The way you tied together the calc 1 and calc 3 methods with how to go about solving an exact differential equation is world class. Thank you. Keep up the great work!
This video was really helpful to me. Unlike other TH-cam videos, you actually explain the concept behind it and I've been looking for a video like that everywhere! Thanks for uploading!
The choice of music is spot on. Yes, the explanation is amazing, but the music makes it seem even more accessible as it suggests "This stuff is not that hard, you can understand it, be optimistic!". The self confidence aspect is really big when it comes to staying motivated while studying. I love your videos!
this one video taught me a concept that i did not understand whatsoever, despite my teacher going over it and reviewing it for 3 days. thank you very much for making these videos.
This man teaches better than many High END profile teachers on those Ivory League Universities. Yes those are top researchers but teaching should be as good as research. Besides all of these theorems deserves a nice Proof. There could be a series of videos proving all these theorems and derivations.
You are a very good teacher. You think about how to explained it so that it connects to everything we have learn so that we can better relate and understand. Great job!
Si me hubiera gustado las matemáticas desde niño de seguro que a los 14 años ya dominaría este tema pero así es la vida, me incline por otras cosas pero que tienen que ver con la ciencia pero al dedicarme a otros temas como la Biología sacaba altas notas e investigaba y lo que ya el profesor iba a dar clase ya me lo sabia de sobra y lo veía muy básico. Por tanto, el interés de una persona por alguna cosa o tema se refuerza con la práctica, la investigación y la perseverancia que le tienes.
They're called exact equations because the total differential is also called the exact differential. It's exact because everything adds to a constant. The actual idea behind exact DE's is that there are two independent variables and no dependent variables, hence F being constant. This means that dF is always zero, but dx and dy are always changing but add up to zero exactly. When bprp did the calc one differentiation, he should have implicitly differentiated with respect to t, as if t was the independent variable, and then asked, "What's this t? I don't see any t's. I know that x and y are supposed to be functions of t, BUUUT, what if there was no t?" Then you multiply by dt to get rid of the dt's and, bam, an exact equation.
In the derivative dy/dx it should be noted that x and y can have only values that are on the actual curve. How is this handled? If (x,y) coordinate value that is not on the curve is substituted to the dy/dx equation, then is that actually a derivatives that is resulted? Then derivative exists also outside the curves line?
10:17 how is even possible that the result is the same? In the first case, y was a function of x, in the second case there was no bond between the variables.
I may be late to the party but I’ll try to explain how I think of this « contradiction ». In the first example, we considered y to be a function of x. From implicit differentiation, we got the dy/dx=something In the second example, F(x,y) = x^2*y^4 + cos(y) has two indépendant variable, so when we differentiate y^4 in terms of x, we get 0 which is completely different from the calc1 case... Thus anyone would think the dy/dx we get in each case will be different. BUT instead of only differentiating with respect to x, we also add a part differentiated with respect to y so it kinda balance things off. However, it is still not enough. F(x,y) is a function with 2 indépendant variable, so if you were to plot F, you would get a surface, so when we take a small step dx, we can’t imagine how dy will grow. We have no idea what dy/dx would be equal to This is because there is no relationship between x and y. One does not determine the other. All we know is: dF= (partial F/partial x)*dx + (Partial F /partial y)*dy One does not determine the other... Unless we add another restraint. Here, we added the restraint: F(x,y)= 1 Notice that F(x,y) is well defined everywhere, however, with the new constraint, we only consider a small part of F. F, with the new restraint is only a curve, not the whole surface. This means that x and y are now intertwined. If you know y, you can find x. If you know x, you can find y. Even if the x and y are not unique, they are still bounded to each other with the restraint F(x,y)=1 And from this constraint, we get dF= 0 which leads to (partial F/partial x)*dx + (Partial F /partial y)*dy = 0 This is the missing link to get dy/dx= something Without the constraint, x and y are independant Without the constraint, we can not get dy/dx in the calc 3 case Hopefully, this solves the original question To be honest, I never thought about this problem and I sure spent a lot of time to try to figure this so thank you for asking! Even if this is obvious to some people, it can help other people who didn’t think about the original problem, so thank you again!
