The book provides a brief presentation of theory of the fundamentals of complex valued functions of a complex variable, together with several worked in detail examples and exercises. Emphasis is given to the understanding of properties of complex numbers, convergence of sequences and series, general properties of complex functions, conformal mappings, computational techniques of integrals, the power series representation of analytic functions, isolated singularities, Laurent series, residues, analytic continuation and integral transforms.

The book will be particularly useful to undergraduate students and beginning graduate students of both pure and applied Mathematics departments and engineering schools. The author has succeeded to provide a large collection of examples and problems with step-by-step solutions, computations and proofs.

Overall, the book is recommended for class use, as well as a supplement of standard textbooks.

Reviewer:

Themistocles M. Rassias

Affiliation:

National Technical University of Athens