A Treatise on the Calculus of Finite Differences |
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Page xi
... satisfy a Differential Equation , 191. Anomalies of Singular Solutions , 193. Explanation of the same , 194. Prin- ciple of Continuity , 198. Recapitulation of the classes of solu- tions that a Difference - Equation may possess , 204 ...
... satisfy a Differential Equation , 191. Anomalies of Singular Solutions , 193. Explanation of the same , 194. Prin- ciple of Continuity , 198. Recapitulation of the classes of solu- tions that a Difference - Equation may possess , 204 ...
Page 38
... satisfied , viz . that for x = α , x = b ... x = k , it shall assume the respective values ua , us ... ux , the expression must contain n constants , whose values those conditions determine . We might therefore assume Ux = A + Bx + Cx2 ...
... satisfied , viz . that for x = α , x = b ... x = k , it shall assume the respective values ua , us ... ux , the expression must contain n constants , whose values those conditions determine . We might therefore assume Ux = A + Bx + Cx2 ...
Page 79
... satisfied provided AΣ " uz in any term is equal to 1u in the preceding term , and this imposes the condition that the constants in Σu be retained without change in " u . And as , if this be done , the equa- tion will be satisfied , it ...
... satisfied provided AΣ " uz in any term is equal to 1u in the preceding term , and this imposes the condition that the constants in Σu be retained without change in " u . And as , if this be done , the equa- tion will be satisfied , it ...
Page 152
... satisfied in all the important series of the form Σ The series to which they lead on application of the Maclaurin sum - formula all converge for a time and then diverge very rapidly . In spite of this diverg- ence we see that they are ...
... satisfied in all the important series of the form Σ The series to which they lead on application of the Maclaurin sum - formula all converge for a time and then diverge very rapidly . In spite of this diverg- ence we see that they are ...
Page 172
... satisfy the given equation ( 4 ) by satisfying the first of the component equations ( 5 ) when x is an even integer , and the second when x is an odd integer . 2 * This statement must be taken with some qualification . The reason why ...
... satisfy the given equation ( 4 ) by satisfying the first of the component equations ( 5 ) when x is an even integer , and the second when x is an odd integer . 2 * This statement must be taken with some qualification . The reason why ...
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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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