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Archive for History of Exact Sciences

, Volume 21, Issue 2, pp 161–200 | Cite as

Heaviside's operational calculus and the attempts to rigorise it

  • Jesper Lützen
Article

Abstract

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 with this unrigorous theory, but in the 20th century several attempts were made to rigorise Heaviside's operational calculus. These attempts can be grouped in two classes. The one leading to an explanation of the operational calculus in terms of integral transformations (Bromwich, Carson, Vander Pol, Doetsch) and the other leading to an abstract algebraic formulation (Lévy, Mikusiński). Also Schwartz's creation of the theory of distributions was very much inspired by problems in the operational calculus.

Keywords

19th Century Differential Operator Physical Problem Pure Mathematician Integral Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Jesper Lützen
    • 1
  1. 1.History of Science DepartmentUniversity of AarhusDenmark

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