The Princeton Colloquium Lectures On Mathematics Delivered September 15 to 17
The Princeton Colloquium Lectures On Mathematics Delivered September 15 to 17
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In our eReader you can find the full English version of the book. Read The Princeton Colloquium Lectures On Mathematics Delivered September 15 to 17 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 The Princeton Colloquium Lectures On Mathematics Delivered September 15 to 17
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Hence the sequence P n (x) converges uniformly to a continuous function y(x] on the interval The equations Pn(x) = 77 + f Pn'Wdx = 77 + f {/(*, P n ) + Pn }dx J( J t hold for every n, and the sequences {f(x, P n ) } and { p n } approach uniformly the limits f(x, y(x}) and zero, respectively. Hence y(x) = 77 + J /(a:, from which it follows by differentiation that y(x) is a solution of the differential equation.
It is easy to show by means of the convergence inequality that there is only one cont...inuous solution y = y(x) of the dif- ferential equation (1) in the region R and passing through (, 77). For suppose there were another, Y(x), distinct from y(x) at a value x' > . There would then be a value 1
What to read after The Princeton Colloquium Lectures On Mathematics Delivered September 15 to 17?
You can find similar books in the "Read Also" column, or choose other free books by American Mathematical Society to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Hence the sequence P n (x) converges uniformly to a continuous function y(x] on the interval The equations Pn(x) = 77 + f Pn'Wdx = 77 + f {/(*, P n ) + Pn }dx J( J t hold for every n, and the sequences {f(x, P n ) } and { p n } approach uniformly the limits f(x, y(x}) and zero, respectively. Hence y(x) = 77 + J /(a:, from which it follows by differentiation that y(x) is a solution of the differential equation.
It is easy to show by means of the convergence inequality that there is only one cont...inuous solution y = y(x) of the dif- ferential equation (1) in the region R and passing through (, 77). For suppose there were another, Y(x), distinct from y(x) at a value x' > . There would then be a value 1
What to read after The Princeton Colloquium Lectures On Mathematics Delivered September 15 to 17?
You can find similar books in the "Read Also" column, or choose other free books by American Mathematical Society to read onlineMoreLess
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