived.

[ManuelHung]

Leibniz wasn't too dim, either!

[beejusbeejus]

Oh for sure. (Gottfried) Leibniz contributed the intuitive notation that most people use in differential calculus.

But Newton was unbelievable for his time. His observations of physical laws and the frameworks he developed for them almost entirely with pencil and paper.

Rowan Hamilton (Hamiltonian, quaternions, etc) was another unreal gift to mankind. He spoke 7 different languages when he was just 7 years old!

Leonard Euler is seen as the most prolific mathematician though.

[ManuelHung]

You know, after reading a little, and not to disparage Newton at all, I think Leibniz was slightly more "hip". Plus, that notation? How can you not love it?

[beejusbeejus]

I guess we all have our favorites!

[cskybrandon]

Close, but by the age of 12 Hamilton had a good grasp on 7 languages: French, Italian, Arabic, Syriac, Persian, Sanskrit, and the obvious English. Almost one per 2 years of life. He also went on to learn Greek and Latin.

[beejusbeejus]

I didn't realize this was apparently a topic of some contention. I read in a physics book that he used to brag at the age of seven that he knew as many languages as he was years old. Interesting. I guess we'll never know for sure.

[lightsaber4]

lol no match for Euler and Gauss

[MrZenic]

Hi im 14, Cool vids you got, ive seen around 6. Keep your up your good work!

btw the karang guni man is CERTAINLY LOUD.

lols

[donylee]

Yup. You're from Singapore I guess from the use of the word 'Karang Guni'.

I just couldn't stop half way during the recording. At least now I got a little smarter, to shoot the videos during the 'quiet' times of the day.

[FarFromEquilibrium]

Thanks for the effort and brilliant explanations XD rock on!

[donylee]

Glad you enjoy them.

You studying Fourier Analysis now? I just uploaded a bunch of videos on that topic.

[panterafan01]

thank you very much!

these videos are excellent!

[panterafan01]

ahhhhhh, yes i see it now, because each partial derivative can be treated as a component. so if the gradient vector is dotted with a directional vector itll give the scalar projection in the direction of the directional vector? and obviously give the answer as a scalar?

[donylee]

Yup, you got it. Gradient vector via del operator is a VECTOR function. The unit vector is also a VECTOR. Directional derivative is gradient VECTOR dot with unit VECTOR to give scalar. It is logical as diectional derivative is rate of change of phi at certain point - a scalar quantity.

Small correction: I wouldn't say it is a scalar projection. It's physically unclear.

[panterafan01]

ok, so im just starting multivarible calculus this semester, so when you say del.phi=(dphi/dx)i + (dphi/dy)j + (dphi/dz)k

its taking the values of each directional derivative and dotting them with the/a unit vector? like del.phi= [(dphi/dx),(dphi/dy),(dphi/dz)­].[i,j,k]??

[donylee]

Hello Pantera,

Heres the clarification: You do NOT dot them with the unit vector, instead you multiply them with the unit vector respectively. (dphi/dx) becomes the coefficient of the VECTOR i and so on. Remember, with the 'del operator' you get a VECTOR field. By dotting them you only get a scalar.

Did I say 'dot'. Sorry, my mistake.

[donylee]

Woah, from Georgia Tech?! I'm really honoured. Thanks.

[foreverjrwalker]

I'm a student at Georgia Tech and I really appreciate these tutorials! Thanks!