Total differentials and the chain rule | MIT 18.02SC Multivariable Calculus, Fall 2010

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  • Опубликовано: 10 фев 2025

Комментарии • 90

  • @eniolaayoola7988
    @eniolaayoola7988 4 года назад +50

    9 years later and I cannot thank you enough for that dependency graph !😭

  • @matrixate
    @matrixate 9 лет назад +117

    1:14 Priceless.

    • @volcomx14
      @volcomx14 4 года назад +1

      TheChosenOne someone please make this a meme lol

    • @nanzzee22
      @nanzzee22 3 года назад

      A solid gold that was

  • @onecanina
    @onecanina 11 лет назад +9

    Best explanation I've ever seen about the two different methods!

  • @matthewocadiz7333
    @matthewocadiz7333 5 лет назад +46

    The dependency graph just cured my anxiety lol

    • @beoptimistic5853
      @beoptimistic5853 4 года назад +1

      ruclips.net/video/XQIbn27dOjE/видео.html 💐💐

  • @Explorer982
    @Explorer982 5 лет назад +4

    You made this so clear and logical, when so many make it look like a mess!, thank you!

    • @beoptimistic5853
      @beoptimistic5853 4 года назад

      ruclips.net/video/XQIbn27dOjE/видео.html 💐.

  • @Teretereteresita
    @Teretereteresita 13 лет назад +17

    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)

  • @LAnonHubbard
    @LAnonHubbard 11 лет назад +1

    I found this very helpful to cement the idea of total differentials and functions that depend on functions that depend on variables.

  • @badrmoubile9219
    @badrmoubile9219 Год назад +1

    The Tree for the chain rule is sooooooooo easy but so genious, wow. Even after 12 years still helpfull.

  • @sthembiso_mkhwanazi
    @sthembiso_mkhwanazi 4 года назад

    9 YEARS LATER THE VIDEO STILL MAKES A HUGE SIGNIFICANT.

    • @beoptimistic5853
      @beoptimistic5853 4 года назад

      ruclips.net/video/XQIbn27dOjE/видео.html 💐.

  • @LAnonHubbard
    @LAnonHubbard 11 лет назад +1

    The dependency graph was an nice little tool that I didn't see in the main lecture.

  • @wesleymesquita8380
    @wesleymesquita8380 4 года назад

    That is quite helpful to write down the dependency graph before starting to solve the equations.

    • @beoptimistic5853
      @beoptimistic5853 4 года назад

      ruclips.net/video/XQIbn27dOjE/видео.html 💐.

  • @TheSunshineRequiem
    @TheSunshineRequiem 5 лет назад +2

    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.

  • @princegbadamosi6805
    @princegbadamosi6805 Год назад

    Bro literally saved my life!!!

  • @enverburtul1908
    @enverburtul1908 7 лет назад +3

    coolest dude in university

  • @shenalranasinghe2856
    @shenalranasinghe2856 3 года назад

    Finally found what I was searching for❤

  • @suwahhlaing5989
    @suwahhlaing5989 9 лет назад

    Thanks, it is so simple coz of your explanation.

  • @videofountain
    @videofountain 7 лет назад +4

    Good Video. The extra check mark by dy could be confusing since it resembles the letter v.

  • @jayant8363
    @jayant8363 3 года назад

    Thank you

  • @user-or7ji5hv8y
    @user-or7ji5hv8y 3 года назад

    That’s great. Added new insights.

  • @malickcamara8214
    @malickcamara8214 9 лет назад

    Explicitly explained.Thanks.

  • @VladimirDjokic
    @VladimirDjokic 10 лет назад

    Very clear explanation.Thanks!

  • @sandeepskumar9928
    @sandeepskumar9928 4 года назад

    Beautiful !

    • @beoptimistic5853
      @beoptimistic5853 4 года назад

      ruclips.net/video/XQIbn27dOjE/видео.html 💐.

  • @peternjini4544
    @peternjini4544 11 лет назад

    Very clear explanation

  • @Mr19daryo
    @Mr19daryo 9 лет назад

    directly what i was searching for

  • @kamesh7818
    @kamesh7818 7 лет назад

    excellent explanation, thanks

  • @reshonsheyal5024
    @reshonsheyal5024 4 года назад

    Great video, thank you...

    • @beoptimistic5853
      @beoptimistic5853 4 года назад

      ruclips.net/video/XQIbn27dOjE/видео.html 💐.

  • @abcdef2069
    @abcdef2069 8 лет назад +1

    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..

  • @iandelprado5978
    @iandelprado5978 7 лет назад +1

    easy to understand

    • @NisseOhlsen
      @NisseOhlsen 7 лет назад

      Ian Benedict L. Del Prado Del Prado so you don't.

  • @benjamincordes207
    @benjamincordes207 10 лет назад

    You are the man!

