Handbook of Complex Variables

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This book is written to be a convenient reference for the working scientist, student, or engineer who needs to know and use basic concepts in complex analysis. It is not a book of mathematical theory. It is instead a book of mathematical practice. All the basic ideas of complex analysis, as well as many typical applica­ tions, are treated. Since we are not developing theory and proofs, we have not been obliged to conform to a strict logical ordering of topics. Instead, topics have been organized for ease of reference, so that cognate topics appear in one place. Required background for reading the text is minimal: a good ground­ ing in (real variable) calculus will suffice. However, the reader who gets maximum utility from the book will be that reader who has had a course in complex analysis at some time in his life. This book is a handy com­ pendium of all basic facts about complex variable theory. But it is not a textbook, and a person would be hard put to endeavor to learn the subject by reading this book.

Author(s): Steven G. Krantz (auth.)
Edition: 1
Publisher: Birkhäuser Basel
Year: 1999

Language: English
Pages: 290
Tags: Functions of a Complex Variable; Several Complex Variables and Analytic Spaces

Front Matter....Pages i-xxiv
The Complex Plane....Pages 1-17
Complex Line Integrals....Pages 19-29
Applications of the Cauchy Theory....Pages 31-39
Isolated Singularities and Laurent Series....Pages 41-68
The Argument Principle....Pages 69-78
The Geometric Theory of Holomorphic Functions....Pages 79-88
Harmonic Functions....Pages 89-101
Infinite Series and Products....Pages 103-115
Applications of Infinite Sums and Products....Pages 117-122
Analytic Continuation....Pages 123-141
Rational Approximation Theory....Pages 143-147
Special Classes of Holomorphic Functions....Pages 149-154
Special Functions....Pages 155-162
Applications that Depend on Conformal Mapping....Pages 163-194
Transform Theory....Pages 195-217
Computer Packages for Studying Complex Variables....Pages 219-229
Back Matter....Pages 231-290