Complex Variables

Kapoor (U. of Hyderabad, India) finds the theory of functions of a complex variable to be one of those areas of mathematics that were created for reasons not even remotely connected to any practical, real-world applications, but turn out to be extremely useful. Mathematicians use it to move toward ever more general and abstract results, he says, and engineers use it to generate concrete results to solve specialized problems. Therefore, designing an introductory course and textbook is a creative challenge. The first part of his text presents the definitions, theorems, proofs and their analysis by example and counter-example--at a level of formality suitable for beginners. The second part contains problems on which to practice the theories and techniques. These are arranged in sessions each focused on a specific objective, among then elementary functions and differential, Cauchy integral formula, and contour integration. This format could be adapted to other sciences, he says, especially for self-study when no teacher or expert is available. Annotation c2011 Book News, Inc., Portland, OR (booknews.com)