Propagation of a Pulse in An Inhomogenous Medium
Propagation of a Pulse in An Inhomogenous Medium
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1) will not be a solution of the Laplace- transformed problem unless it converges. It can be shown to be convergent (except when x = x ) for real positive s. If it also converges on some line parallel to the imaginary axis in the region Re(s) > 0, and is dominated by a function which has an inverse Laplace transform defined by the usual com- plex inversion formula, then term-by-term inversion is legitimate. Now the example f»0, g=l+y which is discussed in Appendix II shows that the series may n...ot converge for Re(s) > in the whole xy-plane. But this example also suggests that term-by-term evaluation may be permissible in a physically important region, which may be called the 'deep shadow 1 ; this region in- cludes a part of the boundary y = which lies in the shadow. (The exact definition of the shadow will be given in the next section. ) We now proceed on the assumption that terra-by-term inversion is permissible. In order to use (8. 6) to derive an approximation for and then one for 0, we must consider to what extent the asymptotic behavior of can be inferred from that of the .
What to read after Propagation of a Pulse in An Inhomogenous Medium?
You can find similar books in the "Read Also" column, or choose other free books by F G Friedlander to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
1) will not be a solution of the Laplace- transformed problem unless it converges. It can be shown to be convergent (except when x = x ) for real positive s. If it also converges on some line parallel to the imaginary axis in the region Re(s) > 0, and is dominated by a function which has an inverse Laplace transform defined by the usual com- plex inversion formula, then term-by-term inversion is legitimate. Now the example f»0, g=l+y which is discussed in Appendix II shows that the series may n...ot converge for Re(s) > in the whole xy-plane. But this example also suggests that term-by-term evaluation may be permissible in a physically important region, which may be called the 'deep shadow 1 ; this region in- cludes a part of the boundary y = which lies in the shadow. (The exact definition of the shadow will be given in the next section. ) We now proceed on the assumption that terra-by-term inversion is permissible. In order to use (8. 6) to derive an approximation for and then one for 0, we must consider to what extent the asymptotic behavior of can be inferred from that of the .
What to read after Propagation of a Pulse in An Inhomogenous Medium?
You can find similar books in the "Read Also" column, or choose other free books by F G Friedlander to read onlineMoreLess
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