An Introduction to Complex Analysis [Hardcover]

This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an Answers or Hints section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.

This senior undergraduate/graduate level textbook has been designed for an introductory course in complex analysis for students in the applied sciences. It follows the proof-theorem approach while presenting the material as 50 class-tested lectures.

-Preface. -Complex Numbers I. - Complex Numbers II. - Complex Numbers III. - Set Theory in the Complex Plane. - Complex Functions. -Analytic Functions I. - Analytic Functions II. - Elementary Functions I. - Elementary Functions II. - Mappings by Functions I. - Mappings by Functions II. - Curves, Contours, and Simply Connected Domains. - Complex Integration. -Independence of Path. - Cauchy-Goursat Theorem. - Deformation Theorem. - Cauchys Integral Formula. - Cauchys Integral Formula for Derivatives. - The Fundamental Theorem of Algebra. - Maximum Modulus Principle. - Sequences and Series of Numbers. - Sequences and Series of Functions. - Power Series. -Taylors Series. -Laurents Series. - Zeros of Analytic Functions. -Analytic Continuation. -Symmetry and Reflection. -Singularities and Poles I. -Singularities and Poles II. -?Cauchys Residue Theorem. - Evaluation of Real Integrals by Contour Integration I. - Evaluation of Real Integrals by ló"