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Book synopsis

This elegant textbook offers a comprehensive course on one-dimensional complex analysis. It includes many topics that, in this scope, are not covered in most other textbooks, such as a detailed investigation of the Schwarzian derivative and its associated differential equation, with applications to conformal mappings of circular polygons; various proofs of the uniformisation theorem for planar domains; an introduction to the theory of ordinary differential equations in the complex domain, culminating in a proof of the Cauchy Kovalevskaya theorem; an introduction to the theory of normal families, including Zalcman's lemma; a proof of the Paley Wiener theorem; a complete discussion of the Laguerre Pólya class; solution of the Dirichlet problem, with special emphasis on harmonic measure and Green's function, and applications to conformal mappings of multiply connected domains; a detailed description of the dynamics of polynomials; and the consistent use of the theory of proper mappings whenever possible.

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Lectures on Complex Analysis
• Author: Norbert Steinmetz
• Language: English
• Binding: Hardback
• Number of pages: 351
• EAN: 9783032139955
• ID: 50028277
• Publisher: Springer, Berlin
• Weight: 784 g
• Dimensions: 235 × 155 mm
• Date of publishing: 13. May 2026

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