rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Lectures on complex analysis
  name:
    name part: Steinmetz, Norbert
    name part: 1949-
    role:
      role term: creator
    role:
      role term: author.
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: sz
    date issued: 2026
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xviii, 369 pages) : illustrations
  abstract: 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.
  table of contents: Chapter 1. Complex Numbers and Functions -- Chapter 2. Two Theorems of Cauchy -- Chapter 3. The Local Theory -- Chapter 4. The Residue Theorem -- Chapter 5. Entire Functions -- Chapter 6. Special Functions -- Chapter 7. Periodic and Elliptic Functions -- Chapter 8. Conformal Mappings of Simply Connected Domains -- Chapter 9. Harmonic Functions -- Chapter 10. Conformal Mappings of Multiply Connected Domains -- Chapter 11. Analytic Continuation -- Chapter 12. Ordinary Differential Equations in the Complex Domain -- Chapter 13. Iterations of Polynomials.
  note: Norbert Steinmetz.
  note: Includes bibliographical references and index.
  subject:
    topic: Functions of complex variables
  subject:
    topic: Differential equations
  subject:
    topic: Fonctions d'une variable complexe
  subject:
    topic: Équations différentielles
  classification: QA331.7 .S74 2026
  classification: 515/.9
  related item:
    identifier: (OCoLC)1549509188
  identifier: 9783032139962 (electronic bk.)
  identifier: 3032139961
  identifier: 9783032139955
  identifier: 3032139953
  location:
    physical location: POD
  record info:
    record content source: GW5XE
    record creation date: 260622
    record change date: 20260801173426.8
    record identifier: in00005789473
    language of cataloging:
      language term: eng