by Theral O Moore (University of Florida, USA) & Edwin H Hadlock (Late Prof. Emeritus)

This is a textbook for a first course in functions of complex variable, assuming a knowledge of freshman calculus. It is designed for students in engineering, physics, and mathematics. Without sacrificing ease and clarity of proofs, mathematical preciseness and rigor are stressed. Cross references are used to justify almost every step in each proof. Solutions and hints are given to many exercises.

• Complex Numbers
• Complex Functions
• Complex Integrals
• Series
• Some Elementary Functions
• Laurent Series, Poles and Residues
• Residue Calculus
• Rouche's Theorem and Open Mapping Theorem
• Harmonic Functions
• Conformal Mapping
• The Riemann Mapping Theorem
• Appendix: The System of Real Numbers
• Countable Sets