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＜電子ブック＞
A Complex Analysis Problem Book / by Daniel Alpay

版	1st ed. 2011.
出版者	(Basel : Springer Basel : Imprint: Birkhäuser)
出版年	2011
大きさ	X, 526 p : online resource
著者標目	*Alpay, Daniel author SpringerLink (Online service)
件　名	LCSH:Functions of complex variables FREE:Functions of a Complex Variable
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-0348-0078-5

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