A Guide to Complex Variables (Dolciani Mathematical Expositions)

This is a book about complex variables that gives the reader a quick and accessible introduction to the key topics. While the coverage is not comprehensive, it certainly gives the reader a solid grounding in this fundamental area. There are many figures and examples to illustrate the principal ideas, and the exposition is lively and inviting. An undergraduate wanting to have a first look at this subject or a graduate student preparing for the qualifying exams, will find this book to be a useful resource. In addition to important ideas from the Cauchy theory, the book also include sthe Riemann mapping theorem, harmonic functions, the argument principle, general conformal mapping and dozens of other central topics. Readers will find this book to be a useful companion to more exhaustive texts in the field. It is a valuable resource for mathematicians and non-mathematicians alike. Willoughby's essay is a gem. It should be in the hands of every young teacher. I wish that I had read it many years ago. I have no doubt that many of his observations and the information he imparts will remain with me for a while. I certainly hope so. A collection of reminiscences from other teachers with their valuable insights and experiences (who could write with such expertise as he does) would make a fine addition to the education literature. James Tattersall, Providence College Stephen S. Willoughby has taught mathematics for 59 years and he has seen everything. Some of it has annoyed him, some has inspired him. This little book is something of a valedictory and he shares some parting thoughts as he contemplates the end of his teaching career. Willoughby has strong, cogent and mostly negative opinions about textbooks, standardized testing, and teacher training. These opinions have been forged in the cauldron of the classroom of a deeply caring teacher. They might not please you, but they ought to make you think. They should spark needed debate in our community. Ultimately this is a human tale with rough parallels to Hardy's Apology; replace "Mathematician's" with "Teacher's" perhaps. Every teacher will sympathize with Willoughby's frustrations and empathize with the humanity and compassion that animated his life's work and that beat at the center of this book. A Guide to Complex Variables gives the reader a quick and accessible introduction to the key topics. While the coverage is not comprehensive, it certainly gives the reader a solid grounding in this fundamental area. There are many figures and examples to illustrate the principal ideas, and the exposition is lively and inviting. An undergraduate wanting to have a first look at this subject or a graduate student preparing for the qualifying exams, will find this book to be a useful resource. In addition to important ideas from the Cauchy theory, the book also includes the Riemann mapping theorem, harmonic functions, the argument principle, general conformal mapping and dozens of other central topics. Readers will find this book to be a useful companion to more exhaustive texts in the field. It is a valuable resource for mathematicians and non-mathematicians alike. Steven Krantz is well-known for his skill in expository writing and this volume confirms it. He is the author of more than 50 books, and more than 150 scholarly papers. The MAA has awarded him both the Beckenbach Book Prize and the Chauvenet Prize Stephen S. Willoughby has taught mathematics for 59 years and he has seen everything. Some of it has annoyed him; some has inspired him. This little book is something of a valedictory and he shares some parting thoughts as he contemplates the end of his teaching career. Willoughby has strong, cogent, and mostly negative opinions about textbooks, standardized testing, and teacher training. These opinions have been forged in the cauldron of the classroom of a deeply caring teacher. They might not please readers, but they ought to make them think. They should spark needed debate in our community. Ultimately, this is a human tale with rough parallels to Hardy's “A Mathematician's Apology”; replace “mathematicians” with “teachers” perhaps. Every teacher will sympathize with Willoughby's frustrations and empathize with the humanity and compassion that animated his life's work and that beat at the center of this book. This quick and easy-to-use guide provides a solid grounding in the fundamental area of complex variables. Copious figures and examples are used to illustrate the principal ideas, and the exposition is lively and inviting. In addition to important ideas from the Cauchy theory, the author also includes the Riemann mapping theorem, harmonic functions, the argument principle, general conformal mapping, and dozens of other central topics. An undergraduate taking a first look at the subject, or a graduate student preparing for their qualifying exams, will find this book to be both a valuable resource and a useful companion to more exhaustive texts in the field. For mathematicians and non-mathematicians alike. The Complex Plane Complex Line Integrals Applications of the Cauchy Theory Laurent Series The Argument Principle The Geometric Theory Harmonic Functions Infinite Series and Products Analytic Continuation. "A quick and easy-to-use introduction to the key topics in complex variables, for mathematicians and non-mathematicians alike." -- Publisher