Selected Topics in the Classical Theory of Functions of a Complex Variable

Elegant and concise, this text is geared toward advanced undergraduate students acquainted with the theory of functions of a complex variable. The treatment presents such students with a number of important topics from the theory of analytic functions that may be addressed without erecting an elaborate superstructure. These include some of the theory's most celebrated results, which seldom find their way into a first course.
After a series of preliminaries, the text discusses properties of meromorphic functions, the Picard theorem, and harmonic and subharmonic functions. Subsequent topics include applications and the boundary behavior of the Riemann mapping function for simply connected Jordan regions. The book concludes with a helpful Appendix containing information on Lebesgue's theorem and other topics.

Maurice Heins taught at the University of Illinois at Champagne–Urbana and at the University of Maryland at College Park.

1. Preliminaries 2. Covering Properties of Meromorphic Functions 3. The Picard Theorem 4. Harmonic and Subharmonic Functions 5. Applications 6. The Boundary Behavior of the Riemann Mapping Function for Simply-connected Jordan Regions Appendix Index