Chapter 3 Cauchy’s “Modern Analysis”

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Abstract

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.