Synopses & Reviews
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.
Dover (2015) republication of the edition originally published by Holt, Rinehart & Winston, New York, 1962.
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Review
For mathematics students who have completed or are completing a firstcourse in the theory of functions of a complex variable, Heins presents a number of important topics from the theory of analyticfunctions that may be treated without erecting an elaborate superstructure. He also assumes that students are well acquaintedwith elementary real analysis and have some knowledge of general topology, but not integration, measure theory, or the theory ofFourier series. His topics are covering properties of meromorphic functions, the Picard theorem, harmonic and sub-harmonic functions,applications, and the boundary behavior of the Riemann mapping function for simply-connected Jordan regions.Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)
Synopsis
Elegant and concise, this text explores properties of meromorphic functions, Picard theorem, harmonic and subharmonic functions, applications, and boundary behavior of the Riemann mapping function for simply connected Jordan regions. 1962 edition.
About the Author
Maurice Heins taught at the University of Illinois at Champagne-Urbana and at the University of Maryland at College Park.