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Complex Variables and Applications

9th Edition

1259072770 · 9781259072772

By James Ward Brown, Ruel V. Churchill

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Colour, print bound version of the complete text

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

Appendixes

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.

Some sections that can be skipped or postponed without disruption are more clearly identified. The statements of Taylors and Laurents theorems, for example, now appear in sections that are separate from the sections containing their proofs.

The treatment of the extended form of the Cauchy integral formula for derivatives has been completely rewritten, with special attention to its immediate consequences.

Other improvements include more details in arguments involving mathematical induction, greater emphasis on rules for using complex exponents, some discussion of residues at infinity, and a clearer exposition of real improper integrals and their Cauchy principal values.

Some important material is presented in a more focused way by placing it in separate sections. For instance, the discussion of upper bounds of moduli of contour integrals is now entirely in one section, and there is a separate section devoted to the definition of isolated singular points.

A revised Students Solutions Manual with solutions for a large number of exercises in Chapters 1-7 is available.

Exercise sets occur more frequently than in earlier editions.

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