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Field name	Details
Dewey Class	515.9
Title	A Complex Analysis Problem Book ([Ebook]) / by Daniel Alpay.
Author	Alpay, Daniel
Other name(s)	SpringerLink (Online service)
Publication	Basel : Springer , 2011.
Physical Details	X, 526 pages : online resource.
ISBN	9783034800785
Summary Note	This is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applicationsÂ andÂ aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercisesÂ showÂ 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 ofÂ important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes aÂ part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-0348-0078-5
Links to Related Works	Subject References: Functions of a Complex Variable . Functions of complex variables . Mathematics . Authors: Alpay, Daniel . Corporate Authors: SpringerLink (Online service) . Classification: 515.9 .

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A Complex Analysis Problem Book

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