The calculus of real numbers can be extended to complex numbers, where the definitions and techniques one learns in calculus carry over to complex variables.

David C. Kay, who has written several books geared for college students, explains this development in his new book. A short review of basic concepts from real variable calculus appears with each new topic. Differentiation and integration in complex variables is clearly explained, with numerical examples.

Other topics include infinite series of complex variables, uniform convergence, the Taylor and Laurent series, and methods for...