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Heaviside and the Operational Calculus*

Published online by Cambridge University Press:  03 November 2016

Extract

The centenary of the birth of Oliver Heaviside last year has been the occasion of celebration by electrical engineers and physicists in this and other countries. In the discussions of his work much has been said about the Operational Calculus ; and as the versions of its history which have been given both in these commemorative celebrations and in most of the textbooks of the subject are seriously incorrect, this may serve as an occasion to recount that history more correctly. The story in widest circulation is that the Operational Calculus was discovered by Heaviside (Boole being sometimes—and incorrectly—named as the discoverer of its applications to ordinary differential equations) and rejected by British mathematicians because of Heaviside’s lack of rigour. The facts, as I shall show, are that the Calculus was well known in Britain and France before Heaviside’s birth, and that the rejection of his paper had nothing to do with his use of symbolic methods.

Type
Research Article
Copyright
Copyright © The Mathematical Association 1952

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Footnotes

*

A lecture given to the London Mathematical Society, on January 18, 1951.

References

Notes : (1) is the best reference for the representational and (2) for the formal calculus in their early years. (5) gives the best general account, including modern developments ; (3) has a useful but one-sided bibliography, which ignores most work by Laplace Transform methods prior to Doetsch. (4) is the most systematic account of symbolic methods. (6) gives an interesting discussion of the peculiarities of the Heaviside calculus.Google Scholar
1. Burkhardt, H.Trigonometrische Reihen und Integralen bis 1850,” Enz. der Math. Wiss., II, 1, II A 12 (1905), 8191354, exp. Parts VI, VII.Google Scholar
2. Pincherle, S.Funktional Operationen und Funktionalgleichungen,” ibid., II. A 12, 761817.Google Scholar
3. Doetsch, G. Theorie und Anwendungen der Laplace Transformation (1937).Google Scholar
4. Jeffreys, H. Operational Methods in Mathematical Physics (1931).Google Scholar
5. Gardiner, and Barnes, , Transients in Linear Systems (1949).Google Scholar
6. Bush, V. Operational Circuit Analysis (1929).Google Scholar
7. Lagrange, J. L. Mem. Acad. Berlin, 3 (1772) ; Œuvres, Vol. 3, 441–54.Google Scholar
8. Laplace, P. S. Théorie Analytique des Probabilités (1820).Google Scholar
9. Gregory, D. F. Examples of the Processes of the Differential and Integral Calculus (1841) ; 9a. Collected Mathematical Works.Google Scholar
10. de Morgan, A. Differential and Integral Calculus (1842).Google Scholar
11. Servois, F. J. Annales de mathématiques, 5 (1814), 93140.Google Scholar
12. Brisson, B. Journal de l’école Polytechnique (7), (1808), 191261.Google Scholar
13. Fourier, J. Théorie analytique de la Chaleur (1822).Google Scholar
14. Cauchy, A. L. Œuvres Complétes, (a) Ser. 1, T. 1 ; (b) Ser. 2, T. 6 ; (c) Ser. 1, T. 2 ; (d) Ser. 1, T. 8. Many papers occur in Ser. 1, T. 4–8.Google Scholar
15. Liouville, J. Journal de l’école polytechnique, 13 (1832), 169, 71–162, 163–186.Google Scholar
16. Brinkley, J. Phil. Trans., 97 (1807).Google Scholar
17. Babbage, C. Phil. Trans., 107 (1817), 197216.Google Scholar
18. Murphy, R. Phil. Trans., 127 (1837), 179210.Google Scholar
19. Boole, G. Phil. Trans., 134 (1844), 225–82.Google Scholar
19a. Treatise on Differential Equations (1859) ; Treatise on the Calculus of Finite Differences (1860).Google Scholar
20. Graves, C. Proc. Roy. Irish Acad., 6 (1853–7), 144–52.Google Scholar
21. Whittaker, E. T. Bull. Calcutta Math. Soc., 20 (1928), 216.Google Scholar
22. Titchmarsh, E. C. Fourier Integrals (1937).Google Scholar
23. Churchill, R. V. Math. Ann., 114 (1937), 591613.Google Scholar
24. Carmichael, R. A Treatise on the Calculus of Operations (1855).Google Scholar
Heaviside’s, Electromagnetic Theory is referred to throughout as E.M.T. Google Scholar