Complex Analysis (Undergraduate Texts in Mathematics)

This unusually lively textbook on complex variables introduces the theory of analytic functions, explores its diverse applications and shows the reader how to harness its powerful techniques. "Complex Analysis" offers new and interesting motivations for classical results and introduces related topics that do not appear in this form in other texts. Stressing motivation and technique, and containing a large number of problems and their solutions, this volume may be used as a text both in classrooms and for self-study. Topics covered include: The complex numbers; functions of a complex variable; analytic functions; line integrals and entire functions; properties of entire functions and of analytic functions; simply connected domains; isolated singularities; the residue theorem and applications; contour integral techniques; conformal mapping and the riemann mapping theorem; maximum-modulus theorems for unbounded domains; harmonic functions; forms of analytic functions; analytic continuation; the gamma and zeta functions; application to other areas of mathematics. For this second edition, the authors have revised some of the existing material and have provided new exercises and solutions.