Functions of a Complex Variable (Classic Reprint) - Softcover

Inhaltsangabe

A clear, student-friendly introduction to complex variables, built from the ground up. This book guides readers from basic ideas of complex numbers to the core concepts of analytic functions, with a steady progression that emphasizes practical understanding over abstraction. It introduces integration early and shows how the key results follow from formal definitions, making the subject approachable for those new to complex analysis.

The text frames the material around what functions of a complex variable can do, including mapping, conformal transformations, and applications in physics. It covers both single-valued and multiple-valued functions, with chapters on series, analytic continuation, and the geometry of mappings. The approach balances theory with concrete examples to help readers connect ideas to real problems.

• Foundations of complex numbers and holomorphic functions, including integral criteria and the Cauchy-Goursat framework


• Mapping, conformal transformation, and linear fractional transformations with geometric interpretation


• Infinite series, power series, and analytic continuation with applications to physics


• Introduction to multiple-valued functions and the beginnings of Riemann surfaces

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