Hidden Harmony—Geometric Fantasies

Part of the series Sources and Studies in the History of Mathematics and Physical Sciences pp 131-216


Chapter 3 Cauchy’s “Modern Analysis”

  • Umberto BottazziniAffiliated withDipertimento di Matematica ‘F. Enriques’, Università degli Studi di Milano
  • , Jeremy GrayAffiliated withDepartment of Mathematics and Statistics, Open University

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Cauchy’s early contributions to complex analysis can properly be dated to the 1820s when he obtained the famous integral and residue theorems and indeed introduced the name the “calculus of residues” (Fig 3.1). Following this, in the 1830s he made such substantial contributions as the integral formula now named after him and the calcul des limites (the method of majorants, as it is called nowadays), which he applied to the integration of differential equations in a complex domain.