A Treatise on the Calculus of Finite Differences |
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Page vi
... course of Mathematical Study at the University of Cambridge , there is considerable difficulty in deciding the question how far they should aim at being exhaustive . I have held it best not to insert investigations that involve ...
... course of Mathematical Study at the University of Cambridge , there is considerable difficulty in deciding the question how far they should aim at being exhaustive . I have held it best not to insert investigations that involve ...
Page 24
... ' = ¢ ( 0 ) C = 4 ( A ) C , and 4 ( E ) C = p ( 1 ) C. It is of course assumed throughout that the coefficients in & are constants . very important case in which n = -1 will be 24 DIRECT THEOREMS OF FINITE DIFFERENCES . [ CH . II .
... ' = ¢ ( 0 ) C = 4 ( A ) C , and 4 ( E ) C = p ( 1 ) C. It is of course assumed throughout that the coefficients in & are constants . very important case in which n = -1 will be 24 DIRECT THEOREMS OF FINITE DIFFERENCES . [ CH . II .
Page 28
... course indifferent which form is used , but where , as in the case before us , two or more would give infinity as result the second form cannot be used . 13. Ex . 8. To shew that $ ( E ) 0 ′′ = E $ ' ( E ) 0 ′′ −1 . . ( 28 ) . Let A ...
... course indifferent which form is used , but where , as in the case before us , two or more would give infinity as result the second form cannot be used . 13. Ex . 8. To shew that $ ( E ) 0 ′′ = E $ ' ( E ) 0 ′′ −1 . . ( 28 ) . Let A ...
Page 34
... course it is supposed that the value of x for which that of the function is required is not very remote from those , or from some of those , values for which the values of the func- tion are given . The same assumption as to the form of ...
... course it is supposed that the value of x for which that of the function is required is not very remote from those , or from some of those , values for which the values of the func- tion are given . The same assumption as to the form of ...
Page 41
... course differ . We say derived from dif- ferent hypotheses , because whichsoever element is regarded as dependent is treated not simply as a function , but as a rational and integral function of the other element ; and thus the choice ...
... course differ . We say derived from dif- ferent hypotheses , because whichsoever element is regarded as dependent is treated not simply as a function , but as a rational and integral function of the other element ; and thus the choice ...
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Algebra applied approximate arbitrary constant Arithmetic assume B₁ Bernoulli's numbers C₁ C₂ Calculus of Finite Cambridge chapter Christ's College cloth College complete primitive convergent Crelle Crown 8vo curve deduce denoted determine difference-equation Differential Calculus differential coefficients differential equation divergent divergent series dy dx English equal Examples expression factor Fcap Finite Differences formula functional equation geometrical given equation gives Grunert Hence independent variable indirect integral integral function Lagrange's formula limits Mathematical method obtain operation ordinates P₁ P₂ particular periodical function problem Professor quantity rational and integral Schlömilch Schools Second Edition second member shew singular solution solve student substituting summation supposed symbol Taylor's Theorem theorem tion u₁ u₂ unity Ux+1 Ux+2 V₁ v₂ Vx+1 whence Их
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