A Treatise on the Calculus of Finite Differences |
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Page vii
... students will aim at an exhaustive study of a few subjects in preference to a super- ficial acquaintance with the whole range of Mathematical research , I have added brief notes referring to most of the papers on the subjects of this ...
... students will aim at an exhaustive study of a few subjects in preference to a super- ficial acquaintance with the whole range of Mathematical research , I have added brief notes referring to most of the papers on the subjects of this ...
Page 16
... student can find instances of the use of Generating Functions in Lacroix , Diff . and Int . Cal . III . 322. Examples of a fourth method , at once elegant and powerful , due originally to Abel , are given in Grunert's Archiv . XVIII ...
... student can find instances of the use of Generating Functions in Lacroix , Diff . and Int . Cal . III . 322. Examples of a fourth method , at once elegant and powerful , due originally to Abel , are given in Grunert's Archiv . XVIII ...
Page 77
... student . It is α ax Σπαφ − n a Δφ 2 ′′ a ° • ( x ) = ( ~ ~ 1 ) = { • ( x ) − ~ ~ ~ 1 A4 φ ( a - + α - ( z ) α 2 n ( n + 1 ) ( _ _ _ ) * A34 ( x ) — & c . } 1.2 + C12 + C12 x + ... + Сn_12-1 * The explanation of this peculiarity is ...
... student . It is α ax Σπαφ − n a Δφ 2 ′′ a ° • ( x ) = ( ~ ~ 1 ) = { • ( x ) − ~ ~ ~ 1 A4 φ ( a - + α - ( z ) α 2 n ( n + 1 ) ( _ _ _ ) * A34 ( x ) — & c . } 1.2 + C12 + C12 x + ... + Сn_12-1 * The explanation of this peculiarity is ...
Page 81
... student , or to adopt the correct form C + Σ¡ ( 4 ; cos 2iπx + В¡ sin 2iπx ) vi i We shall usually do the former . ( 4 ) . 5. The student will doubtless already have perceived how much the branch of mathematics that forms the subject of ...
... student , or to adopt the correct form C + Σ¡ ( 4 ; cos 2iπx + В¡ sin 2iπx ) vi i We shall usually do the former . ( 4 ) . 5. The student will doubtless already have perceived how much the branch of mathematics that forms the subject of ...
Page 83
... student who desires practice in the symbolical methods cannot do better than take one of these papers and employ himself in demonstrating by such methods the results there given . Should he desire however a statement of the nature and ...
... student who desires practice in the symbolical methods cannot do better than take one of these papers and employ himself in demonstrating by such methods the results there given . Should he desire however a statement of the nature and ...
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Common terms and phrases
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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