A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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Side 4
... observed that each sum of differences may either be formed from the preceding sum by successive subtractions in accordance with the definition of the symbol A , or calcu- lated from the general expressions for Au , Au , & c . by assign ...
... observed that each sum of differences may either be formed from the preceding sum by successive subtractions in accordance with the definition of the symbol A , or calcu- lated from the general expressions for Au , Au , & c . by assign ...
Side 28
... observed indicates what kind of assumption is best . If for instance these values are of a periodical character , circular functions ought to be employed . But where no such indications exist it is customary to assume for the general ...
... observed indicates what kind of assumption is best . If for instance these values are of a periodical character , circular functions ought to be employed . But where no such indications exist it is customary to assume for the general ...
Side 30
... observed that the second member is really a rational and integral function of x of the degree n 1 , while the coefficients are made determinate by the data . - In applying this theorem the value of x may be con- ceived to express the ...
... observed that the second member is really a rational and integral function of x of the degree n 1 , while the coefficients are made determinate by the data . - In applying this theorem the value of x may be con- ceived to express the ...
Side 35
... observation , u , u , ... u , the observed values , x the time for which the value is required , and u that value . Then the value of u , is given by ( 10 ) , and the differential coefficients can thence be deduced in the usual way ...
... observation , u , u , ... u , the observed values , x the time for which the value is required , and u that value . Then the value of u , is given by ( 10 ) , and the differential coefficients can thence be deduced in the usual way ...
Side 36
... observed magnitude by ua , uv , ... un , and u , we must by the solution of the same equation ( 10 ) determine x ... observations of a quantity near its time of maxi- mum or minimum being taken , to find its time of maximum or minimum ...
... observed magnitude by ua , uv , ... un , and u , we must by the solution of the same equation ( 10 ) determine x ... observations of a quantity near its time of maxi- mum or minimum being taken , to find its time of maximum or minimum ...
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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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