A Treatise on Infinitesimal Calculus ... |
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Page 30
... equal ; then the 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 ...
... equal ; then the 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 ...
Page 31
... equal factors ; so that f ( x ) = ( x − α1 ) TM p ( x ) . By the Theorem in Vol . I , Art . 74 , Equation ( 84 ) ... equal to the numerator of the original fraction , divided by its denominator short of the set of equal factors ...
... equal factors ; so that f ( x ) = ( x − α1 ) TM p ( x ) . By the Theorem in Vol . I , Art . 74 , Equation ( 84 ) ... equal to the numerator of the original fraction , divided by its denominator short of the set of equal factors ...
Page 32
... equal factors , the series of partial fractions corresponding to them must be deter- mined in a manner precisely analogous to that applied above . The method also is applicable to sets of equal factors involv- ing impossible roots , in ...
... equal factors , the series of partial fractions corresponding to them must be deter- mined in a manner precisely analogous to that applied above . The method also is applicable to sets of equal factors involv- ing impossible roots , in ...
Page 88
... equal to n . If mn , the integral becomes , 0 ( 8 ) S ( cos mx ) 2 dx = + sin 2 mx 4m π 0 = ( 9 ) Similarly S Ex . 13 . 00 П 2 sin ma sin nx dx = O , if m is not equal to n ; ( 10 ) π = if m = n . 2 ' [ " e2x " dx = [ −e ̄'x " + nfe ...
... equal to n . If mn , the integral becomes , 0 ( 8 ) S ( cos mx ) 2 dx = + sin 2 mx 4m π 0 = ( 9 ) Similarly S Ex . 13 . 00 П 2 sin ma sin nx dx = O , if m is not equal to n ; ( 10 ) π = if m = n . 2 ' [ " e2x " dx = [ −e ̄'x " + nfe ...
Page 96
... equal distances from έ on either side of it , that is , if r ′ ( § — x ) = F ′ ( + x ) ; then the series , the sums of which are * } denoted by fr F ′ ( x ) dæ and [ ** r ′ ( x ) da , will consist of terms which are , term by term , equal ...
... equal distances from έ on either side of it , that is , if r ′ ( § — x ) = F ′ ( + x ) ; then the series , the sums of which are * } denoted by fr F ′ ( x ) dæ and [ ** r ′ ( x ) da , will consist of terms which are , term by term , equal ...
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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