Question: in the calc 1 and calc 3 methods is y a function of x in both examples, if so does it matter weather or not the variables in a function are independant of each other or not when doing the exact equation method?
very nice video. but the volume is very low. i maxed out everything but it is still hard to hear what you say. (i am using laptop speakers, maybe it's power is not good as desktop speakers)
Hi BPRP - a question to this video - why haven't we found Y? I mean why is that we did not finish with an equation of a form Y=f(x)+c? You started the video with one of the equation's form (the one including cos(x)) and you have finished with the same form - is it not possible to find Y in this type of equations? Or is it something entirely different that we are looking for in this type of equations?
Manan Seth Yes he did, but what is the purpouse of this kind of equations if we cannot calculate anything out of them? (Please forgive me my spelling, I have no corrector on hand)
Piotr S we can calculate and graph it, but probably just not by hand. And most people will probably never use equations like this in their lives but you never know when it might come in handy.
also my prof told me the reason why you add the original function for checking exactness to the equation concerninig F(x,y), is because one cannot simply integrate multi variable functions. But if you can differentiate 2 and differentiation is opposite to integration(but necessary for antiderivatives) , why is this?
![Exact Equations [ODE]](http://i.ytimg.com/vi/pgJci5CI9n4/mqdefault.jpg)
The way you tied together the calc 1 and calc 3 methods with how to go about solving an exact differential equation is world class. Thank you. Keep up the great work!
This is the best video about differential equation I have never seen.....
thanks!
I founded the solutions for my questions. Thank you sir
i guess it's kinda randomly asking but do anyone know of a good site to stream newly released movies online ?
@Ares Bishop Try Flixzone. You can find it by googling =)
Glaze
This video was really helpful to me. Unlike other TH-cam videos, you actually explain the concept behind it and I've been looking for a video like that everywhere! Thanks for uploading!
Lily Zhong you're welcome Lily. I am glad that you found my video helpful.
Underrated youtuber....thanks for the help
Frank Champion thank you 😊
The choice of music is spot on. Yes, the explanation is amazing, but the music makes it seem even more accessible as it suggests "This stuff is not that hard, you can understand it, be optimistic!". The self confidence aspect is really big when it comes to staying motivated while studying. I love your videos!
exactly broooooo. spot on explaination
Cringe breath
I have searched alot to figure what why exact diffrential equations work 😄 until I finally found this video.It's so amazing
Your videos are helping me a ton for my Diff Eq class, thanks for all the time you put into them! It is much appreciated.
Man, i love your videos. Don't stop.
Thanks!
How to solve exact equations!
Im ME major and you really help me relate unlike a professor can. great job, you are helping us all :)
Your intros are the best on youtube, hands down
Taking calculus for the third time already, I finally get it now thank you! Should have found your videos the first time
this one video taught me a concept that i did not understand whatsoever, despite my teacher going over it and reviewing it for 3 days. thank you very much for making these videos.
Thanks man, helped a lot. Do not stop with the videos.Good explanation, thanks
You're welcome!!
Thanks my guy! you and Professor Leonard have saved me soo much frustration!
This man teaches better than many High END profile teachers on those Ivory League Universities. Yes those are top researchers but teaching should be as good as research.
Besides all of these theorems deserves a nice Proof. There could be a series of videos proving all these theorems and derivations.
I actually did not believe it would be good, but it was the best. 19 min was totally worth it
Very nice videos. I really appreciate you starting discussions from the very root of the concept. Keep up!
You are a very good teacher. You think about how to explained it so that it connects to everything we have learn so that we can better relate and understand. Great job!
This is a very nice prep for my next semester :)
SuperDreamliner787 glad to hear! I am also preparing for next semester, let's see how many I can do this winter
I am taking Thermodynamics this year without having taken Calc 3, this saved me from tears, thank you so much!
I'm learning about exact equations after my first test, this will be a good video to watch! Thanks alot BPRP!!!!
