Complex Analysis Problem Book

Prof. Daniel Alpay is a faculty member of the department of mathematics at Ben-Gurion University, Beer-Sheva, Israel. He is the incumbent of the Earl Katz Family chair in algebraic system theory. He has a double formation of electrical engineer (Telecom Paris, graduated 1978) and mathematician (PhD, Weizmann Institute, 1986). His research includes operator theory, stochastic analysis, and the theory of linear systems. Daniel Alpay is one of the initiators and responsible of the dual track electrical-engineering mathematics at Ben-Gurion University. He is the author of "An Advanced Complex Analysis Problem Book" (Birkhäuser, 2015). Together with co-authors, he has written seven books and close to 240 research papers, and edited fifteen books of research papers, and in particular the Springer Reference Work on Operator Theory.

• Part I Complex Numbers.- Complex Numbers: Algebra.- Complex Numbers: Geometry.- Complex Numbers and Analysis.- Part II Functions of a Complex Variable.- Cauchy–Riemann Equations and C-differentiable Functions.- Cauchy’sTheorem.- Morera, Liouville, Schwarz, et les autres: First Applications.- Laurent Expansions, Residues, Singularities and Applications.- Computations of Definite Integrals Using the Residue Theorem.- Part III Applications and More Advanced Topics.- Harmonic Functions.- Conformal Mappings.- A Taste of Linear System Theory and Signal Processing.- Rational Functions.- Special Functions and Transforms.- Part IV Appendix.- Some Topology.- Some Functional Analysis Essentials.- A Brief Survey of Integration.

"This volume is a collection of exercises in the theory of analytic functions, with complete and detailed solutions. ... The reviewer considers that the book can be used as a primary text for a course in complex analysis. A reader of the full book will know the basic of one complex variable theory and will have seen it integrated into mathematics as a whole. Research mathematicians will discover several novel perspectives." (Vicentiu D. Radulescu, zbMATH 1356.30001, 2017)