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The Problem of the Constant Coefficient Linear Differential Operators
Published online by Cambridge University Press: 03 November 2016
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1. An article by my friend, Mr. R. J A. Barnard, of this university, in the October number of the Gazette, impels me to join in the discussion of which it is a part. For, while the article in itself is an interesting application, to “constant coefficient” equations, of methods of wider applicability, the thesis of “avoiding” what is plainly the right method for such equations is, I feel sure, a mistaken one: it recalls the fin de siècle game of “dodging the calculus” (from which we seem now to be swinging to the opposite extreme—of teaching infinitesimal calculus without sufficient regard to the requisite maturity of mental development of the pupil).
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- Copyright © Mathematical Association 1933
References
page 257 note * Math. Gazette XVI, 254 (1932).
page 257 note † It is to be observed that the methods used are peculiarly applicable to second order equations, whereas, of course, the strength of the “symbolic methods” is their applicability to the general equation of the “constant coefficient” type.
page 257 note ‡ The writer owes early inspiration on this subject (as on much else) to Mr. W. E. Philip, a former Fellow of Clare College, Cambridge, now Chief Inspector of Schools of the Aberdeen District. (This footnote may be regarded as a dedication of a sort.)
page 257 note ** See Underwood, Math. Gazette XV, p. 99 (1930-1), Dalton, ibid., p. 369.
page 258 note * The writer contributed a Note on this case to the Edinburgh Mathematical Society, so long ago as 1904. See Proc. E.M.S., vol. xxii.
page 259 note * The product P(x) ψ (x) = 1 + a finite number of terms in powers of x of degree higher than xm .
page 259 note † Something turns on what he means by “expansible in integral powers” (3rd edn., pp. 56-8).
page 259 note ‡ The usefulness of this and following forms is for cases of v (such as xm), such that the expansion (as expressed) is a finite one.
page 259 note ** In consideration for economy of valuable space, the details of proof are left to the reader.
page 260 note * As Mr. Underwood affirmed in his article. Were the grounds of his affirmation purely empirical?
page 260 note † XVI, 131 (1932).
page 260 note ‡ As indeed Mr. Lowry does.