A Course in Mathematical Analysis volume 1
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In our eReader you can find the full English version of the book. Read A Course in Mathematical Analysis volume 1 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 A Course in Mathematical Analysis volume 1
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The iden tity assumed may therefore be written in the form r. R + D or, simplifying the left-hand side, -1 _ Cx + D 2(1 + x 3 ) ~ 1 + x 2 It follows that C = and 7) = 1/2, and we have, finally, 1 1 1 1 T" A / ~t "I \ . ^ / V 1-. - 11 */ ( nr* \ 1 ^ *^ -L V t !/ -Ly Trl*^ ^^ / \ 1^ / which gives rfa; 1, (x - 1\ 1 V, 104] RATIONAL FUNCTIONS 211 Note. The preceding method, though absolutely general, is not always the simplest. The work may often be shortened by using a suitable device. Let us cons...ider, for example, the integral dx 2 - 1)" If n > 1, we may either break up the integrand into partial frac tions byliieans of the roots + 1 and 1, or we may use a reduction formula similar to that for /. But the most elegant method is to make the substitution x = (1 -f )/(! 2), which gives 4* 2dz dx = (!-*) (I-*) /7 O /"* /1 ~\2 2 (* - 1)- = 4"- J " * rf * Developing (1 z) 2n ~ 2 by the binomial theorem, it only remains to integrate terms of the form Az* t where \L may be positive or negative. 104.
What to read after A Course in Mathematical Analysis volume 1?
You can find similar books in the "Read Also" column, or choose other free books by Edouard Goursat to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The iden tity assumed may therefore be written in the form r. R + D or, simplifying the left-hand side, -1 _ Cx + D 2(1 + x 3 ) ~ 1 + x 2 It follows that C = and 7) = 1/2, and we have, finally, 1 1 1 1 T" A / ~t "I \ . ^ / V 1-. - 11 */ ( nr* \ 1 ^ *^ -L V t !/ -Ly Trl*^ ^^ / \ 1^ / which gives rfa; 1, (x - 1\ 1 V, 104] RATIONAL FUNCTIONS 211 Note. The preceding method, though absolutely general, is not always the simplest. The work may often be shortened by using a suitable device. Let us cons...ider, for example, the integral dx 2 - 1)" If n > 1, we may either break up the integrand into partial frac tions byliieans of the roots + 1 and 1, or we may use a reduction formula similar to that for /. But the most elegant method is to make the substitution x = (1 -f )/(! 2), which gives 4* 2dz dx = (!-*) (I-*) /7 O /"* /1 ~\2 2 (* - 1)- = 4"- J " * rf * Developing (1 z) 2n ~ 2 by the binomial theorem, it only remains to integrate terms of the form Az* t where \L may be positive or negative. 104.
What to read after A Course in Mathematical Analysis volume 1?
You can find similar books in the "Read Also" column, or choose other free books by Edouard Goursat to read onlineMoreLess
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