The Calculus of Finite Differences

Abstract

THE last edition of Boole's “Finite Differences” appeared in 1880, and was in fact a reprint of the edition of 1872. The interval of sixty years has seen in the elementary field Sheppard's introduction of central differences, Thiele's strange invention of reciprocal differences, Everett's discovery of the interpolation formula that bears his name, and the recent development of methods of numerical interpolation which dispense with formulae altogether; Poincare's attention to the asymptotic behaviour of solutions suggested new and tractable problems regarding insoluble equations; as a branch of analysis the calculus of finite differences has been revolutionised by Norlund in the course of the last twelve years; Birkhoff, to add one name which is absent from the book under review, has handled the system of linear difference equations by matrix methods which would have won Boole's heart. The publication of an English treatise on finite differences is therefore something of an event to the student of mathematics in Great Britain.

The Calculus of Finite Differences.

By Prof. L. M. Milne-Thomson. Pp. xxiii + 558. (London: Macmillan and Co., Ltd., 1933.) 30s. net.