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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.
The Complex Plane.
Complex Line Integrals.
Applications of the Cauchy Theory.
Isolated Singularities and Laurent Series.
The Argument Principle.
The Geometric Theory of Holomorphic Functions.
Harmonic Functions.
Infinite Series and Products.
Applications of Infinite Sums and Products.
Analytic Continuation.
Rational Approximation Theory.
Special Classes of Holomorphic Functions.
Special Functions.
Applications that Depend on Conformal Mapping.
Transform Theory.
Computer Packages for Studying Complex Variables