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3The development of the Laplace transform, 1737–1937: I. Euler to spitzer, 1737–1880Archive for History of Exact Sciences 25 (4): 343-390. 1981.This paper, the first of two, follows the development of theLaplace Transform from its earliest beginnings withEuler, usually dated at 1737, to the year 1880, whenSpitzer was its major, if himself relatively minor, protagonist. The coverage aims at completeness, and shows the state which the technique reached in the hands of its greatest exponent to that time,Petzval. A sequel will trace the development of the modern theory from its beginnings withPoincaré to its present form, due toDoetsch.
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The Wine/Water Paradox: background, provenance and proposed resolutionsThe Australian Mathematical Society Gazette 33 (3). 2006.The Wine/Water Paradox: background, provenance and proposed resolutions.
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135On Urbach's analysis of the ‘iq debate’British Journal for the Philosophy of Science 37 (1): 60-65. 1986.
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81Catastrophe modelling in the biological sciencesActa Biotheoretica 38 (1): 3-22. 1990.Catastrophe Theory was developed in an attempt to provide a form of Mathematics particularly apt for applications in the biological sciences. It was claimed that while it could be applied in the more conventional physical way, it could also be applied in a new metaphysical way, derived from the Structuralism of Saussure in Linguistics and Lévi-Strauss in Anthropology.Since those early beginnings there have been many attempts to apply Catastrophe Theory to Biology, but these hopes cannot be said …Read more
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73The development of the Laplace Transform, 1737–1937 II. Poincaré to Doetsch, 1880–1937Archive for History of Exact Sciences 26 (4): 351-381. 1982.An earlier paper, to which this is a sequel, traced the history of the Laplace Transform up to 1880. In that year Poincaré reinvented the transform, but did so in a more powerful context, that of properly conceived complex analysis. Rapid developments followed, culminating in Doetsch' work in which the transform took its modern shape.
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477On Urbach's analysis of the ‘iq debate’British Journal for the Philosophy of Science 27 (1): 60-65. 1976.
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47Euler's invention of integral transformsArchive for History of Exact Sciences 33 (4): 307-319. 1985.Euler invented integral transforms in the context of second order differential equations. He used them in a fragment published in 1763 and in a chapter of Institutiones Calculi Integralis (1769). In introducing them he made use of earlier work in which a concept akin to the integral transform is implicit. It would, however, be reading too much into that earlier work to see it as contributing to the theory of the integral transform. Other work sometimes cited in this context in fact has different…Read more
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59The ascendancy of the Laplace transform and how it came aboutArchive for History of Exact Sciences 44 (3): 265-286. 1992.The modern Laplace transform is relatively recent. It was first used by Bateman in 1910, explored and codified by Doetsch in the 1920s and was first the subject of a textbook as late as 1937. In the 1920s and 1930s it was seen as a topic of front-line research; the applications that call upon it today were then treated by an older technique — the Heaviside operational calculus. This, however, was rapidly displaced by the Laplace transform and by 1950 the exchange was virtually complete. No other…Read more
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32Nineteenth century anticipations of modern theory of dynamical systemsArchive for History of Exact Sciences 39 (2): 183-194. 1988.The “Laplace demon”, an intelligence capable of knowing the position and the velocity of every particle in the universe and so, using the laws of classical physics, knowing all their future states, seemed in the last century to pose a contradiction between the laws of physics and the freedom of the human will. In addressing this apparent paradox, Maxwell, Boussinesq and Saint-Venant were led to consider aspects of the theory of systems of differential equations. These aspects, though for differe…Read more
