1. Judith Grabiner, The Origins of Cauchy’s Rigorous Calculus (Cambridge MA: MIT Press, 1981) and Grattan-Guinness, The Development of the Foundations of Mathematical Analysis from Euler to Riemann (Cambridge: Cambridge University Press, 1970).
2. See John Heilbron, Electricity in the Seventeenth and Eighteenth Centuries (Berkeley CA: University of California Press, 1979). Here we are dealing with Physics, narrowly defined.
3. See Christa Jungknickel and Russell McCormmach, Intellectual Mastery of Nature, 2 vols. (Chicago IL: University of Chicago Press, 1986), vol. 1, p. 55.
4. For example see Robert Friedman, “The Creation of a New Science: Joseph Fourier’s Analytical Theory of Heat,” Historical Studies in the Physical Sciences
8 (1977): 73–100. In this account mathematics is supplementary to the essential physical problem of heat conduction. Friedman focusses on the concepts Fourier used but does not look at the problem of how, or if, Fourier used these ideas in his mathematical theory of heat.
5. John Herivel, Joseph Fourier: The Man and the Physicist (Oxford: Clarendon Press, 1975).