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Partial differential = the change?

  1. Nov 21, 2012 #1
    partial differential = the change??

    1. The problem statement, all variables and given/known data

    How is
    Δy/Δx = [itex]\partial y[/itex] / [itex]\partial x[/itex] ?

    I just don't know the logic behind this.
     
  2. jcsd
  3. Nov 22, 2012 #2

    lurflurf

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    Re: partial differential = the change??

    That is only approximately or asymptotically true. If Δy and Δx are small Δy/Δx will be near ∂y / ∂x.
     
  4. Nov 22, 2012 #3

    SammyS

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    Re: partial differential = the change??

    Do you understand how [itex]\Delta y/\Delta yx\approx dy/dx\ ?[/itex]

    Usually, x & y are independent variables -- and often there are additional independent variables.

    If f is a function of independent variables, x and y, then we write f(x,y).

    [itex]\partial f/\partial x\ \ [/itex] is essentially [itex]\ \ df/dx\ \ [/itex] if we treat y as being held at some fixed value.

    Then [itex]\ \ \Delta f/\Delta x \approx \partial f/\partial x\ \ [/itex] keeping y fixed at some value.



    By the Way: If x & y are independent variables, then [itex]\ \ \partial y/\partial x=0 \ .[/itex]
     
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