Article ID: CBB001202206

Integral Equations between Theory and Practice: The Cases of Italy and France to 1920 (2014)

unapi

In 1899, Ivar Fredholm discovered how to treat an integral equation using conceptual methods from linear algebra and use these ideas to solve certain classes of boundary value problems. He formulated a theory allowing him both to unify large classes of problems and to attack several problems fruitfully. The historical literature on the theory of integral equations has concentrated largely on the unification that was afforded by Hilbert and his school, but has not throughly investigated the roots of the subject in the older theory of partial differential equations, as developed for instance by Fredholm himself but also by Volterra and Levi-Civita. By concentrating on work issuing from this older tradition, in particular on French and Italian work, the paper shows how the new theory of integral equations was enthusiastically received, especially for its fruitful applications to areas of mathematical physics such as hydrodynamics, elasticity, and heat theory.

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Authors & Contributors
Ehrhardt, Caroline
Scalambro, Elena
Terracini, Lea
Villeneuve, Jean-Philippe
Tournès, Dominique
Stedall, Jacqueline Anne
Concepts
Mathematics
Algebra
Linear algebra
Integral equations
Mathematicians
Group theory
Time Periods
19th century
20th century, early
17th century
20th century
18th century
16th century
Places
France
Italy
England
Turin (Italy)
Scotland
Turkey
Institutions
Académie des Sciences, Paris
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