A Complex Analysis Problem Book (PDF)
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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.
- Autor: Daniel Alpay
- 2011, 2011, 526 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3034800789
- ISBN-13: 9783034800785
- Erscheinungsdatum: 20.08.2011
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- Dateiformat: PDF
- Größe: 5.02 MB
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“This volume contains a collection of exercises in the theory of analytic functions. The author also provides detailed solutions to all proposed problems. … The book under review is mainly addressed to upper undergraduate students from mathematics and electrical engineering.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1226, 2012)
“This is a substantial book (more than 500 pages long) which starts with a sketch of the construction of the field of complex numbers … and proceeds to much more advanced material. … this book is more than just a collection of exercises and solutions … . anyone teaching such a course would undoubtedly find this book a useful supplement, as would graduate students studying for their qualifier examinations, who could use this book to brush up on both theory and technique.” (Mark Hunacek, The Mathematical Association of America, December, 2011)
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