Complex Numbers and Functions

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

Chapter 1 in Lectures on Complex Analysis, 2026, pp 1-27 from Springer

Abstract: Abstract At the heart of complex analysis are complex-valued, differentiable functions that are defined on subdomains of the complex plane. In this chapter the algebraic, geometric, and topological properties of the complex numbers and the fundamental properties of the holomorphic functions are examined. Particular emphasis is placed on Möbius transformations and elementary conformal mappings.

Date: 2026
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DOI: 10.1007/978-3-032-13996-2_1

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