Invitation to Complex Analysis

Ralph P. Boas

2020-ж. май · AMS/MAA Textbooks 20-китеп · American Mathematical Soc.

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Ideal for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written at a level accessible to advanced undergraduates and beginning graduate students, the book is suitable for readers acquainted with advanced calculus or introductory real analysis. The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of intriguing topics that are uncommon in a book at this level. The flexibility afforded by the supplementary topics and applications makes the book adaptable either to a short, one-term course or to a comprehensive, full-year course. Detailed solutions of the exercises both serve as models for students and facilitate independent study. Supplementary exercises, not solved in the book, provide an additional teaching tool. This second edition has been painstakingly revised by the author's son, himself an award-winning mathematical expositor.

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Ralph P. Boas (1912–1992), a well-known mathematical researcher, educator, author, editor, and translator, received his Ph.D. from Harvard University in 1937. He was executive editor of Mathematical Reviews between 1945 and 1950, and spent the next three decades on the faculty at Northwestern University, retiring in 1980 as Henry S. Noyes Professor Emeritus of Mathematics. His activities with the Mathematical Association of America (MAA) included chairing the Committee on the Undergraduate Program in Mathematics, serving as MAA President (1973–1974), and editing The American Mathematical Monthly (1976–1981); the MAA awarded him the Lester R. Ford Award for expository excellence in 1978 and the Award for Distinguished Service to Mathematics in 1981. He served the American Mathematical Society both as a vice president and as a trustee. His other books include Entire Functions, the MAA Carus Monograph A Primer of Real Functions, and Lion Hunting and Other Mathematical Pursuits. He published numerous articles in mathematical journals. Harold P. Boas received his PhD from MIT in 1980. Between 1980 and 1984 he was J. F. Ritt Assistant Professor of Mathematics at Columbia University. Since 1984 he has been on the faculty at Texas A & M University. He has served as book-review editor of The American Mathematical Monthly (1998–1999) and as editor of the Notices of the American Mathematical Society (2001–2003). In 1995, he and his collaborator Emil J. Straube received the Stefan Bergman Prize from the American Mathematical Society for their research on the boundary regularity theory of the multidimensional inhomogeneous Cauchy-Riemann equations. The Mathematical Association of America has recognized him for an outstanding expository article with the Lester R. Ford Award (2007) and the Chauvenet Prize (2009). He received the Student Led Award for Teaching Excellence from Texas A & M University in 2009. He previously revised his father's A Primer of Real Functions (fourth edition, 1996).