Ordinary Differential Equations in the Complex Domain

Norbert Steinmetz ()
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Norbert Steinmetz: TU Dortmund, Department of Mathematics

Chapter 12 in Lectures on Complex Analysis, 2026, pp 285-305 from Springer

Abstract: Abstract This chapter provides a brief introduction into the field of ordinary differential equations in the complex domain from the complex analysis perspective. The main topics are existence and uniqueness, analytic dependence on parameters, and analytic continuation of solutions. Cauchy’s largely forgotten ‘calcul des limites’ is applied to various problems and culminates in a proof of the Cauchy-Kovalevskaya theorem.

Date: 2026
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DOI: 10.1007/978-3-032-13996-2_12

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