A Complex Analysis Problem Book [recurso electrónico] / by Daniel Alpay.
Tipo de material: TextoEditor: Basel : Springer Basel, 2011Descripción: X, 526p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783034800785Tema(s): Mathematics | Functions of complex variables | Mathematics | Functions of a Complex VariableFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 515.9 Clasificación LoC:QA331-355Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA331 -355 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 373052-2001 |
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QA329 -329.9 Boundary Element Methods with Applications to Nonlinear Problems | QA331 -355 An Introduction to Complex Analysis | QA331 -355 Complex Analysis | QA331 -355 A Complex Analysis Problem Book | QA331 -355 Complex Analysis | QA331 -355 Symmetries of Compact Riemann Surfaces | QA331 -355 Elementi di Analisi Complessa |
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.
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