A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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Side 16
... respect to any constant coefficients in the terms of the subject to which it is applied . Thus a being constant , Δακ = ακα + 1 = aua - = αΔω ....... ...... ( 4 ) . And from this law in combination with the preceding one , we have , a ...
... respect to any constant coefficients in the terms of the subject to which it is applied . Thus a being constant , Δακ = ακα + 1 = aua - = αΔω ....... ...... ( 4 ) . And from this law in combination with the preceding one , we have , a ...
Side 36
... respect to x , we find x = ( b2 — c2 ) u1 + ( c2 — a2 ) u , + ( a2 — b2 ) u . - a - - 2 { ( b − c ) u 。 + ( c − a ) u 。 + ( a − b ) u } α ( 13 ) . This formula enables us to approximate to the meridian altitude of the sun or of a ...
... respect to x , we find x = ( b2 — c2 ) u1 + ( c2 — a2 ) u , + ( a2 — b2 ) u . - a - - 2 { ( b − c ) u 。 + ( c − a ) u 。 + ( a − b ) u } α ( 13 ) . This formula enables us to approximate to the meridian altitude of the sun or of a ...
Side 55
... respect the operation A is unlike that of differentiation , which involves essentially a procedure to the limit , and in the limit new forms arise . Ex . Required Σ 1 cos ax . cos a ( x + 1 ) * The integral must be trigonometrical , and ...
... respect the operation A is unlike that of differentiation , which involves essentially a procedure to the limit , and in the limit new forms arise . Ex . Required Σ 1 cos ax . cos a ( x + 1 ) * The integral must be trigonometrical , and ...
Side 56
... is n . Accordingly , E , denoting integration with respect to n , we have x2 + x4 + 1 ... + x " = Σ1x + 1 = xx = 2n + 1 + C. To determine C we observe that when na the series x - 1 56 [ CH . IV . FINITE INTEGRATION .
... is n . Accordingly , E , denoting integration with respect to n , we have x2 + x4 + 1 ... + x " = Σ1x + 1 = xx = 2n + 1 + C. To determine C we observe that when na the series x - 1 56 [ CH . IV . FINITE INTEGRATION .
Side 65
... respects its terms and as respects the sum of its terms . 2. Two cases present themselves . 1st . That in which the terms of a series are all of the same or are ultimately all of the same sign . 2ndly . That in which they are , or ulti ...
... respects its terms and as respects the sum of its terms . 2. Two cases present themselves . 1st . That in which the terms of a series are all of the same or are ultimately all of the same sign . 2ndly . That in which they are , or ulti ...
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2ndly A³u algebraic applying arbitrary constant ascending powers assume ax+b B₁ C₁ C₂ Calculus of Finite Cambridge Chap CHARLES KINGSLEY cloth CO.'S PUBLICATIONS complete primitive condition Crown 8vo curve deduce denoted determine develope Differential Calculus differential coefficients differential equation English Notes equation of differences Examples expression Fcap Finite Differences functional equation GEORGE BOOLE given equation Hence independent variable indirect integral limit linear equation M.A. Second Edition MACMILLAN & CO.'S method mixed differences operation ordinates particular value periodical function rational and integral reduced represented result roots second member Sermons shew singular solution substituting successive values supposed symbol theorem tion TODHUNTER Treatise Trinity College u₁ u₂ unity University of Cambridge Ux,y Ux+1 Ux+2 v₂ Vx+1 whence Их
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