Theory of Differential Equations volume 4
Theory of Differential Equations volume 4
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In our eReader you can find the full English version of the book. Read Theory of Differential Equations volume 4 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 Theory of Differential Equations volume 4
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Hence the quantities Te", T^, ... , T^e" all remain finite within that range, that is, no one of them can become infinite, for a value of X sufficiently large* to make the quadratic form positive.
Next, suppose that the constants are complex, so that T, T lt ... Can have complex values ; but let t still be real. Then we write * For the tests, see Williamson s Differential Calculus, 3rd ed. , p. 408. In the case of k = 4, the conditions are : \>0, so that it is sufficient to take X greater than ...the greatest positive value which makes the left-hand side in the last inequality vanish.
102. ] THEOREM 321 for all values of r, where (f> r and ^ r are real ; the system of equations takes the form -F- -**~ *&-, _ where > =0, ^r Q = ^, and P s =p s + iq s . We now have 2A; equations; on substituting they give the modified set r - 1 = - (Pi - Hence r=l fc-2 :X 2 I k-l , 2 + ^ r 2 ) + (X - i + ) + bilinear terms.
As before, by choosing a sufficiently large value of X, the right- hand side can be made always positive.
What to read after Theory of Differential Equations volume 4?
You can find similar books in the "Read Also" column, or choose other free books by Forsyth, Andrew Russell, 1858-1942 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Hence the quantities Te", T^, ... , T^e" all remain finite within that range, that is, no one of them can become infinite, for a value of X sufficiently large* to make the quadratic form positive.
Next, suppose that the constants are complex, so that T, T lt ... Can have complex values ; but let t still be real. Then we write * For the tests, see Williamson s Differential Calculus, 3rd ed. , p. 408. In the case of k = 4, the conditions are : \>0, so that it is sufficient to take X greater than ...the greatest positive value which makes the left-hand side in the last inequality vanish.
102. ] THEOREM 321 for all values of r, where (f> r and ^ r are real ; the system of equations takes the form -F- -**~ *&-, _ where > =0, ^r Q = ^, and P s =p s + iq s . We now have 2A; equations; on substituting they give the modified set r - 1 = - (Pi - Hence r=l fc-2 :X 2 I k-l , 2 + ^ r 2 ) + (X - i + ) + bilinear terms.
As before, by choosing a sufficiently large value of X, the right- hand side can be made always positive.
What to read after Theory of Differential Equations volume 4?
You can find similar books in the "Read Also" column, or choose other free books by Forsyth, Andrew Russell, 1858-1942 to read onlineMoreLess
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