Ebook: Handbook of Complex Variables
Author: Steven G. Krantz (auth.)
- Genre: Mathematics
- Tags: Functions of a Complex Variable, Several Complex Variables and Analytic Spaces
- Year: 1999
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
Content:
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
Content:
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
....