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I don't understand a step in my notes, about Taylor expansion

  1. Oct 12, 2012 #1

    fluidistic

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    1. The problem statement, all variables and given/known data
    [itex]P_0 (t+dt)=P_0(t)(1-\gamma dt )[/itex] (1)
    Therefore [itex]P_0 (t)+\frac{dP_0 (t)}{dt} \approx P_0 (t)-\gamma P_0(t)dt[/itex]. (2)
    Where the approximation is due to a Taylor expansion apparently.

    2. Relevant equations
    Taylor expansion of f around [itex]x_0[/itex] : [itex]f(x)\approx f(x_0)+\frac{df(x_0)}{dx}(x-x_0)[/itex].


    3. The attempt at a solution
    Considering that (1) holds true, I do not understand the implication. In other words I don't understand why (2) is true.
    I also do not understand the Taylor expansion used in equation (2). What is the point being expanded around?
    Thanks for any help!
     
  2. jcsd
  3. Oct 12, 2012 #2
    From (1), they obtain an expression for the first derivative, using the definition of first derivative from the Taylor expanson. They then plug that in on the left hand side of (2) to obtain the right hand side.

    Also, the function is expanded around the point [itex]t[/itex].
     
  4. Oct 12, 2012 #3

    fluidistic

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    Gold Member

    Hi Sourab, thanks for helping me.
    Edit: I got it! thanks a lot!
     
    Last edited: Oct 12, 2012
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