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Mathematical Wave please help

  1. Mar 20, 2007 #1
    Hi all.
    I am learning some mathematics about wave.
    This thread is rather long becaue I find it really difficult for me to comprehend the stuff completely. I have scanned 3 pages of the book I am reading. I REALLY hope you guys won't mind reading my long thread and the 3 pages and lend me your HELPING HAND. I am really frustrted now....

    The example is illustrating the ues of asymptotic expansion to solve the wave propagation equtaion (1.94).

    First of all, in page 39, under euqation (1.95), it states that we are seeking a solution for x=O(1) and t=O(1). How should I interpret this? Apparetly, it means x is bounded by some constant, right? But why it says later that we would solve the equation in the domain -infinity < x < +infinity?
    Does x=O(1) only means x is bounded by some constant as epsilon approaches o, but it doesn't follow that x is bounded itself?

    Secondly, in page 40 bottom, it says "For f(x) on compact support....Further, for our stated condition on f(x), we need consider only zeta = O(1)..."
    What kind of "stated condition" is it referring to? And why we need to consider only zeta = O(1)?

    Even I accept that we only need to consider zeta = O(1), on page 41, second paragraph, why for zeta = x-t = O(1), then t = O(epsilon ^-1) implies that x = O(epsilon ^-1)? I am further confused by Figure 1.7....
    I don't understand why the subtraction of t from x, both of O(epsilon^-1), will result in a zerta of O(1).....

    For those who understand these, please kindly explain them to me....
     

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    Last edited: Mar 20, 2007
  2. jcsd
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