Awesome! Though I am an economic and accounting major, I find this explanation of Total differentials easy to understand. :)) And it is really useful for Mathematical Economics (In a way)
great video. I think they are pretty much the same in terms of speed, in the video you only calculated half of the chain rule, normally you would need to find dz/dv as well,this problem you picked easier x and y functions to work with, you can tell dz/dv from dz/du by the symmetry of x and y functions.
In the equation (dz/du) = (dz/dx)*(dx/du) + (dz/dy)*(dy/du), why is it that if you cancel the dx's in the first term of the right hand side and cancel the dy's in the second term of the right hand side you get (dz/du) = (dz/du) + (dz/du) = 2(dz/du), which means 1 = 2?
i havent seen anyone except for herbert gross who can explain partial derivatives with what is fixed and what not fixed, why is it needed. this video's partial derivatives looks like partial dz/du = 2 times partial dz/du..
Why don't you just divide your equation for the total differential dz by du? Then you'd have the result immediately, that is, the chain rule expression b) directly derived from the expression for total differential a) ?
+Niels Ohlsen The differential, in general, is not a real or complex number to be operated in such a way, in general, _du_ would just yield another expression for the differential. However, according to the definition of a differential as a linear approximation to the increment change, we would be able to justify the operations as was demonstrated with the application of the chain rule that would be derived from writing differentials as increments before thus taking the limit (assuming continuity). I understand some of the terminologies I used may seem a bit off, regardless, in short, _du_ is not a real or complex number for which we would operate with it as if it were, to be mathematically rigorous is to use theorems that are justified according to the definition of the differential, which, in this case, is the chain rule. For a greater understanding of what I'm attempting to convey, I recommend reading Richard Courant's and Frit John's two introductory texts on calculus and analysis.
@@mitocw Where can i get problem set of a specific video? like say what the professer solved it lecture 21 of multivariable calculus? i mean the f sub x= some function and f sub y= some function thingy that he solved.
Lecture 21 material can be found in Session 62 of the course: ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/3.-double-integrals-and-line-integrals-in-the-plane/part-b-vector-fields-and-line-integrals/session-62-gradient-fields
9 years later and I cannot thank you enough for that dependency graph !😭
1:14 Priceless.
TheChosenOne someone please make this a meme lol
A solid gold that was
The dependency graph just cured my anxiety lol
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐💐
Best explanation I've ever seen about the two different methods!
Awesome! Though I am an economic and accounting major, I find this explanation of Total differentials easy to understand. :)) And it is really useful for Mathematical Economics (In a way)
You made this so clear and logical, when so many make it look like a mess!, thank you!
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐.
The Tree for the chain rule is sooooooooo easy but so genious, wow. Even after 12 years still helpfull.
I found this very helpful to cement the idea of total differentials and functions that depend on functions that depend on variables.
9 YEARS LATER THE VIDEO STILL MAKES A HUGE SIGNIFICANT.
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐.
coolest dude in university
Bro literally saved my life!!!
That is quite helpful to write down the dependency graph before starting to solve the equations.
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐.
Finally found what I was searching for❤
The dependency graph was an nice little tool that I didn't see in the main lecture.
that's a big ass chalk
Or a really small man
César Ventura - Kilroy FN we’ll never know..
great video. I think they are pretty much the same in terms of speed, in the video you only calculated half of the chain rule, normally you would need to find dz/dv as well,this problem you picked easier x and y functions to work with, you can tell dz/dv from dz/du by the symmetry of x and y functions.
directly what i was searching for
In the equation (dz/du) = (dz/dx)*(dx/du) + (dz/dy)*(dy/du), why is it that if you cancel the dx's in the first term of the right hand side and cancel the dy's in the second term of the right hand side you get (dz/du) = (dz/du) + (dz/du) = 2(dz/du), which means 1 = 2?
Good Video. The extra check mark by dy could be confusing since it resembles the letter v.
Thanks, it is so simple coz of your explanation.
Explicitly explained.Thanks.
That’s great. Added new insights.
i havent seen anyone except for herbert gross who can explain partial derivatives with what is fixed and what not fixed, why is it needed. this video's partial derivatives looks like partial dz/du = 2 times partial dz/du..
the graph of Derivative looks so interesting
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐.
Why don't you just divide your equation for the total differential dz by du?
Then you'd have the result immediately, that is, the chain rule expression b) directly derived from the expression for total differential a)
?
+Niels Ohlsen
The differential, in general, is not a real or complex number to be operated in such a way, in general, _du_ would just yield another expression for the differential. However, according to the definition of a differential as a linear approximation to the increment change, we would be able to justify the operations as was demonstrated with the application of the chain rule that would be derived from writing differentials as increments before thus taking the limit (assuming continuity).
I understand some of the terminologies I used may seem a bit off, regardless, in short, _du_ is not a real or complex number for which we would operate with it as if it were, to be mathematically rigorous is to use theorems that are justified according to the definition of the differential, which, in this case, is the chain rule.
For a greater understanding of what I'm attempting to convey, I recommend reading Richard Courant's and Frit John's two introductory texts on calculus and analysis.
Very clear explanation.Thanks!
At 6:03 where does he get the values for dz, dx, and y?
Very clear explanation
What's the name of this joker
Great video, thank you...
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐.
excellent explanation, thanks
Thank you
Thanks... now I have 2 different method in my toolbox to solve this kind of derrivative
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐.
easy to understand
Ian Benedict L. Del Prado Del Prado so you don't.
Beautiful !
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐.
You are the man!
That Chalk...
Now it looks so simple! Thanks!
Great video, thanks for the help :)
very nice and simple.....thanks
i just looking for this video
but the camera man did not cover full board
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐.
Teaching assistants at MIT, usually Grad students.
His nose looks charming
Very helpful. Thank you.
Yesss thank you!
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐.
thanks! helped me
Thanks a lot!
Thank you sir
thank you!
Where can u get the problem set?
See the course on MIT OpenCourseWare for materials at: ocw.mit.edu/18-02SCF10. Best wishes on your studies!
@@mitocw Where can i get problem set of a specific video? like say what the professer solved it lecture 21 of multivariable calculus? i mean the f sub x= some function and f sub y= some function thingy that he solved.
Lecture 21 material can be found in Session 62 of the course: ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/3.-double-integrals-and-line-integrals-in-the-plane/part-b-vector-fields-and-line-integrals/session-62-gradient-fields
@@mitocw but there are not problems like f sub x =x^2 and f sub y = y^2 . there are no problems like this
My questions is, who are the guys that did this video ? Are they MIT's students or what ?
Thanks a lot !
Hi after a decade😂
superb ^^
thanks
Danny D
where is the proof of the total derivative??? , I need it
I got it if you need it
@@justadreamerforgood69 That was 6 years ago bro, people change interests very often :)
@@abdelrahmangamalmahdy
Ok!!
I need it, please help ..
@@sheetalmadi336
I have a pdf of it, send me your email or something and I can forward it to you
sir please teach me hyperbolic radian-- thank u sir
you need lessons in teaching
thicc chalk
Coming from intro to AI
th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐.
Thankyou so much