A Treatise on the Calculus of Finite Differences |
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Page 11
... determined by expressing both mem- bers of the equation in ascending powers of x , equating coeffi- cients and ... determining a , b , c , ... h , we have $ ( x ) = $ ( 0 ) + A $ ( 0 ) x + Δ Φ ( 0 ) Δ Φ ( 0 ) 20 ( 2 ) + 2013 ) + & c ...
... determined by expressing both mem- bers of the equation in ascending powers of x , equating coeffi- cients and ... determining a , b , c , ... h , we have $ ( x ) = $ ( 0 ) + A $ ( 0 ) x + Δ Φ ( 0 ) Δ Φ ( 0 ) 20 ( 2 ) + 2013 ) + & c ...
Page 22
... determined in various ways , the simplest in principle being perhaps to de- velope the right - hand member of ( 13 ) by the polynomial theorem , and then seek the aggregate coefficients of the suc- cessive powers of t . But the ...
... determined in various ways , the simplest in principle being perhaps to de- velope the right - hand member of ( 13 ) by the polynomial theorem , and then seek the aggregate coefficients of the suc- cessive powers of t . But the ...
Page 28
... determine a law , the problem of interpolation is an indeterminate one . To find an analytical expression of a function from a limited number of its numerical values corresponding to given values of its independent variable x is , in ...
... determine a law , the problem of interpolation is an indeterminate one . To find an analytical expression of a function from a limited number of its numerical values corresponding to given values of its independent variable x is , in ...
Page 29
... determine A , B ... E . To avoid the solving of these equations other but equivalent modes of procedure are employed , all such being in effect reducible to the two following , viz . either to an application of that property of the ...
... determine A , B ... E . To avoid the solving of these equations other but equivalent modes of procedure are employed , all such being in effect reducible to the two following , viz . either to an application of that property of the ...
Page 33
... determine an approximate general expression for uz • We shall assume this expression rational and integral , Art . 1 ... determine . We might therefore assume u = A + Bx + Cx2 ... + Ex " -1 ( 8 ) , and determine A , B , C by the linear ...
... determine an approximate general expression for uz • We shall assume this expression rational and integral , Art . 1 ... determine . We might therefore assume u = A + Bx + Cx2 ... + Ex " -1 ( 8 ) , and determine A , B , C by the linear ...
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Common terms and phrases
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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