Exact equations intuition 1 (proofy) | First order differential equations | Khan Academy
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- Опубликовано: 29 сен 2024
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Chain rule using partial derivatives (not a proof; more intuition).
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Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
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Khan is better than MIT :)
Javad Hikmati he went to MIT
Very true-MIT hard to see and hear.
doesn't this create an infinite loop? if dpsi/dx = dpsi/dx + dpsi/dy * dy/dx then how do you know what dpsi/dx is?
😊🎉
Verkar vara ungefär 2 st / år. :)
you can't really SEE me in the next video... or can you?
någon svenks här?
hey khan, marry me?
Oh my god, thank you so much for this. I might just pass my DiffEq class coming this semester.
did you pass your class?
@@austinrussell3166 Got an A. One of my best math classes of all time. Went on to get a degree in Civil Engineering. I dunno if you asked as a joke, but I think its worth noting that my life changed after succeeding in math courses in community college.
@@OuterRem Congrats mate!
@@OuterRem Congratulations! This is an inspiration for me to work hard, thank you.
Mr. Khan seems to have had some nasal congestion, on the 30th of August, 2008. lulz.
How is g(y) a constant if y is a function of x???
Thanks a lot just wanna say. you have definitely done one of the finest works for the students. Please keep on doing it and save students all over the world. lots of well wishes from Bangladesh.
The Greek letter psi is pronounced the same way as the Gangnam Style guy, not with a "z" sound
The Greek letter you use here is called Psi, not Zi. Psi looks like a trident and capitol Zi looks like three horizontal lines, while it's lower case looks like a capitol cursive E. Good brush ups though.
So x and y in the psi function are independent or just simply function of one variable??
thanks a lot Salman. you have really made my mechanical engineering easy.
I feel stupid asking this, and really I wonder if it's even necessary to ask, but is this touching on multi-variable stuff? Because it seems to me that you have a variable x and a function of that variable y(x). But perhaps y(x) is, in itself, a variable? I've been through the first two calcs and this is completely new to me. Our prof. never touched on any of this.
Very lucid explanation. Helped me in understanding the fuzzy areas in the basics of exact differential equations. Partial derivatives on a general function is sometimes a complex path to understand the proof. Thanks a lot professor.
Ψ is not "zi" it's pronounced "pse".
"psi" may also pronounced as "zi" like the word psychology. i= ai(y).
Dude trust me I am from Greece I know how a letter of our alphabet is pronounced :P
Then you would know its pronounced "psi" :)
"psee" is how it's pronounced. Every single authority in any subject that uses this letter except this man has pronounced this letter correctly. Thanasakis is right.
Just look it up on wikipedia :)
en.wikipedia.org/wiki/Psi_(letter)
I always thought the same thing until I started taking engineering classes. Unfortunately this shit is really really useful in the real world
Mr Khan, you seem to stutter a bit which is distracting.
If youtube videos can be 'food for thought' Khan Academy is a fucking banquet
Back in the day when you had 10 minutes to make your point on RUclips
thought he was gunna begin singing it out at 5:40 XD hehe great video imo, ty for this
6:58 What is the conclusion of this argument?
Is this the full statement and conclusion :
Given the differential equation
*(f1 ' (x) g1(y) +... fn ' (x) gn(y))+ (f1(x) g1 '(y)+... fn(x) gn' (y)) dy/dx =0*
which by the chain rule is equivalent to
*d/dx( f1(x)g1(y) + ... fn(x) gn(y) )=0*
it follows that
*f1(x)g1(y) + ... fn(x) gn(y) = C* is an implicit solution
or using Sal's Ψ definition, *Ψ = C* is an implicit solution.
But why is Sal looking at this specific type of differential equation. In general exact equations do not have this nice form.
Intuitively, it isn't at all obvious to me why you can just add the two partials. How does adding rate-of-change in two different directions make sense? Is this just the definition?
Why does the chain rule apply to the partial derivative d/dy? Is it because you is a function of x?
Differential Equations usually comes after Multivariable Calculus, where partial differentials is fully covered. I believe this set of videos is fine without the partial differentials review. Nice work, as always Khan!
My teachers basicialy would say just roll with it. Same with pitagorian theorm or volume of pyramid etc. I need to know why a formula works and you explain it very well.
9:46 "i havent told you yet what an exact equation is." Thanks a lot for saying that. Else, it would have made me cry. I like you for accepting everything (the gaps and quirks in the topic itself, as well as in the videos) and not faking it like schools.
Ok, stutter is not the correct word for it then.
Finally understanding something ❤
@ibizaboyz its xi pronounced "zi" with a symbol like an equals sign but one more line on top( Ξ ). it is the equivalent to the english x. Im in a fraternity, I had to learn the greek alphabet and all the symbols and english equivalents. :)
complete
Is this Grant?
Sir, please make a lesson on Partial Differential Equations as soon as possible.
Is this video supposed to be here in the playlist? We've only just done first order seperable equations and this next video is on partial derivatives?
PSI not ZI
Glöm inte mig!:]
@MrNoturaveragerednek Differential equations are mostly used in physics in engineering. Basically it's very useful when working with objects in perpetual movement. The car you drive, the satellites that allows GPS to function and much more were designed much more effectively because of differential equations.
psy function , we can replaced with another function " to make it easier psy looks scariness " just for that
yeah, it looked kinda proofy :P
good reminder for the chain rule in multivariable calculus
Almost 10 minutes and not one number...😅
I had to view this video 5 times before I noticed that y is a function of x -.-
Just two more videos and you'll reach 2,000!!!!! Congratulations!!!
he is god in differential i swear
He is already happily married :P
I feel stupid
Haha he is so adorable
we love you khan academy
Great vidoe!! ty"!
there are 1's: f1(x)g1(y) :p
great video
Thanks a lot
His words ... omgggg. I can't see clearly
240p rip LMAO
whats a proofy?
It means that the video is a lot like a mathematical proof. As opposed to an example, he's explaining fundamentally how exact equations work.
Think you are confused, I kept seeing it as poofy.
I never understood algebra, or calculus or Trigonometry or whatever rocket science math this is supposed to be, who the hell uses this stuff in real life anyway?
Why is the dy/dx necessary at the end when finding the derivative of the multiplied functions? I don't remember writing it when using that rule.