You're welcome!
OHHHHH. Thank you, for giving me hope as I continue on and the exam looms closer and closer.
I like how you sepeate the X world from the Y world. Great as always!
this dude deserves more subscribers
This is the only video which actually made me understand
I love the way u said "total" at 6:26
You sir, are a gentleman, and a scholar! And you have my thanks!
The best teacher ever
i literally self studying myself for next semesters and now i ace the class for de thanks you so much
THANK YOU SO MUCH for making this video, you made Exact DEs make so much sense!
you deserve a million subs sir
currently a first year uni student cramming and you've saved my ass, great vid !!!
the best video i have ever seen
serious talk
Wow, Excellent video. It makes it all so approachable. Thanks!
Si me hubiera gustado las matemáticas desde niño de seguro que a los 14 años ya dominaría este tema pero así es la vida, me incline por otras cosas pero que tienen que ver con la ciencia pero al dedicarme a otros temas como la Biología sacaba altas notas e investigaba y lo que ya el profesor iba a dar clase ya me lo sabia de sobra y lo veía muy básico. Por tanto, el interés de una persona por alguna cosa o tema se refuerza con la práctica, la investigación y la perseverancia que le tienes.
I love the way you teach.
have I ever told you I love you?
No yet. But now I know! Thank you~!
Learnt a lot. It is like how we apply this to find the stream function or potential function in potential flow theory.
such an adorable host who explains so well !
Great job! Rapid and very well explained.
Thanks. Your video makes me understand the topic very well
Your videos are always excellent. I suggest: those viewers that want music can put some on. But not if you do.
This guy is such a beast
Amazing!! This video SHOULD HAVE MORE VIEWS. :)
thanks!!!
1:26 why would you use product rule if you're differentiating with regards to x? shouldn't y^4 be treated like a constant?
This man is saving me in college
Now that is very well explained. Thanks you sir ❤
They're called exact equations because the total differential is also called the exact differential. It's exact because everything adds to a constant. The actual idea behind exact DE's is that there are two independent variables and no dependent variables, hence F being constant. This means that dF is always zero, but dx and dy are always changing but add up to zero exactly. When bprp did the calc one differentiation, he should have implicitly differentiated with respect to t, as if t was the independent variable, and then asked, "What's this t? I don't see any t's. I know that x and y are supposed to be functions of t, BUUUT, what if there was no t?" Then you multiply by dt to get rid of the dt's and, bam, an exact equation.
I need to get in touch with this lecturer
Thanks again. Your explanations are well thought through.
greetings from sri lanka... good explanation
Thank you so much bprp!
WOOW!The best of the best its an incredible video
5:50 it could by Bernoulli where y is independent variable
You’re the best
5:53 Calc3 method
thanks so much btw :)
wow i didn't get it during my lecture but now i do thank you
You're simply amazing bro
Your videos are soooo awesome! thanks again! I feel like I'm falling love with you.:)
Thanks!
best explanation ever
this is just perfect,well explained thank you
01:35 What? Why? shouldn't it be 2x*y^4?
Thank you soooooo much....🥰🥰🥰🥰🥰🥰😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍
This is exact differential equationade easy
The world needs an ASMR version of this.
You are the best man🔥🔥🔥🔥🔥🔥
Great demo. Thanks!!
😍😍😍wow...great explanation...!!
you are the best
big fan bro
What if after finding for their partial differentiation , both are not the same
What are you going to do
thank you so much this makes so much sense
Hi, I was wondering why we always put the C on the RHS?
Don't quite understand what you mean by the ' total differential.' Could you elaborate? [ ps. thanks for great videos]
Excellent job mate
Awesome video 🤩🤩
How did you come up with that initial value..??
In the derivative dy/dx it should be noted that x and y can have only values that are on the actual curve. How is this handled?
If (x,y) coordinate value that is not on the curve is substituted to the dy/dx equation, then is that actually a derivatives that is resulted? Then derivative exists also outside the curves line?
