Applied Complex Variables for Scientists and Engineers

This introduction to complex variable methods begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration. Taylor and Laurent series. singularities, residues transform methods and conformal mappings. Both algebraic and geometric tools are employed to provide the greatest understanding with many diagrams illustrating the concepts introduced. This book distinguishes from other texts in complex function theory by placing greater emphaisi on how to use complex variable methods. Throughout the text, many of the important theoretical results in complex function theory are followed by relevant and vivid examples in physical sciences. These examples are drawn from a wide range of physical and engineering applications, Such as potential theory, steady-state temperature problems. hydrodynamics, seepage flows. electrostatics, and gravitation.

This second edition now contains 350 stimulating exercises of high quality. with solutions given to many of them. Material has been updated and additional proofs on some of the important theorems in complex function theory are now included. Such as the Weierstrass-Casorati theorem. The book will be highly suitable for students wishing to learn the elements of complex analysis in an applied context.

"This text achieves a mixture of rigor and application that is not found in many books on complex variable theory. I think this is an advantage, allowing one to acquire the best of mathematical precision alongside applications to physics and engineering...This must surely appeal to a wide range of learning styles and ensure a greater understanding for anyone who chooses to read this text...this book if acquired is bound to be consulted frequently on any time frame because of its breadth, versatility, completeness, and mix of theory with applications." W.Joyce, Contemporary physics