A Treatise on the Calculus of Finite Differences |
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Page 1
... denote the operation of taking the increment of that function correspond- B. F. D. 1 ing to a given constant increment Ax of the variable DIFFERENCE- AND SUM-CALCULUS CHAPTER NATURE OF THE CALCULUS OF FINITE DIFFERENCES.
... denote the operation of taking the increment of that function correspond- B. F. D. 1 ing to a given constant increment Ax of the variable DIFFERENCE- AND SUM-CALCULUS CHAPTER NATURE OF THE CALCULUS OF FINITE DIFFERENCES.
Page 3
... denoted by A and defined by the equation Aux = Ux + 1 - Ux · But we shall , where convenience suggests , consider the more general operation Aux Ax Ux + h - Ux h 2 where Axh . Read CHAPTER II . DIRECT THEOREMS OF FINITE DIFFERENCES . 1 ...
... denoted by A and defined by the equation Aux = Ux + 1 - Ux · But we shall , where convenience suggests , consider the more general operation Aux Ax Ux + h - Ux h 2 where Axh . Read CHAPTER II . DIRECT THEOREMS OF FINITE DIFFERENCES . 1 ...
Page 4
... denoted by A is capable of repetition . For the difference of a function of x , being itself a function of x , is subject to operations of the same kind . In accordance with the algebraic notation of indices , the difference of the ...
... denoted by A is capable of repetition . For the difference of a function of x , being itself a function of x , is subject to operations of the same kind . In accordance with the algebraic notation of indices , the difference of the ...
Page 5
... denoted by A , A3 , ... A " are always possible when the subject - function u is given , there are certain elementary cases in which the forms of the results are deserving of particular attention , and these we shall next consider ...
... denoted by A , A3 , ... A " are always possible when the subject - function u is given , there are certain elementary cases in which the forms of the results are deserving of particular attention , and these we shall next consider ...
Page 9
... denoted by merges , on supposing Ax to become Δη infinitesimal but the subject - function to remain unchanged , into the operation denoted by d dx • The following are illus- trations of the mode in which some of the general theorems of ...
... denoted by merges , on supposing Ax to become Δη infinitesimal but the subject - function to remain unchanged , into the operation denoted by d dx • The following are illus- trations of the mode in which some of the general theorems of ...
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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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