On Systems of Linear Ordinary Differential Equations
On Systems of Linear Ordinary Differential Equations
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In our eReader you can find the full English version of the book. Read On Systems of Linear Ordinary Differential Equations Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book On Systems of Linear Ordinary Differential Equations
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N-k -13- The scattering matrix S is defined "by 33) 1 ' ' FroBi the last two equations we obtain 3^^) S(^, z^; n-k provided that 35) -^-^Vk. N-k^^ • The scattering matrix S given "by eq, . (3I+) yields the amplitudes of the scattered waves at ^ emd z in terms of the amplitudes of the incident waves at the same points, when the phases of the wpves at f and z are referred to z-^ and Zq respectively. Its definition is independent of the presence or ahsence of turning points. In most cases of inter...est S approaches a limit as ^ end z approach plus and minus infinity respectively, and this limit is v/hat is usually called the scattering matrix. It depends only upon the reference points z, and -llt- VI, Asymptotic Expansion of the Solution .
If the matrix A(z) depends upon a parameter k in an appropriate way, then the Bolution of equations (l) posseBses an asymptotic expansion in reciprocal powers of k in regions where the latent roots of A are distinct. This result was o'btained by Birklioff [s J for an nth order equation and has since heen ex- tended to nth order systems.
What to read after On Systems of Linear Ordinary Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by Herbert Bishop Keller to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
N-k -13- The scattering matrix S is defined "by 33) 1 ' ' FroBi the last two equations we obtain 3^^) S(^, z^; n-k provided that 35) -^-^Vk. N-k^^ • The scattering matrix S given "by eq, . (3I+) yields the amplitudes of the scattered waves at ^ emd z in terms of the amplitudes of the incident waves at the same points, when the phases of the wpves at f and z are referred to z-^ and Zq respectively. Its definition is independent of the presence or ahsence of turning points. In most cases of inter...est S approaches a limit as ^ end z approach plus and minus infinity respectively, and this limit is v/hat is usually called the scattering matrix. It depends only upon the reference points z, and -llt- VI, Asymptotic Expansion of the Solution .
If the matrix A(z) depends upon a parameter k in an appropriate way, then the Bolution of equations (l) posseBses an asymptotic expansion in reciprocal powers of k in regions where the latent roots of A are distinct. This result was o'btained by Birklioff [s J for an nth order equation and has since heen ex- tended to nth order systems.
What to read after On Systems of Linear Ordinary Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by Herbert Bishop Keller to read onlineMoreLess
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