THAAAAAAANK YOOOOOU!!!!! The process is very easy but i didn't know the REASON why we had to find the Jacobian. Once you said "integrating factor," everything fell into place. :]
Man ur explanation is more than wonderful believe me even da big proofs in the world can do wat u did in 8 minute u really help me so much when i start to lose hope that no one will know this
Thank you so incredibly much! I have been looking for a video or guide on how to do this for over an hour, and nothing was helpful at all. This explained it excellently!
For anybody wondering about how he got x=2u and y=2u+4v: We want to convert the region to a unit square having vertices(0,0), (0,1),(1,0),(1,1) We let the transformations be, x=a1u+b1v+c1 y=a2u+b2v+c2 (Geometrically we want u and v to be new axis, and hence we are transforming everything to that co-ordinate) So, for (0,0), y=0 0=a2*0+b2*0+c2 So, c2=0 For(0,1), y=4 4=a2*0+b2*1+c2 4=0+b2+0(as c2=0) b2=4 For(1,0), y=2 2=a2*1+b2*0+c2 2=a2+0+0(as c2=0) a2=2 So, y=2u+4v You can pull off for x
I wonder if you can help me with something that's been bothering me for a while. Let's focus on polar coordinates: x=r cos(theta) and y = r sin(theta) Therefore: dx = cos (theta).dr - r.sin(theta).dtheta dy = sin (theta).dr + r.cos (theta).dtheta. Why, if you multiply dx by dy, the answer is NOT r.dr.dtheta?
Very nice, but how did you come up with the equations for u and v that ended up simplifying the area of integration so conveniently? Thanks for explaining.
hmm, im a bit confused here....So we are calculating the area bounded by the 2 lines which is (base x height)= 2 * 4 = 8. And the final answer with the u and v results in 80/3.... someone please helppppp
Cf W is correct. If you were only trying to find the area then you would not have used the xy product converted to u and v. You would have only integrated the Jacobian of 8 to have 8 dvdu with the same limits of integration. That would give you a result of 8.
It was given in this case but it can be derived. Since they wanted u to go from 0 to 1, that meant x = 2u since x was going from 0 to 2. If you rewrite the other equations to y - x = 0 and y - x = 4 then let v = y - x. Since they also wanted v to go from 0 to 1, that meant 4v = y - x. If you solve the system x = 2u and y - x = 4v then you have y = 2u + 4v by addition. I worked the problem with x = u and y - x = v which gave me y = u + v. In this case, u is going from 0 to 2 and v is going from 0 to 4. The Jacobian was equal to 1 instead of 8 but the new limits of integration produced the same answer of 80/3. Of course, I was integrating u*(u+v) which were my transformations.
@@dirklerxstpratt2112 its been a year since your comment but i had to let you know that your explanation has helped me immensely. It seems no one on youtube has explained how to derive the transformation equations other than you
@@dirklerxstpratt2112 people liike you ememrge as a god in these sort of situation because no way here it was given how the transformation took place from (x,y) to (u,v)!!!!
THAAAAAAANK YOOOOOU!!!!!
The process is very easy but i didn't know the REASON why we had to find the Jacobian. Once you said "integrating factor," everything fell into place. :]
Clear, concise, and straight to the point on top of great use of different marker colour! Thanks!
Man ur explanation is more than wonderful believe me even da big proofs in the world can do wat u did in 8 minute u really help me so much when i start to lose hope that no one will know this
Thank you so incredibly much! I have been looking for a video or guide on how to do this for over an hour, and nothing was helpful at all. This explained it excellently!
So how do you find x = g(u,v) and y = h(u,v) if they are not given? 🤔
Excelent explanation! Thank you very much.
Perhaps a silly question: Where did you get x=2u and y=4x+2u ?
I asked The Same Question ?
That’s what I’m about to say. That point should be made as clear as the video. Because that’s the key
Definately I`m going to get this question correct on my calculus exam tomorrow. THANK YOU SIR
For anybody wondering about how he got
x=2u and y=2u+4v:
We want to convert the region to a unit square having vertices(0,0), (0,1),(1,0),(1,1)
We let the transformations be,
x=a1u+b1v+c1
y=a2u+b2v+c2
(Geometrically we want u and v to be new axis, and hence we are transforming everything to that co-ordinate)
So, for (0,0), y=0
0=a2*0+b2*0+c2
So, c2=0
For(0,1), y=4
4=a2*0+b2*1+c2
4=0+b2+0(as c2=0)
b2=4
For(1,0), y=2
2=a2*1+b2*0+c2
2=a2+0+0(as c2=0)
a2=2
So, y=2u+4v
You can pull off for x
Thank you. This was short and simple and explains the theory through the example. Very much appreciated.
