A Treatise on Infinitesimal Calculus ... |
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Page xxii
... preceding article 243 184. On comparable and incomparable series 185-188 . Tests of convergence and divergence of series derived from the comparison of series with known series 245 189. Directions as to the application of the preceding ...
... preceding article 243 184. On comparable and incomparable series 185-188 . Tests of convergence and divergence of series derived from the comparison of series with known series 245 189. Directions as to the application of the preceding ...
Page xxvii
Bartholomew Price. 287. An extension of the theorem of the preceding article 288. A further extension to the case wherein the limits are given by a more general inequality .. .. 289. Another form of definite integral determined by means ...
Bartholomew Price. 287. An extension of the theorem of the preceding article 288. A further extension to the case wherein the limits are given by a more general inequality .. .. 289. Another form of definite integral determined by means ...
Page 11
... those of the pre- ceding term , and the preceding term is [ ** vdu ; therefore udv = u „ vn — U。。 ́ ΤΟ = [ uo ] * - √ * v uv xo xo v du v du . C 2 ( 21 ) ( 22 ) And therefore resubstituting [ " f ( x ) × 8. ] 11 INTEGRATION BY PARTS .
... those of the pre- ceding term , and the preceding term is [ ** vdu ; therefore udv = u „ vn — U。。 ́ ΤΟ = [ uo ] * - √ * v uv xo xo v du v du . C 2 ( 21 ) ( 22 ) And therefore resubstituting [ " f ( x ) × 8. ] 11 INTEGRATION BY PARTS .
Page 25
... preceding section ; and the fractional part by the method which we now proceed to explain . The most general form therefore of such a fraction is 1 - n - 1 x " — P1x " −1 + PqX1 n - 2 + An_x An Pn - 1x + Pn ; ...... which , for ...
... preceding section ; and the fractional part by the method which we now proceed to explain . The most general form therefore of such a fraction is 1 - n - 1 x " — P1x " −1 + PqX1 n - 2 + An_x An Pn - 1x + Pn ; ...... which , for ...
Page 30
... preceding process of resolution does not admit of being applied directly , because in the right - hand member of ( 23 ) there will not be n undetermined constants ; and consequently the number of unknown constants is not sufficient to ...
... preceding process of resolution does not admit of being applied directly , because in the right - hand member of ( 23 ) there will not be n undetermined constants ; and consequently the number of unknown constants is not sufficient to ...
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A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No preview available - 2015 |
Common terms and phrases
a₁ a₂ angle application axis Beta-function bx dx consequently convergent series coordinates cosec cx² cycloid definite integral denoted determined differential double integral dx a² dx dx dx dy dx Ex dx² dy dx dy² e-ax element-function ellipse equal evaluation expressed find the area finite and continuous fraction function Gamma-function geometrical given Hence infinite infinitesimal infinitesimal element Integral Calculus intrinsic equation involute left-hand member length let us suppose limits of integration multiple integrals plane curve polar coordinates preceding proper fraction radius range of integration replaced result right-hand member subject-variable substituting surface symbols theorem tion values variable x-integration x₁ x²)¹ x²)³ αξ πα