How can we say that it is capital F in the final answer even though it is in the partial derivative form with respect to y?
10:17 how is even possible that the result is the same? In the first case, y was a function of x, in the second case there was no bond between the variables.
Davide Carrea you need to study more before you watch that method
I may be late to the party but I’ll try to explain how I think of this « contradiction ».
In the first example, we considered y to be a function of x. From implicit differentiation, we got the dy/dx=something
In the second example,
F(x,y) = x^2*y^4 + cos(y)
has two indépendant variable, so when we differentiate y^4 in terms of x, we get 0 which is completely different from the calc1 case... Thus anyone would think the dy/dx we get in each case will be different.
BUT instead of only differentiating with respect to x, we also add a part differentiated with respect to y so it kinda balance things off.
However, it is still not enough. F(x,y) is a function with 2 indépendant variable, so if you were to plot F, you would get a surface, so when we take a small step dx, we can’t imagine how dy will grow.
We have no idea what dy/dx would be equal to
This is because there is no relationship between x and y. One does not determine the other.
All we know is:
dF= (partial F/partial x)*dx + (Partial F /partial y)*dy
One does not determine the other... Unless we add another restraint.
Here, we added the restraint:
F(x,y)= 1
Notice that F(x,y) is well defined everywhere, however, with the new constraint, we only consider a small part of F.
F, with the new restraint is only a curve, not the whole surface.
This means that x and y are now intertwined.
If you know y, you can find x.
If you know x, you can find y.
Even if the x and y are not unique, they are still bounded to each other with the restraint F(x,y)=1
And from this constraint, we get dF= 0 which leads to
(partial F/partial x)*dx + (Partial F /partial y)*dy = 0
This is the missing link to get dy/dx= something
Without the constraint, x and y are independant
Without the constraint, we can not get dy/dx in the calc 3 case
Hopefully, this solves the original question
To be honest, I never thought about this problem and I sure spent a lot of time to try to figure this so thank you for asking!
Even if this is obvious to some people, it can help other people who didn’t think about the original problem, so thank you again!
Loved 😍🤩🤩🤩 the video!
I love your video. This will save me from an impending F.
Why you using blue pen?
Question: in the calc 1 and calc 3 methods is y a function of x in both examples, if so does it matter weather or not the variables in a function are independant of each other or not when doing the exact equation method?
Sir, is it possible that the equation is exact and is not homogenous? If possible, is there a method on how to solve?
I love this guy. ❤
Thank you
kind a confused; where do you get f(y) from? I thought that the integral answer includes a constant..
you're just the best
was in the dark before this...many thanks
very nice video. but the volume is very low. i maxed out everything but it is still hard to hear what you say. (i am using laptop speakers, maybe it's power is not good as desktop speakers)
Super helpful. Thank you.
You're welcome!
Could I know the beautiful music you used in this video?
Very helpful, thanks! Have you had any plans to do some calc 3 videos?
Hi BPRP - a question to this video - why haven't we found Y? I mean why is that we did not finish with an equation of a form Y=f(x)+c? You started the video with one of the equation's form (the one including cos(x)) and you have finished with the same form - is it not possible to find Y in this type of equations? Or is it something entirely different that we are looking for in this type of equations?
In the beginning he said the equation cannot be isolated in terms of y right?
Manan Seth Yes he did, but what is the purpouse of this kind of equations if we cannot calculate anything out of them? (Please forgive me my spelling, I have no corrector on hand)
Piotr S we can calculate and graph it, but probably just not by hand. And most people will probably never use equations like this in their lives but you never know when it might come in handy.
well explaind sir!
Thanks!
How do you even identify if it's exactly, linear, homogeneous or any other form 😩
Thank you so much!
Simple and clear
whats the difference when solving for a normal linear DE vs total differential?
also my prof told me the reason why you add the original function for checking exactness to the equation concerninig F(x,y), is because one cannot simply integrate multi variable functions. But if you can differentiate 2 and differentiation is opposite to integration(but necessary for antiderivatives) , why is this?
what is Y(root2divided by phi)=phi