Thank you for the comment. I'm glad I could help.
this was a life saver. thank you for the useful content.
I wonder if you can help me with something that's been bothering me for a while. Let's focus on polar coordinates:
x=r cos(theta) and y = r sin(theta)
Therefore:
dx = cos (theta).dr - r.sin(theta).dtheta
dy = sin (theta).dr + r.cos (theta).dtheta.
Why, if you multiply dx by dy, the answer is NOT r.dr.dtheta?
I have a better feel for this now. Thank you very much :D
David Ladu Same!! :D
Best explanation available
My professor explained this in a long and confusing way so this made it much more simple. :)
how to find u&v if it is not given
how did you find the equations for u and v
It is usually given
Awab elmahe what if not
Very nice, but how did you come up with the equations for u and v that ended up simplifying the area of integration so conveniently? Thanks for explaining.
usually given
Still effective after 10 years
Simply awesome! Great video. Thank you so much.
this is a good vidoeo , helped me understand this concept
Thank you sir... You cleared my doubts..
Superbbly explained
Thank you
Hi! I love your video its so clear end I understood perfectly.
ruclips.net/video/vFDMaHQ4kW8/видео.html .💐.
Can you explain how x
+Elijah Paul Nevermind....got it...y=x has a slope 1 which is the minimum value y can take
this is really useful thankss
Thank you so much for explaining so calmly... i Appreciate you effort.. :)
Superb tutorial. Tanks.
Thank you so much, I don't understand a thing from my prof,
if we have x=U²-V² and y=2UV ? i can't find the new region... can some one help me?
everytime, it will be in function of another V or U...
Thanx for such nice explanation
Thanks
Excellent
simple and helpful
thankyou! this is so clear!
hmm, im a bit confused here....So we are calculating the area bounded by the 2 lines which is (base x height)= 2 * 4 = 8. And the final answer with the u and v results in 80/3.... someone please helppppp
the 8 is the area(unit^2), 80/3 is the volume(unit^3).
Cf W is correct. If you were only trying to find the area then you would not have used the xy product converted to u and v. You would have only integrated the Jacobian of 8 to have 8 dvdu with the same limits of integration. That would give you a result of 8.
can anybody tell me how he determined x=2u and y=4v+2u?please
Austin D it was a given
Andrew Riederer No bro its not given
It was given in this case but it can be derived. Since they wanted u to go from 0 to 1, that meant x = 2u since x was going from 0 to 2. If you rewrite the other equations to y - x = 0 and y - x = 4 then let v = y - x. Since they also wanted v to go from 0 to 1, that meant 4v = y - x. If you solve the system x = 2u and y - x = 4v then you have y = 2u + 4v by addition. I worked the problem with x = u and y - x = v which gave me y = u + v. In this case, u is going from 0 to 2 and v is going from 0 to 4. The Jacobian was equal to 1 instead of 8 but the new limits of integration produced the same answer of 80/3. Of course, I was integrating u*(u+v) which were my transformations.
@@dirklerxstpratt2112 its been a year since your comment but i had to let you know that your explanation has helped me immensely. It seems no one on youtube has explained how to derive the transformation equations other than you
@@dirklerxstpratt2112 people liike you ememrge as a god in these sort of situation because no way here it was given how the transformation took place from (x,y) to (u,v)!!!!
how to u choose x and y values?
JustBe Brave yes, thats a good question :D
any one here knows?
THANX A LOT
awesome!!
thank u so much
I'm glad you found the video helpful.
Thank You so Much I Understand It supers Welll !!!
You are very welcome.
@@Mathispower4u please, I just Have A Simple question Where did you get The x= 2u and Y=4v+2u ?
thank you :)
thanks
thank you so much ^_*
Rip for dislikers
Any kscjian 😂?
brushed fdjd
Thank you
thank you