This unusually lively textbook introduces the theory of analytic functions, explores its diverse applications and shows the reader how to harness its powerful techniques. The book offers new and interesting motivations for classical results and introduces related topics that do not appear in this form in other texts. For the second edition, the authors have revised some of the existing material and have provided new exercises and solutions. The third edition contains a new section on Schwarz–Christoffel mappings, an improved treatment of the Schwarz Reflection Principle, and an expanded section on applications to number theory.

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