APPLIED COMPLEX VARIABLESy FOR SCIENTISTS AND ENGINEERS
Y.K. Kwok, Cambridge University Press, 2002, pp: 388, ISBN 0-521-00462-4 (pbk), 0-521-80302-0 (hc); Price: $34.95/$90.00.

In this book, Kwok undertakes a thorough and complete exposition of the area of complex variables in which the basic notions of complex variables are developed systematically from most elementary ideas. Starting with the basic ideas of complex numbers and expanding the content to include the functions of complex variables, the author moves to the complex variables of exponential, logarithmic and trigonometric functions. From this solid basis, he develops the notion of complex integration and Taylor and Laurent series. His approach flows naturally into content relating to singularities and the calculus of residues. He completes the book with a section on complex methods for solving boundary value problems and the use of conformal mappings.

The author does not confine the application of complex methods only to the last two chapters; there are excellent connections throughout the book to applications such as static temperature distributions, wave propagation, heat conduction, seepage flows, and fluid flows; there are many excellent and non-trivial problems solved in each section, each of which ends with a collection of problems.

In this book, the author emphasizes applications of complex methods and in doing so, provides many mathematical theorems without proof. Still, for students with a basic familiarity with calculus, line integrals and Green's theorems, the mathematical ideas are fitting and comprehensible, and the essential proofs are there or outlined.

In the opinion of the reviewer, the author has done a terrific job of organizing the vast area of complex variables. Simply put, this is one of the best textbooks ever written for undergraduates in physical sciences on the application of complex variables Students and professors will appreciate the clearly worked solutions in the exposition and the answers to many of the problems listed in the back of the book. I would highly recommend this as a textbook to all undergraduates in the sciences.

C. Carbno
Saskatchewan Telecommunications