Complex Variables and Applications, 8E” will serve, just as the earlier editions did, as a textbook for an introductory course in the theory and application of functions of a complex variable. This new edition preserves the basic content and style of the earlier editions.
The text is designed to develop the theory that is prominent in applications of the subject. You will find a special emphasis given to the application of residues and conformal mappings. To accommodate the different calculus backgrounds of students, footnotes are given with references to other texts that contain proofs and discussions of the more delicate results in advanced calculus. Improvements in the text include extended explanations of theorems, greater detail in arguments, and the separation of topics into their own sections.
2 Analytic Functions
3 Elementary Functions
6 Residues and Poles
7 Applications of Residues
8 Mapping by Elementary Functions
9 Conformal Mapping
10 Applications of Conformal Mapping
11 The Schwarzâ€“Christoffel Transformation
12 Integral Formulas of the Poisson Type