A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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Side 3
... assuming thx we have At hAx , whence Ax = 1 . = Thus it suffices to establish the rules of the calculus on the assumption that the finite difference of the independent variable is unity . At the same time it will be noted that this A ...
... assuming thx we have At hAx , whence Ax = 1 . = Thus it suffices to establish the rules of the calculus on the assumption that the finite difference of the independent variable is unity . At the same time it will be noted that this A ...
Side 11
... Assume ... ......... ( 1 ) . ( x ) = a + bx + cx ( 2 ) + dx ( 3 ) + hx ( m ) The legitimacy of this form is evident , for it represents a rational and integral function of x of the nth degree , contain- ing a number of arbitrary ...
... Assume ... ......... ( 1 ) . ( x ) = a + bx + cx ( 2 ) + dx ( 3 ) + hx ( m ) The legitimacy of this form is evident , for it represents a rational and integral function of x of the nth degree , contain- ing a number of arbitrary ...
Side 28
... assumed a priori . It may be that the evident character of succession in the values observed indicates what kind of ... assume for the general expression of the values under consideration a rational and integral function of x , and to ...
... assumed a priori . It may be that the evident character of succession in the values observed indicates what kind of ... assume for the general expression of the values under consideration a rational and integral function of x , and to ...
Side 29
... assumes different forms , according as the values given are equidistant , i . e . corre- spondent to equidifferent ... assuming as the approximate general expression of ux ux = A + Bx + Сx2 ... + Ex2 - 1 ( 1 ) , a form which is rational ...
... assumes different forms , according as the values given are equidistant , i . e . corre- spondent to equidifferent ... assuming as the approximate general expression of ux ux = A + Bx + Сx2 ... + Ex2 - 1 ( 1 ) , a form which is rational ...
Side 33
... assume this expression rational and integral , Art . 1 . Now there being n conditions to be satisfied , viz . that for x = a , x = b ... x = n , it shall assume the respective values ua , u ... un , the expression must contain n ...
... assume this expression rational and integral , Art . 1 . Now there being n conditions to be satisfied , viz . that for x = a , x = b ... x = n , it shall assume the respective values ua , u ... un , the expression must contain n ...
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A₁ A³u algebraic applying arbitrary constant ascending powers assume ax+b B₁ c₂ Calculus of Finite Cambridge CHARLES KINGSLEY cloth CO.'S PUBLICATIONS complete primitive CONIC SECTIONS convergent Crown 8vo curve deduce denoted determine Differential Calculus differential equation divergent English Notes equation of differences expression Fcap Fellow of St Finite Differences functional equation GEORGE BOOLE given equation Hence independent variable indirect integral John's College limit linear equation M.A. Second Edition MACMILLAN & CO.'S method mixed differences operation ordinates P. G. TAIT particular value periodical function rational and integral reduced result Schools second member Sermons shew singular solution substituting successive values supposed symbol theorem tion TODHUNTER Treatise Trinity College u₁ u₂ unity University of Cambridge Ux+1 Ux+2 v₂ Vx+1 Vx+2 whence Их
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