Method of Characteristics 3: The general case

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  • เผยแพร่เมื่อ 22 ธ.ค. 2024

ความคิดเห็น • 24

  • @oliveraherne5547
    @oliveraherne5547 5 ปีที่แล้ว +2

    For anyone confused, the last result on the page at 11:11 should read -1/5 outside the brackets rather than 1/5.

  • @daohung1112
    @daohung1112 7 ปีที่แล้ว +8

    explaint more about why you get x(0) =s, and y(0)=0?. thanks

  • @ALternaprof
    @ALternaprof 3 ปีที่แล้ว +1

    At 7:34, I would recommend using the root method and the method of underdetermined coefficients instead. This lets you avoid doing all the annoying integration by parts.

    • @raba2d723
      @raba2d723 3 ปีที่แล้ว +3

      make a video. im sure people appreciate that

    • @ALternaprof
      @ALternaprof 2 ปีที่แล้ว +1

      @@raba2d723 I already did make a couple of videos about this. Here they are... th-cam.com/video/aX8KDpI-q2A/w-d-xo.html, th-cam.com/video/sM6YvEUiTp4/w-d-xo.html

  • @rahulmukherjee37
    @rahulmukherjee37 หลายเดือนก่อน

    Thank you very much, for that excellent step by step explanation

  • @bryano4613
    @bryano4613 7 ปีที่แล้ว +2

    you're a lifesaver man, good vids

  • @sushants12
    @sushants12 7 ปีที่แล้ว

    Thanks a lot for providing simple explanations for these cases.

  • @valeriiaokhmak3329
    @valeriiaokhmak3329 5 หลายเดือนก่อน

    amazing explanation

  •  7 ปีที่แล้ว

    on 8:05 how and where did you get the integration? i got lost help p.z

  • @bonbonpony
    @bonbonpony 4 ปีที่แล้ว

    How about the 2nd-order ones? I know that at least the wave equation can be solved with characteristics.

  • @rythemofgermay5590
    @rythemofgermay5590 10 หลายเดือนก่อน

    find so difficult to understand how you get c(x) and the integration of each colorful terms

  • @tag_of_frank
    @tag_of_frank 7 ปีที่แล้ว +5

    you dont really say how this relates to the others... 1 you paramatize one you just know the slope... shouldn't this be called a different method all together?

    • @thequarrymen58
      @thequarrymen58 ปีที่แล้ว

      It is the method of characteristic curves, but without a theory where these parameterizations come from, this solution cannot be understood much.

  • @vonneumannoperator566
    @vonneumannoperator566 9 ปีที่แล้ว +2

    Brilliant!

  • @daohung1112
    @daohung1112 7 ปีที่แล้ว

    you are good at mathematics. thanks

  • @Lyradopon96
    @Lyradopon96 7 ปีที่แล้ว

    Thx alot my friend. What did you study if im allowed to ask? :=)

  • @NothingYouknow96
    @NothingYouknow96 9 ปีที่แล้ว +1

    thanks, well explained

  • @finnjake6174
    @finnjake6174 8 ปีที่แล้ว

    really happy for this!!

    • @daohung1112
      @daohung1112 7 ปีที่แล้ว

      help me????

    • @daohung1112
      @daohung1112 7 ปีที่แล้ว

      +Hung Dao why he get x(0)=s, y(0)=0?

    • @ryukyu_9278
      @ryukyu_9278 5 ปีที่แล้ว

      @@daohung1112 Did you find out why he got that ? What I don't understand is why it is possible to arbitrarily set t=0 for the initial condition.

  • @busracalsr2687
    @busracalsr2687 4 ปีที่แล้ว

    i cannot solve the question. can u help me please?
    Given the linear equation: Ux-Uy=0 with the initial conditions: x(0,s)=0, y(0,s)=s, u(0,s)=g(s) where g(s) is an arbitrary differentiable function.
    a) Write the Characterist equations: a(x,y,u)Ux+b(x,y,u)Uy=c(x,y,u)
    dx = a(x,y,u) (1) dy = b(x,y,u) (2) du = c(x,y,u) (3)
    dt dt dt
    b) Integrate equations (1-2), use the initial conditions and determine x and y interms of the parameters t and s, then inverting these, write t and s interms of x and y.
    c) Integrate equations (3), use the initial conditions and determine u interms of t and s and then write u interms of x and y:u(x,y)

  • @daohung1112
    @daohung1112 7 ปีที่แล้ว

    help me, help me, help me please!