A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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... methods with those of the Differential Calculus - a connexion which in some instances involves far more than a merely formal analogy . Indeed the work is in some measure designed as a sequel to my Treatise on Differential Equations ...
... methods with those of the Differential Calculus - a connexion which in some instances involves far more than a merely formal analogy . Indeed the work is in some measure designed as a sequel to my Treatise on Differential Equations ...
Side
... Methods , 59. Condi- tions of extension of direct to inverse forms , 61. Exercises , 63 . CHAPTER V. CONVERGENCY AND DIVERGENCY OF SERIES Definitions , 65. Fundamental Proposition , 66. First derived Criterion , 69. Supplemental ...
... Methods , 59. Condi- tions of extension of direct to inverse forms , 61. Exercises , 63 . CHAPTER V. CONVERGENCY AND DIVERGENCY OF SERIES Definitions , 65. Fundamental Proposition , 66. First derived Criterion , 69. Supplemental ...
Side
... Method of Generating Functions , 191. Equations of Mixed Differences , 193. Simultaneous Equations , 205. Exercises , 206 . CHAPTER XI . OF THE CALCULUS OF FUNCTIONS 179 • 208 Direct Problems , 209. Periodical Functions , 215 ...
... Method of Generating Functions , 191. Equations of Mixed Differences , 193. Simultaneous Equations , 205. Exercises , 206 . CHAPTER XI . OF THE CALCULUS OF FUNCTIONS 179 • 208 Direct Problems , 209. Periodical Functions , 215 ...
Side 12
... method , hereafter to be explained , called the method of Generating Functions . But having been once established , the very forms of the theorems 12 DIRECT THEOREMS OF FINITE DIFFERENCES . [ CH . II .
... method , hereafter to be explained , called the method of Generating Functions . But having been once established , the very forms of the theorems 12 DIRECT THEOREMS OF FINITE DIFFERENCES . [ CH . II .
Side 13
... methods will be illustrated in the following example . Ex . Required to express un in terms of u , and its suc- cessive differences . We have Uz +1 = Uz + Au ,; •• Ux + 2 = U2 + Aux + △ ( ux + Aux ) = ux + 2 △ ux + △ 3u ̧ • Hence ...
... methods will be illustrated in the following example . Ex . Required to express un in terms of u , and its suc- cessive differences . We have Uz +1 = Uz + Au ,; •• Ux + 2 = U2 + Aux + △ ( ux + Aux ) = ux + 2 △ ux + △ 3u ̧ • Hence ...
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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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