Explores the interrelations between real and complex numbers by adopting both generalization and specialization methods to move between them, while simultaneously examining their analytic and geometric characteristics

Engaging exposition with discussions, remarks, questions, and exercises to motivate understanding and critical thinking skills

Encludes numerous examples and applications relevant to science and engineering students

Autorentext

Inhalt

Algebraic and Geometric Preliminaries.- Topological and Analytic Preliminaries.- Bilinear Transformations and Mappings.- Elementary Functions.- Analytic Functions.- Power Series.- Complex Integration and Cauchy's Theorem.- Applications of Cauchy's Theorem.- Laurent Series and the Residue Theorem.- Harmonic Functions.- Conformal Mapping and the Riemann Mapping Theorem.- Entire and Meromorphic Functions.- Analytic Continuation.