Total differentials and the chain rule | MIT 18.02SC Multivariable Calculus, Fall 2010
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- เผยแพร่เมื่อ 27 มิ.ย. 2024
- Total differentials and the chain rule
Instructor: David Jordan
View the complete course: ocw.mit.edu/18-02SCF10
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
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
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Best explanation I've ever seen about the two different methods!
I found this very helpful to cement the idea of total differentials and functions that depend on functions that depend on variables.
You made this so clear and logical, when so many make it look like a mess!, thank you!
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directly what i was searching for
Thanks, it is so simple coz of your explanation.
Very clear explanation.Thanks!
Explicitly explained.Thanks.
Finally found what I was searching for❤
excellent explanation, thanks
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 are the man!
The dependency graph was an nice little tool that I didn't see in the main lecture.
coolest dude in university
The Tree for the chain rule is sooooooooo easy but so genious, wow. Even after 12 years still helpfull.
Bro literally saved my life!!!
Very clear explanation
Great video, thanks for the help :)
That’s great. Added new insights.
Good Video. The extra check mark by dy could be confusing since it resembles the letter v.
Very helpful. Thank you.
thank you!
very nice and simple.....thanks
Thank you
9 YEARS LATER THE VIDEO STILL MAKES A HUGE SIGNIFICANT.
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thanks! helped me
Thanks a lot!
Thankyou so much
That is quite helpful to write down the dependency graph before starting to solve the equations.
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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.
Thank you sir
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?
superb ^^
Beautiful !
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thanks
Great video, thank you...
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Now it looks so simple! Thanks!
the graph of Derivative looks so interesting
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Yesss thank you!
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that's a big ass chalk
Or a really small man
César Ventura - Kilroy FN we’ll never know..
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.
easy to understand
Ian Benedict L. Del Prado Del Prado so you don't.
That Chalk...
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
Thanks... now I have 2 different method in my toolbox to solve this kind of derrivative
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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😂
His nose looks charming
i just looking for this video
but the camera man did not cover full board
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Teaching assistants at MIT, usually Grad students.
What's the name of this joker
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
thicc chalk
you need lessons in teaching
Coming from intro to AI
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