The development of the Laplace Transform, 1737–1937 II. Poincaré to Doetsch, 1880–1937
@article{Deakin1982TheDO, title={The development of the Laplace Transform, 1737–1937 II. Poincar{\'e} to Doetsch, 1880–1937}, author={Michael A. B. Deakin}, journal={Archive for History of Exact Sciences}, year={1982}, volume={26}, pages={351-381} }
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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References
SHOWING 1-10 OF 71 REFERENCES
The development of the Laplace transform, 1737–1937
- Mathematics
- 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…
Euler's Version of the Laplace Transform
- History
- 1980
It is shown by specific examples how the earlier versions of the Laplace Transform can be made to work in practice-made to work, in fact, in cases where the standard modem theory breaks down.
Introduction to the Theory of Fourier Integrals
- Mathematics
- 1938
SINCE the publication of Prof. Zygmund's “Trigonometric Series” in 1935, there has been considerable demand for another book dealing with trigonometric integrals. Prof. Titchmarsh's book meets this…
Heaviside's operational calculus and the attempts to rigorise it
- Mathematics
- 1979
At the end of the 19th century Oliver Heaviside developed a formal calculus of differential operators in order to solve various physical problems. The pure mathematicians of his time would not deal…
On Laplace’s integral equations
- Mathematics
- 1926
which is known in the literature as Laplace's integral equation. The contour (C) and the function f(z) are supposed given and F(x) is to be found. In the case when the contour (C) consists of the…
On the Heaviside operational calculus
- Mathematics
- 1940
Some theorems in the operational calculus, taking definite integration as the fundamental operator, are proved for discrete systems. It is suggested that it is physically more satisfactory to regard…
Motivating the Laplace transform
- Mathematics
- 1981
The Laplace transform clearly provides a rigorization of the operational calculus. This paper proceeds in the opposite direction. It relies heavily on work by Carson, but removes it from its…
On a simple type of irregular singular point
- Mathematics, Philosophy
- 1913
provided that a proper determination of the constant c1 be made. In the present paper I wish to consider the solutions of (1) in the vicinity of x = so, but under the restriction that p ( x ) and q (…
Fourier Transforms in the Complex Domain
- Mathematics
- 1934
Introduction Quasi-analytic functions Szasz's theorem Certain integral expansions A class of singular integral equations Entire functions of the exponential type The closure of sets of complex…
Singular points of ordinary linear differential equations
- Mathematics
- 1909
in which the functions X;ff(Z) are anaZytic or have a pote at Z oo, will transform (1) into a system of equations (1) with coefficients aij(z) of the same form (2), although q is not necessarily…