Example of a Change of Variables for a Double Integral: Jacobian

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  • Опубликовано: 29 окт 2024

Комментарии • 70

  • @gardeniabeauty16
    @gardeniabeauty16 11 лет назад +9

    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. :]

  • @Lexyvil
    @Lexyvil 2 года назад +1

    Clear, concise, and straight to the point on top of great use of different marker colour! Thanks!

  • @bboys1992
    @bboys1992 11 лет назад

    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

  • @itsSmc128
    @itsSmc128 9 лет назад +1

    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!

  • @nellvincervantes6233
    @nellvincervantes6233 3 года назад +4

    So how do you find x = g(u,v) and y = h(u,v) if they are not given? 🤔

  • @desarrollojava
    @desarrollojava 7 лет назад +7

    Excelent explanation! Thank you very much.
    Perhaps a silly question: Where did you get x=2u and y=4x+2u ?

    • @azzouguenachour909
      @azzouguenachour909 5 лет назад +5

      I asked The Same Question ?

    • @halimayusufahmad9355
      @halimayusufahmad9355 Год назад

      That’s what I’m about to say. That point should be made as clear as the video. Because that’s the key

  • @gautalawrencebusa7474
    @gautalawrencebusa7474 6 лет назад +4

    Definately I`m going to get this question correct on my calculus exam tomorrow. THANK YOU SIR

  • @Channel_Math_and_Physics
    @Channel_Math_and_Physics 2 года назад +5

    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

  • @jayjaypepers
    @jayjaypepers 10 лет назад

    Thank you. This was short and simple and explains the theory through the example. Very much appreciated.

    • @Mathispower4u
      @Mathispower4u  10 лет назад

      Thank you for the comment. I'm glad I could help.

  • @hanto2982
    @hanto2982 Год назад +1

    this was a life saver. thank you for the useful content.

  • @fernandocunhapeixoto2262
    @fernandocunhapeixoto2262 4 года назад

    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?

  • @davidladu7159
    @davidladu7159 9 лет назад +1

    I have a better feel for this now. Thank you very much :D

  • @DetectiveMcGarnacle
    @DetectiveMcGarnacle 11 лет назад

    Best explanation available

  • @WizardToby
    @WizardToby 5 лет назад

    My professor explained this in a long and confusing way so this made it much more simple. :)

  • @kevinding8184
    @kevinding8184 5 лет назад +1

    how to find u&v if it is not given

  • @MrJoeCoolBoy
    @MrJoeCoolBoy 9 лет назад +13

    how did you find the equations for u and v

  • @angeluomo
    @angeluomo 10 лет назад +8

    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.

  • @sarthakvaish2520
    @sarthakvaish2520 3 года назад +1

    Still effective after 10 years

  • @frankcarey250
    @frankcarey250 6 лет назад

    Simply awesome! Great video. Thank you so much.

  • @samsmith3961
    @samsmith3961 2 года назад

    this is a good vidoeo , helped me understand this concept

  • @sarthakthakur4131
    @sarthakthakur4131 7 лет назад +1

    Thank you sir... You cleared my doubts..

  • @juliocerono_stone5365
    @juliocerono_stone5365 Год назад

    Superbbly explained

  • @Mathispower4u
    @Mathispower4u  11 лет назад

    Thank you

  • @karlafloreslopez2898
    @karlafloreslopez2898 4 года назад

    Hi! I love your video its so clear end I understood perfectly.

    • @beoptimistic5853
      @beoptimistic5853 3 года назад

      ruclips.net/video/vFDMaHQ4kW8/видео.html .💐.

  • @elijahantony4300
    @elijahantony4300 8 лет назад

    Can you explain how x

    • @elijahantony4300
      @elijahantony4300 8 лет назад

      +Elijah Paul Nevermind....got it...y=x has a slope 1 which is the minimum value y can take

  • @巫金發
    @巫金發 5 месяцев назад

    this is really useful thankss

  • @solomanjain915
    @solomanjain915 12 лет назад

    Thank you so much for explaining so calmly... i Appreciate you effort.. :)

  • @ebrimajallow33
    @ebrimajallow33 7 лет назад

    Superb tutorial. Tanks.

  • @kevinpatrick8655
    @kevinpatrick8655 2 года назад

    Thank you so much, I don't understand a thing from my prof,

  • @TheMaximedu17
    @TheMaximedu17 4 года назад

    if we have x=U²-V² and y=2UV ? i can't find the new region... can some one help me?

    • @TheMaximedu17
      @TheMaximedu17 4 года назад

      everytime, it will be in function of another V or U...

  • @abhishekmishra3939
    @abhishekmishra3939 7 лет назад

    Thanx for such nice explanation

  • @SurinderKumar-os5il
    @SurinderKumar-os5il 2 года назад

    Thanks
    Excellent

  • @lesprit1
    @lesprit1 13 лет назад +1

    simple and helpful

  • @keatonmcsweeney7772
    @keatonmcsweeney7772 8 лет назад

    thankyou! this is so clear!

  • @poppyblop484
    @poppyblop484 7 лет назад

    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

    • @nesswong3454
      @nesswong3454 7 лет назад +1

      the 8 is the area(unit^2), 80/3 is the volume(unit^3).

    • @dirklerxstpratt2112
      @dirklerxstpratt2112 7 лет назад

      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.

  • @austind6694
    @austind6694 8 лет назад +1

    can anybody tell me how he determined x=2u and y=4v+2u?please

    • @andrewriederer670
      @andrewriederer670 8 лет назад

      Austin D it was a given

    • @sarthakthakur4131
      @sarthakthakur4131 7 лет назад +2

      Andrew Riederer No bro its not given

    • @dirklerxstpratt2112
      @dirklerxstpratt2112 7 лет назад +2

      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.

    • @rainingjokerRevived
      @rainingjokerRevived 5 лет назад

      @@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

    • @samsmith3961
      @samsmith3961 2 года назад

      ​@@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)!!!!

  • @JM995able
    @JM995able 10 лет назад

    how to u choose x and y values?

    • @hassanhashemi6478
      @hassanhashemi6478 9 лет назад

      JustBe Brave yes, thats a good question :D
      any one here knows?

  • @anujbhakat852
    @anujbhakat852 4 года назад

    THANX A LOT

  • @embzr
    @embzr 10 лет назад

    awesome!!

  • @hhusername
    @hhusername 10 лет назад

    thank u so much

    • @Mathispower4u
      @Mathispower4u  10 лет назад

      I'm glad you found the video helpful.

  • @azzouguenachour909
    @azzouguenachour909 5 лет назад

    Thank You so Much I Understand It supers Welll !!!

    • @Mathispower4u
      @Mathispower4u  5 лет назад

      You are very welcome.

    • @azzouguenachour909
      @azzouguenachour909 5 лет назад

      @@Mathispower4u please, I just Have A Simple question Where did you get The x= 2u and Y=4v+2u ?

  • @keensaj
    @keensaj 9 лет назад

    thank you :)

  • @bognessy
    @bognessy 10 лет назад

    thanks

  • @montasirtahir4949
    @montasirtahir4949 11 лет назад

    thank you so much ^_*

  • @revanthvarma2000
    @revanthvarma2000 6 лет назад

    Rip for dislikers

  • @jacksummer4041
    @jacksummer4041 3 года назад +1

    Any kscjian 😂?

  • @shravannani4704
    @shravannani4704 9 лет назад

    brushed fdjd

  • @mahakjauhri6759
    @mahakjauhri6759 4 года назад

    Thank you

  • @FromNoob2Pro
    @FromNoob2Pro 9 лет назад

    thank you