Handbook of Complex Variables [Paperback]

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.1 The Complex Plane.- 1.1 Complex Arithmetic.- 1.2 The Exponential and Applications.- 1.3 Holomorphic Functions.- 1.4 The Relationship of Holomorphic and Harmonic Functions.- 2 Complex Line Integrals.- 2.1 Real and Complex Line Integrals.- 2.2 Complex Differentiability and Conformality.- 2.3 The Cauchy Integral Theorem and Formula.- 2.4 A Coda on the Limitations of the Cauchy Integral Formula.- 3 Applications of the Cauchy Theory.- 3.1 The Derivatives of a Holomorphic Function.- 3.2 The Zeros of a Holomorphic Function.- 4 Isolated Singularities and Laurent Series.- 4.1 The Behavior of a Holomorphic Function near an Isolated Singularity.- 4.2 Expansion around Singular Points.- 4.3 Examples of Laurent Expansions.- 4.4 The Calculus of Residues.- 4.5 Applications to the Calculation of Definite Integrals and Sums.- 4.6 Meromorphic Functions and Singularities at Infinity.- 5 The Argument Principle.- 5.1 Counting Zeros and Poles.- 5.2 The Local Geometry of Holomorphic FlÓ