Complex variables and applications - Brown, James Ward, 1934-; Churchill, Ruel Vance, 1899-1987 (New York : McGraw-Hill, 2014)
Complex Variables and Applications, 9e 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.
Chapter 1. Complex Numbers Chapter 2. Analytic Functions Chapter 3. Elementary Functions Chapter 4. Integrals Chapter 5. Series Chapter 6. Residues and Poles Chapter 7. Applications of Residues Chapter 8. Mapping by Elementary Functions Chapter 9. Conformal Mapping Chapter 10. Applications of Conformed Mapping Chapter 11. The Schwarz-Christoffel Transformation Chapter 12. Integral Formulas of the Poisson Type
Keywords: Functions of complex variables; Functietheorie