A Guide to Complex Variables

(Dolciani Mathematical Expositions)

Steven G. Krantz

Mathematical Association of America | 2008 |202 páginas | 1 Mb

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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.

Table of Contents
Preface
1. The complex plane
2. Complex line integrals
3. Applications of the Cauchy theory
4. Isolated singularities and Laurent series
5. The argument principle
6. The geometric theory of holomorphic functions
7. Harmonic functions
8. Infinite series and products
9. Analytic continuation.