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Operational Methods in Mathematical Physics

Published online by Cambridge University Press:  03 November 2016

H. S. Carslaw
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Extract

This essay-review of Jeffreys’ very welcome and valuable Tract with the above title has been written at the editor’s request. Many readers of the Gazette must have heard of Heaviside’s operational method of solving the equations of dynamics and mathematical physics. If they have tried to learn about them from Heaviside’s own works, they have attempted a difficult task. Nothing more obscure than his mathematical writings is known to me. A Cambridge Tract is now at their disposal. Prom it much may be learned; but the air of mystery still—at least in part—remains.

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Type
Research Article
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The Mathematical Gazette , Volume 14 , Issue 196 , October 1928 , pp. 216 - 226
Copyright
Copyright © Mathematical Association 1928

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References

page 216 note * Cambridge Tracts in Mathematics and Mathematical Physics. No. 23, by Harold Jeffreys, (Camb. Univ. Press), 1927. Price 6s. 6d. net.

page 216 note † Electromagnetic Theory, by Oliver Heaviside, vol. 2, p. 13, 1899.

page 217 note * If p stands for , one would expect p -1 to denote integration. Then, for positive integral values of n, we would have

If this final formula is to hold for fractional values of n, we would have

And

page 217 note † Cf. loc. cit., p.4.

page 219 note * This is usually known as Heaviside’s Expansion Theorem, or the Partial Fraction Rule. Cf. loe. cü., p. 127.

page 220 note * The revived interest in Heaviside’s operational method is due chiefly to a paper by Brom-wich on “Normal Co-ordinates in Dynamical Systems,” Proc. London Math. Soc. (2), vol. 15, 1916, and to other papers of his in which the method is freely used.

page 221 note * Cf. loe. cit., Proc. London Math. Soc. (2), vol. 15, 1916, p. 421. But see also pp. 438 et seq.

page 223 note * In this section I follow the method and use the diagrams oí Chapter XI. of my book on Conduction of Heat (Ed. 1921 ). See also Chapter X. §§ 80-90.

page 225 note * Cf. my book on Fourier’s Series and Integrals (Ed. 1921) Ex. 13 p. 195.

page 225 note † Cf. loe. cit., Chapter X

page 226 note * Proc. Camb. Phil. Soc. 23, 1927, 768-778.