A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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... APPROXIMATE SUMMATION OF SERIES Development of Zu , 80. Bernoulli's Numbers , 83. Applications , 84 . Limits of the Series for Zu , 91. Other forms of Zu , 94. Exercises , 97 . 1 4 28 45 65 1 80 PAGE CHAPTER VII . EQUATIONS OF ...
... APPROXIMATE SUMMATION OF SERIES Development of Zu , 80. Bernoulli's Numbers , 83. Applications , 84 . Limits of the Series for Zu , 91. Other forms of Zu , 94. Exercises , 97 . 1 4 28 45 65 1 80 PAGE CHAPTER VII . EQUATIONS OF ...
Side 29
... approximate general expression of ux ux = A + Bx + Сx2 ... + Ex2 - 1 ( 1 ) , a form which is rational and integral and involves n arbitrary coefficients , the data in succession give u = A + Ba + Ca2 ... + Ea " , u2 = A + Bb + Cb2 ... + ...
... approximate general expression of ux ux = A + Bx + Сx2 ... + Ex2 - 1 ( 1 ) , a form which is rational and integral and involves n arbitrary coefficients , the data in succession give u = A + Ba + Ca2 ... + Ea " , u2 = A + Bb + Cb2 ... + ...
Side 30
... approximate value of log 3.14159 . Here , omitting the decimal point , we have the following table of numbers and differences : wo И1 Иг 3 4969296 4983106 4996871 5010593 A 13810 A2 -45 13765 - 43 13722 A3 2 The first column gives the ...
... approximate value of log 3.14159 . Here , omitting the decimal point , we have the following table of numbers and differences : wo И1 Иг 3 4969296 4983106 4996871 5010593 A 13810 A2 -45 13765 - 43 13722 A3 2 The first column gives the ...
Side 32
... being 24858 . To shew the gradual closing of the approximation as the number of the values given is increased , the following results are added : Data . U 6 Calculated value of u̸5 · • 32 [ CH . III . OF INTERPOLATION .
... being 24858 . To shew the gradual closing of the approximation as the number of the values given is increased , the following results are added : Data . U 6 Calculated value of u̸5 · • 32 [ CH . III . OF INTERPOLATION .
Side 33
... approximate general expression for uz • We shall 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 ...
... approximate general expression for uz • We shall 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 ...
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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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