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Method of stationary phase

  1. Oct 24, 2011 #1
    1. The problem statement, all variables and given/known data

    Find asymptotic expansions for the following integral, as [itex]x \to \infty[/itex], using the method of stationary phase.

    [tex]\int^1_0 e^{ixt^p} dt, p > 1[/tex]

    2. Relevant equations



    3. The attempt at a solution

    1. let the phase be [itex]t^2[/itex]. is this correct?
    2. [itex]\frac{d}{dt} t^2 = 2t = 0[/itex], so phase stationary is [itex]0[/itex].
    3. expand phase about stationary point [itex]t=0[/itex] and i get [itex]0[/itex]. something is wrong, should i be doing this?
     
  2. jcsd
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