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Finding Minimum Value with Mathematica

  1. Feb 4, 2012 #1
    ∂ω2 = (1-cos2(Δt)e-2γ(t))/(nTtsin2(Δt)e-2γ(t))

    n,T are assumed as constants. How can I use Mathematica to find the values of Δ and t that will give the minimum values for ∂ω2 ?
  2. jcsd
  3. Feb 5, 2012 #2
    If I use Expand on your function I get

    1/(n T t)((E^(2 gamma[t]) Csc[delta t]^2 - Cot[delta t]^2)

    Without knowing the signs of n and T we can't know the sign of the result and can't know minimum.

    Both Csc^2 and Cot^2 go to infinity at multiples of Pi. Depending on what your gamma function is, either the term with Csc or Cot will win the race to infinity and I believe you can determine the minimum by inspection.
  4. Feb 5, 2012 #3
    What do you mean with sign of n and T ?
  5. Feb 5, 2012 #4
    If n*T is negative the whole function will be flipped upside down, what was a minimum would be a maximum, etc.
  6. Feb 6, 2012 #5
    n and T are integers and always positive.
  7. Feb 6, 2012 #6
    Then I believe, if you can verify the result from Expand, that n and T can be ignored and you focus on

    E^(2 gamma[t]) Csc[delta t]^2 - Cot[delta t]^2

    If E^(2 gamma[t]) can be < 1 when delta t=Pi then the minimum appears to be -Infinity.
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