  • @sijcecilio
    @sijcecilio 8 лет назад +32

    that's a big ass chalk

  • @ConnerReeves
    @ConnerReeves 13 лет назад +1

    Great video, thanks for the help :)

  • @chHJChang
    @chHJChang 5 лет назад

    the graph of Derivative looks so interesting

    • @beoptimistic5853
      @beoptimistic5853 4 года назад

      ruclips.net/video/XQIbn27dOjE/видео.html 💐.

  • @bsnravi
    @bsnravi 11 лет назад

    very nice and simple.....thanks

  • @shrimatkapoor2200
    @shrimatkapoor2200 4 года назад

    Yesss thank you!

    • @beoptimistic5853
      @beoptimistic5853 4 года назад

      ruclips.net/video/XQIbn27dOjE/видео.html 💐.

  • @jessemikulec4618
    @jessemikulec4618 2 года назад +2

    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?

  • @wangzhiqiao1045
    @wangzhiqiao1045 6 лет назад

    Thank you sir

  • @赵䟏
    @赵䟏 8 лет назад

    Thanks a lot!

  • @chrisellis333
    @chrisellis333 12 лет назад

    Very helpful. Thank you.

  • @TaeNyFan
    @TaeNyFan 8 лет назад

    thanks! helped me

  • @annalam8624
    @annalam8624 8 лет назад

    thank you!

  • @the_eternal_student
    @the_eternal_student 4 месяца назад

    At 6:03 where does he get the values for dz, dx, and y?

  • @bostangpalaguna228
    @bostangpalaguna228 4 года назад

    Thanks... now I have 2 different method in my toolbox to solve this kind of derrivative

    • @beoptimistic5853
      @beoptimistic5853 4 года назад

      ruclips.net/video/XQIbn27dOjE/видео.html 💐.

  • @NisseOhlsen
    @NisseOhlsen 7 лет назад +2

    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)
    ?

    • @analysis-sb4ri
      @analysis-sb4ri 6 лет назад

      +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.

  • @maurodefreitasjr3678
    @maurodefreitasjr3678 10 лет назад

    Now it looks so simple! Thanks!

  • @annakh9543
    @annakh9543 7 лет назад

    superb ^^

  • @shahwaliullah2292
    @shahwaliullah2292 8 лет назад

    thanks

  • @sameris6581
    @sameris6581 9 лет назад +10

    That Chalk...

  • @ShamimsVlogig
    @ShamimsVlogig 4 года назад

    i just looking for this video
    but the camera man did not cover full board

    • @beoptimistic5853
      @beoptimistic5853 4 года назад

      ruclips.net/video/XQIbn27dOjE/видео.html 💐.

  • @El3ziiiz
    @El3ziiiz Месяц назад

    you r god

  • @BkSenko24
    @BkSenko24 12 лет назад

    Teaching assistants at MIT, usually Grad students.

  • @ElboxD
    @ElboxD 12 лет назад +1

    My questions is, who are the guys that did this video ? Are they MIT's students or what ?
    Thanks a lot !

  • @joychanning4128
    @joychanning4128 7 лет назад +1

    His nose looks charming

  • @Learnwithme-v4c
    @Learnwithme-v4c 3 года назад +1

    What's the name of this joker

  • @aashsyed1277
    @aashsyed1277 3 года назад

    Where can u get the problem set?

    • @mitocw
      @mitocw  3 года назад

      See the course on MIT OpenCourseWare for materials at: ocw.mit.edu/18-02SCF10. Best wishes on your studies!

    • @aashsyed1277
      @aashsyed1277 3 года назад

      @@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.

    • @mitocw
      @mitocw  3 года назад

      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

    • @aashsyed1277
      @aashsyed1277 3 года назад

      @@mitocw but there are not problems like f sub x =x^2 and f sub y = y^2 . there are no problems like this

  • @kumarsanufansite2949
    @kumarsanufansite2949 5 лет назад

    Danny D

  • @adamg.515
    @adamg.515 3 года назад

    you need lessons in teaching

  • @abdelrahmangamalmahdy
    @abdelrahmangamalmahdy 11 лет назад

    where is the proof of the total derivative??? , I need it

  • @ko-Daegu
    @ko-Daegu 4 года назад

    Coming from intro to AI

    • @beoptimistic5853
      @beoptimistic5853 4 года назад

      ruclips.net/video/XQIbn27dOjE/видео.html 💐.

  • @pisanghangus2
    @pisanghangus2 3 года назад

    thicc chalk

  • @karimkhan1312
    @karimkhan1312 10 лет назад

    sir please teach me hyperbolic radian-- thank u sir

  • @anubhavvevosongs3791
    @anubhavvevosongs3791 3 года назад

    Thankyou so much