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Taylor expansion

  1. Apr 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi

    Say I want to Taylor-expand
    [tex]
    f(\omega + m\sin(\Omega t))
    [/tex]
    where ω and Ω are frequencies, m is some constant and t denotes time. Then I would get
    [tex]
    f(\omega + m\sin(\Omega t)) = f(\omega) + (m\sin(\Omega t)\frac{dI}{d\omega} + \ldots
    [/tex]
    Is it necessary to make any assumptions on the sizes of m and Ω in order to make the above expansion?

    Best,
    Niles.
     
  2. jcsd
  3. Apr 5, 2012 #2

    Dick

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    If you are Taylor expanding in the quantity you are adding to ω and I means f(ω) that's fine. If you are going to truncate the expansion there and wondering if it's a accurate expansion that's going to depend on the size of the quantity you are adding to ω and the behaviour of f''(ω). You'll want to look at Taylor series remainder terms if you are concerned about how good it is.
     
  4. Apr 6, 2012 #3
    Thanks!

    Best,
    Niles.
     
  5. Apr 15, 2012 #4
  6. Apr 15, 2012 #5

    Dick

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    Sure it is. It's 'around' ω. I say the expansion is 'in' msin(Ωt) because that's the thing that appears in all the powers. Just terminology.
     
  7. Apr 15, 2012 #6
    Ah, I see. Thanks for clarifying.

    Best,
    Niles.
     
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