This introduction to complex variable methods begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. Throughout the text, many of the important theoretical results in complex function theory are followed by relevant and vivid examples in physical sciences. 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, e.g. the Weierstrass–Casorati theorem. The book is highly suitable for students wishing to learn the elements of complex analysis in an applied context.

‘This text achieves a mixture of rigour 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 both 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.'

W. Joyce Source: Contemporary Physics

‘… 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 Source: Contemporary Physics

‘… clear and comprehensible …'

Source: Bulletin of the Belgian Mathematical Society

‘The book is just right for students learning the elements of function theory in an applied context.'

Source: Zeitschrift für Angewandte Mathematik und Mechanik