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A Complex Analysis Problem Book / by Daniel Alpay

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: Basel : Springer Basel, 2011Description: Online-Ressource (X, 526p, digital)ISBN:
  • 9783034800785
Subject(s): Additional physical formats: 9783034800778 | Buchausg. u.d.T.: A complex analysis problem book. Basel : Birkhäuser [u.a.], 2011. X, 526 S.MSC: MSC: *00A07 | 30A99RVK: RVK: SK 600LOC classification:
  • QA331-355
DOI: DOI: 10.1007/978-3-0348-0078-5Online resources: Summary: Prologue -- I Complex numbers -- 1 Complex numbers: algebra -- 2 Complex numbers: geometry -- 3 Complex numbers and analysis -- 4. Remarks and generalizations: quaternions, etc -- II Functions of a complex variable -- 5 C-differentiable functions -- 6 Cauchy's theorem -- 7 First applications -- 8 Laurent expansions and applications -- 9 Computations of definite integrals -- 10 Harmonic functions -- 11 Conformal mappings.-III Complements -- 12 Some useful theorems -- 13 Some topology -- References -- Index.Summary: This is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applications and aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises show the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes a part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.PPN: PPN: 1651018286Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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