A Guide to Complex Variables

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MAA, Oct 16, 2008 - Mathematics - 182 pages
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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.
 

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Contents

The Complex Plane
1
Complex Line Integrals
19
Applications of the Cauchy Theory
33
Laurent Series
43
The Argument Principle
71
The Geometric Theory
83
Harmonic Functions
95
Infinite Series and Products
111
Analytic Continuation
125
Glossary of Terms from Complex Variable Theory and Analysis
143
Bibliography
175
About the Author
182
Copyright

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About the author (2008)

Steven G. Krantz is currently Deputy Director of the American Institute of Mathematics. He is the holder of the Chauvenet Prize and the Beckenbach Book Award, both awarded by the Mathematical Association of America, and is a recipient of the UCLA Alumni Association Distinguished Teaching Award.