@inbook{eeac154218414256845f6432758ec6a3,
title = "The Interaction of Physics, Mechanics and Mathematics in Joseph Liouville's Research",
abstract = "As many of his contemporaries did, Joseph Liouville often emphasized the importance of physics for mathematical research. His own works provide a host of examples of interactions between mathematics and physics. This paper analyses some of them. It is shown how Laplacian physics gave rise to Liouville{\textquoteright}s theory of differentiation of arbitrary order, how Kelvin{\textquoteright}s research on electrostatics gave rise to Liouville{\textquoteright}s theorem about conformal mappings and how the theory of heat conduction gave rise to Sturm-Liouville theory. It will be shown how the problem of the shape of the planets was an important inspiration for Liouville{\textquoteright}s far reaching studies of Lam{\'e} functions and spectral theory of a particular type of integral operators. Finally the interactions between Liouville{\textquoteright}s work on mechanics and differential geometry will be discussed.",
keywords = "Faculty of Science, Matematikhistorie",
author = "Jesper L{\"u}tzen",
year = "2013",
language = "English",
isbn = "987-94-007-5379-2",
series = "History of Mechanism and Machine Science",
publisher = "Springer",
pages = "79--96",
editor = "Evelyne Barbin and Rafaele Pisano",
booktitle = "The Dialectic Relation Between Physics and Mathematics in the XIXth Century",
}