B. A. Fuchs – författare

Functions of a Complex Variable and Some of Their Applications, Volume 1, discusses the fundamental ideas of the theory of functions of a complex variable. The book is the result of a complete rewriting and revision of a translation of the second (1957) Russian edition. Numerous changes and additions have been made, both in the text and in the solutions of the Exercises. The book begins with a review of arithmetical operations with complex numbers. Separate chapters discuss the fundamentals of complex analysis; the concept of conformal transformations; the most important of the elementary functions; and the complex potential for a plane vector field and the application of the simplest methods of function theory to the analysis of such a field. Subsequent chapters cover the fundamental apparatus of the theory of regular functions, i.e. basic integral theorems and expansions in series; the general concept of an analytic function; applications of the theory of residues; and polygonal domain mapping. This book is intended for undergraduate and postgraduate students of higher technical institutes and for engineers wishing to increase their knowledge of theory.

Functions of a Complex Variable and Some of Their Applications, Volume I focuses on the fundamental ideas of the theory of functions of a complex variable. This book consists of eight chapters. Chapter I presents the fundamentals of complex analysis, while Chapter II discusses the concept of conformal transformations. The elementary functions are introduced in Chapter III. In Chapter IV, the complex potential for a plane vector field and application of the simplest methods of function theory are elaborated. Chapter V deals with the basic integral theorems, followed by a description of the expansions in series in Chapter VI. Chapters VII and VIII are devoted to the analytical and geometric applications of the theory. This volume is intended for undergraduate and postgraduate students of higher technical institutes and engineers aiming to increase their knowledge of theory.