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The study of complex variables is important for students in engineering and the physical science and is a central subject in mathematics. In addition to being mathematically elegant, compelx variables provide a powerful tool for solving problems that are either very difficult or virtually impossible to solve in any other way.Part 1 of this text provides and introduction to the subject, including analytic functions, integration, series, and residue calculus. It also includes transform methods, ordinary differential equations in the complex plane, numerical methods, and more. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann-Hilbert problems. he authors provide an extensive array of applications, illustrative examples and homework exercises. This new edition has been improved throughout and is ideal for use in undergraduate and introductory graduate level courses in complex variables.ContentsPrefacePart I: Fundamnetals and Techniques of Complex Function Theory1. Complex numbers and elementary functions 2. Analytic functions and integration3. Sequences, series and singularities of complex functions4. Residue calculus and applications of contour integrationPart II: Applications of Complex Function Theory5. Conformal mapping and applications6. Asymptotic evaluation of integrals7. Riemann-Hilbert problemsAppendix A Answers to Odd-Numbered ExercisesBibliographyIndex.