Vannevar Bush (with Norbert Wiener).*Operational Circuit Analysis*. New York, John Wiley & Sons, 1929. First edition. x, 392pp. Includes an appendix ("B") "Fourier Analysis and Asymptotic Series", p366-379. 197x135mm. Bound in sturdy ribbed publisher's cloth. At least a Very Good copy, and possibly a Fine copy. $200

"The technological, professional, and intellectual context out of which the development of the continuous integraph or product integraph-as the immediate forerunner of Vannevar Bush's differential analyzer-evolved is outlined. In particular the affinity between transmission line research and teaching at MlT's electrical engineering department under Bush's guidance, on the one hand, and the creation of the product integraph for evaluating integrals, which resulted from the appropriate differential equations of the transmission problems, on the other hand, is detailed. I emphasize Bush's perception of promoting engineering by easing the applied mathematics in this field as it appeared in his contribution to the development of operational circuit analysis as an appropriate engineering mathematics as well as in creating analog machinery that was inspired by the formulation of transmission line problems in terms of that very operational methods after Oliver Heaviside."--Abstract, "On the role of mathematics and mathematical knowledge in the invention of Vannevar Bush's early analog computers",* IEEE Annals of the History of Computing* ( Volume: 18, Issue: 4, Oct-Dec 1996 )

Also this, from page 52 of the same source:

- “Despite his rather good knowledge of mathematics, during this period Bush learned to appreciate the value of cooperating with a professional mathematician for his expertise on intricate mathematical details. Jackson, who always sought to foster cooperation between his department and the departments of mathematics and physics, enrolled the young MIT mathematician Norbert Wiener in this enterprise. It was no accident that just Wiener had been picked, since he was one of the few mathematicians in the United States at that time who was very open to ideas from fields outside mathematics. Moreover, he was an ardent admirer of Heaviside’s work. Thus Bush probably learned as much as his students did about operational calculus, clearing problems together in class, often after he had consulted Wiener. In the course of these discussions, Wiener saw the “possibility of translating the Heaviside work into a more classical form in which the chief tool was harmonic analysis or the use of trigonometric development...This work led him and others to approach operational calculus via the Fourier transformation and to work on generalized harmonic analysis. Bush’s 1929 book on operational circuit analysis reflected that productive cooperation between a mathematician and an engineer. On the one hand, it contained an appendix by Wiener on “Fourier Analysis and Asymptotic Series” with his approach to operational calculus via the Fourier transformation, which was explained and made more comprehensible to the readers by Bush in the main text. “